1024 lines
130 KiB
YAML
1024 lines
130 KiB
YAML
---
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- sesion: Set Theory and its Interactions
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organizadores:
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- nombre: Carlos Di Prisco
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mail: ca.di@uniandes.edu.co
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- nombre: Christina Brech
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mail: brech@ime.usp.br
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charlas:
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- titulo: Around (*)
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abstract: In this talk I will present work motivated by the derivation of the \(\mathbb P_{max}\) axiom \((*)\) from Martin's Maximum\(^{++}\).
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speaker: David Asperó (University of East Anglia, Inglaterra)
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- titulo: Group operations and universal minimal flows
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abstract: Every topological group admits a unique, up to isomorphism, universal minimal that maps onto every minimal (with respect to inclusion) flow. We study interactions between group operations and corresponding universal minimal flows.
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speaker: Dana Bartosova (University of Florida, Estados Unidos)
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- titulo: Preservation of some covering properties by elementary submodels
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abstract: |
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Given a topological space \((X, \tau)\) and an elementary submodel \(M\), we can define the topological space \(X_M = (X\cap M, \tau _M)\), where \(\tau _M\) is the topology on \(X \cap M\) generated by \(\{ V\cap M : V \in \tau \cap M \}\). It is natural to ask which topological properties are preserved by this new operation. For instance, if \(X\) is \(T_2\), then \(X_M\) is also \(T_2\). On the other hand, \(X_M\) compact implies \(X\) compact. A systematic study of it was initiated by L. Junqueira and F. Tall in 1998.
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In the paper ``More reflection in topology'', published in Fudamenta Mathematicae in 2003, F. Tall and L. Junqueira, studied the reflection of compactness and, more specifically, when can we have, for \(X\) compact, \(X_M\) compact non trivially, {\it i.e.}, with \(X \neq X_M\). It is natural to try to extend this study for other covering properties.
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We will present some results concerning the preservation of Lindelöfness. We will also discuss the perservation of some of its strengthenings, like the Menger and Rothberger properties.
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speaker: Lucia Junqueira (Universidade de São Paulo, Brasil) joint with Robson A. Figueiredo and Rodrigo R. Carvalho
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- titulo: The Katetov order on MAD families
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abstract: The Katetov order is a powerful tool for studying ideals on countable sets. It is specially interesting when restricted to the class of ideals generated by MAD families. One of the reasons we are interested in it is because it allows us to study the destructibility of MAD families under certain forcing extensions. In this talk, I will survey the main known results regarding the Katetov order on MAD families and state some open problems.
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speaker: Osvaldo Guzmán (Universidad Nacional Autónoma de México, México)
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- titulo: Hereditary interval algebras and cardinal characteristics of the continuum
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abstract: |
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An interval algebra is a Boolean algebra which is isomorphic to the algebra of finite
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unions of half-open intervals, of a linearly ordered set. An interval algebra is hereditary
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if every subalgebra is an interval algebra. We answer a question of M. Bekkali and S.
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Todorcevic, by showing that it is consistent that every $\sigma$-centered interval algebra of size
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\(\mathfrak{b}\) is hereditary. We also show that there is, in ZFC, an hereditary interval algebra of
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cardinality \(\aleph_1\).
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speaker: Carlos Martinez-Ranero (Universidad de Concepción, Chile)
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- titulo: Groups definable in partial differential fields with an automorphism
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abstract: |
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Model theory is a branch of mathematical logic with strong interactions with other branches of mathematics, including algebra, geometry and number theory.
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In this talk we are interested in differential and difference fields from the model-theoretic point of view.
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A differential field is a field with a set of commuting derivations and a difference-differential field is a differential field equipped with an automorphism which commutes with the derivations.
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The model theoretic study of differential fields with one derivation, in characteristic $0$ started with the work of Abraham Robinson and of Lenore Blum. For several commuting derivations,
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Tracey McGrail showed that the theory of differential fields of characteristic zero
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with \(m\) commuting derivations has a model companion called \(DCF\). This theory is complete, \(\omega\)-stable and eliminates quantifiers and imaginaries.
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In the case of difference-differential fields, Ronald Bustamante Medina (for the case of one derivation) and Omar León Sánchez (for the general case) showed that the theory of difference-differential fields with $m$ derivations admits a model companion called \(DCF_mA\). This theory is model-complete, supersimple and eliminates imaginaries.
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Cassidy studied definable groups in models of $DCF$, in particular she studied Zariski dense definable subgroups of simple algebraic groups and showed that they are isomorphic to the rational points of an algebraic group over some definable field.
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In this talk we study groups definable in models of \(DCF_mA\), and show an analogue of Phyllis Cassidy's result.
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speaker: Samaria Montenegro (Universidad de Costa Rica, Costa Rica), joint work with Ronald Bustamente Medina and Zoé Chatzidakis
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- titulo: Some lessons after the formalization of the ctm approach to forcing
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abstract: |
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In this talk we'll discuss some highlights of our computer-verified proof of the construction, given a countable transitive set model \(M\) of \(\mathit{ZFC}\), of a generic extension \(M[G]\) satisfying \(\mathit{ZFC}+\neg\mathit{CH}\). In particular, we isolated a set \(\Delta\) of \(\sim\)220 instances of the axiom schemes of Separation and Replacement and a function \(F\) such that such that for any finite fragment \(\Phi\subseteq\mathit{ZFC}\), \(F(\Phi)\subseteq\mathit{ZFC}\) is also finite and if \(M\models F(\Phi) + \Delta\) then \(M[G]\models \Phi + \neg \mathit{CH}\). We also obtained the formulas yielded by the Forcing Definability Theorem explicitly.
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To achieve this, we worked in the proof assistant Isabelle, basing our development on the theory Isabelle/ZF by L. Paulson and others.
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The vantage point of the talk will be that of a mathematician but elements from the computer science perspective will be present. Perhaps some myths regarding what can effectively be done using proof assistants/checkers will be dispelled.
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We'll also compare our formalization with the recent one by Jesse M. Han and Floris van Doorn in the proof assistant Lean.
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speaker: Sánchez Terraf (Universidad Nacional de Córdoba, Argentina) joint with Emmanuel Gunther, Miguel Pagano, and Matías Steinberg
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- titulo: On non-classical models of ZFC
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abstract: |
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In this talk we present recent developments in the study of non-classical models of ZFC.
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We will show that there are algebras that are neither Boolean, nor Heyting, but that still give rise to models of ZFC. This result is obtained by using an algebra-valued construction similar to that of the Boolean-valued models. Specifically we will show the following theorem.
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There is an algebra \(\mathbb{A}\), whose underlying logic is neither classical, nor intuitionistic such that \(\mathbf{V}^{\mathbb{A}} \vDash\) ZFC. Moreover, there are formulas in the pure language of set theory such that \(\mathbf{V}^{\mathbb{A}} \vDash \varphi \land \neg \varphi\).
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The above result is obtained by a suitable modification of the interpretation of equality and belongingness, which are classical equivalent to the standard ones, used in Boolean-valued constructions.
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Towards the end of the talk we will present an application of these constructions, showing the independence of CH from non-classical set theories, together with a general preservation theorem of independence from the classical to the non-classical case.
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speaker: Giorgio Venturi (Universidade Estadual de Campinas, Brasil), joint work with Sourav Tarafder and Santiago Jockwich
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- sesion: Combinatoria algebraica de funciones simétricas, cuasisimétricas y sus generalizaciones
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organizadores:
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- nombre: Rafael S. González D'León
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mail: rafael.gonzalezl@usa.edu.co
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- nombre: Yannic Vargas Lozada
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mail: yannicmath@gmail.com
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charlas:
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- titulo: Hopf monoids of type B, their antipode and examples
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abstract: Combinatorial species provide a unified framework to study families of combinatorial objects. If the family of combinatorial objects has natural operations to merge and break structures, the corresponding species becomes a Hopf monoid. In this talk, we present a novel definition of type B Hopf monoids. In the same spirit as the work of Bergeron and Choquette, we consider structures over finite sets with a fixed-point free involution. However, instead of defining a monoidal structure on the category of type B species, our construction involves an action of the monoidal category of (standard) species on the category of Type B species. We present the basic definitions and some examples of Type B Hopf monoids constructed from (type B) set compositions, (symplectic) matroids, and (type B) generalized permutahedra. This is work in progress with M. Aguiar.
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speaker: José Bastidas (LACIM/Université du Québec à Montréal, Canadá)
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- titulo: Chromatic symmetric functions for Dyck paths and \(q\)-rook theory
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abstract: |
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Given a graph and a set of colors, a coloring is a function that associates each vertex in the graph with a color. In 1995, Stanley generalized this definition to symmetric functions by looking at the number of times each color is used and extending the set of colors to \(\mathbb{Z}^+\). In 2012, Shareshian and Wachs introduced a refinement of the chromatic functions for ordered graphs as \(q\)-analogues.
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In the particular case of Dyck paths, Stanley and Stembridge described the connection between chromatic symmetric functions of abelian Dyck paths and square hit numbers, and Guay-Paquet described their relation to rectangular hit numbers. Recently, Abreu-Nigro generalized the former connection for the Shareshian-Wachs \(q\)-analogue, and in unpublished work, Guay-Paquet generalized the latter.
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In this talk, I want to give an overview of the framework and present another proof of Guay-Paquet's identity using \(q\)-rook theory. Along the way, we will also discuss $q$-hit numbers, two variants of their statistic, and some deletion-contraction relations. This is recent work with Alejandro H. Morales and Greta Panova.
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speaker: Laura Colmenarejo (North Carolina State University, Estados Unidos)
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- titulo: Peak algebra for combinatorial Hopf algebras
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abstract: The peak algebra is originally introduced by Stembridge using enriched \(P\)-partitions. Using the character theory by Aguiar-Bergeron-Sottile, the peak algebra is also the image of \(\Theta\), the universal morphism between certain combinatorial Hopf algebras. We introduce a shuffle basis of quasi-symmetric functions that has a shuffle-like Hopf structure and is also the eigenfunctions of \(\Theta\). Using this new basis, we extend the notion of peak algebras and theta maps to shuffle, tensor and symmetric algebras. As examples, we study the peak algebras of symmetric functions in non-commuting variables and the graded associated Hopf algebra on permutations.
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speaker: Shu Xiao Li (Dalian University of Technology, China)
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- titulo: A multiset partition algebra
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abstract: Classical Howe duality provides a representation theoretic framework for classical invariant theory. In the classical Howe duality the general linear group \(GL_n\) is dual to \(GL_k\) when acting on the polynomial ring on variables \(x_{ij}\) where \(1\leq i\leq n\) and \(1\leq j \leq k\). In this talk we restrict the action of \(GL_n\) to the group of permutation matrices and show that the Howe dual is an algebra whose basis is indexed by multiset partition algebra.
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speaker: Rosa C. Orellana (Dartmouth College, Estados Unidos)
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- titulo: Valuations and the Hopf Monoid of Generalized Permutahedra
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abstract: Many combinatorial objects, such as matroids, graphs, and posets, can be realized as generalized permutahedra - a beautiful family of polytopes. This realization respects the natural multiplication of these objects as well as natural "breaking" operations. Surprisingly many of the important invariants of these objects, when viewed as functions on polytopes, satisfy an inclusion-exclusion formula with respect to subdivisions. Functions that satisfy this formula are known as valuations. In this talk, I will discuss recent work with Federico Ardila that completely describes the relationship between the algebraic structure on generalized permutahedra and valuations. Our main contribution is a new easy-to-apply method that converts simple valuations into more complicated ones. We also describe an universality property of the Hopf monoid of indicator functions of generalized permutahedra that extends the relationship between Combinatorial Hopf algebras and QSYM.
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speaker: Mario Sanchez (UC Berkeley, Estados Unidos)
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- titulo: Computation of Kronecker coefficients
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abstract: |
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A Kronecker coefficient is a non-negative integer that depends on three partitions of a natural number n. It is the multiplicity of an irreducible representation of the symmetric group of degree n in the tensor (or Kronecker) product of two other irreducible representations of the same group.
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The study of ways of computing Kronecker coefficients is an important topic on algebraic combinatorics. It was initiated by Francis Murnaghan more than eighty years ago. Several tools have been used to try to understand them, notably from representation theory, symmetric functions theory and Borel-Weil theory. These numbers generalize the well-known Littlewood-Richardson coefficients, but are still very far to be fully grasped.
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It is known that each Kronecker coefficient can be described as an alternating sum of numbers of integer points in convex polytopes.
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In this talk we present a new family of polytopes that permit very fast computations on Kronecker coefficients associated to partitions with few parts. This family provides, in particular, insight into some properties of Kronecker coefficients as well as into Murnaghan stability.
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speaker: Ernesto Vallejo (Universidad Nacional Autónoma de México, México)
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- titulo: The Castelnuovo-Mumford Regularity of Matrix Schubert Varieties
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abstract: The Castelnuovo-Mumford regularity of a graded module provides a measure of how complicated its minimal free resolution is. In work with Rajchogt, Ren, Robichaux, and St. Dizier, we noted that the CM-regularity of matrix Schubert varieties can be easily obtained by knowing the degree of the corresponding Grothendieck polynomial. Furthermore, we gave explicit, combinatorial formulas for these degrees for symmetric Grothendieck polynomials. In this talk, I will present a general degree formula for Grothendieck polynomials. This is joint work with Oliver Pechenik and David Speyer.
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speaker: Anna E. Weigand (Massachusetts Institute of Technology, Estados Unidos)
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- titulo: 'Chromatic symmetric homology for graphs: some new developments'
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abstract: |
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In his study of the four colour problem, Birkhoff showed that the number of ways to colour a graph with k colours is a polynomial chi(k), which he called the chromatic polynomial. Later, Stanley defined the chromatic symmetric function X(x_1, x_2, ... ), which is a multivariable lift of the chromatic polynomial so that when the first k variables are set to 1, it recovers chi(k). This can be further lifted to a homological setting; we can construct a chain complex of graded S_n-modules whose homology has a bigraded Frobenius characteristic that recovers X upon setting q=t=1.
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In this talk, we will explain the construction of the homology, discuss some new results regarding the strength of the homology as a graph invariant, and state some surprising conjectures regarding integral symmetric homology for graphs. This is based on joint work with Chandler, Sazdanovic, and Stella.
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speaker: Martha Yip (University of Kentucky, Estados Unidos)
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- sesion: Lógica y Computación
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organizadores:
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- nombre: Alexandre Miquel
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mail: amiquel@fing.edu.uy
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- nombre: Martin Hyland
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mail: M.Hyland@dpmms.cam.ac.uk
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charlas:
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- titulo: Random!
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abstract: Everyone has an intuitive idea about what is randomness, often associated with ``gambling'' or ``luck''. Is there a mathematical definition of randomness? Are there degrees of randomness? Can we give examples of randomness? Can a computer produce a sequence that is truly random? What is the relation between randomness and logic? In this talk I will talk about these questions and their answers.
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speaker: Verónica Becher (Universidad de Buenos Aires, Argentina)
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- titulo: Relating logical approaches to concurrent computation
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abstract: |
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This talk will present ongoing work towards the description and study of concurrent interaction in proof theory.
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Type systems that are designed to ensure behavioural properties of concurrent processes (input/output regimes, lock-freeness) generally have unclear logical meanings. Conversely, proofs-as-programs correspondences for processes (e.g. with session types) tend to impose very functional behaviour and little actual concurrency. Besides, relationships between type systems and denotational models of concurrency are rarely established.
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A possible reason for this state of things is the ambiguous status of non-determinism in logic and the importance of scheduling concerns in models of concurrency, to which traditional proof theory is not accustomed. Unifying logical approaches in a consistent framework requires to put a focus on these issues, and this talk will propose, building on recent developments in proof theory, in the veins of linear logic and classical realizability.
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speaker: Emmanuel Beffara (Université Grenoble Alpes, Francia)
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- titulo: A framework to express the axioms of mathematics
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abstract: 'The development of computer-checked formal proofs is a major step forward in the endless quest for mathematical rigor. But it also has a negative aspect: the multiplicity of systems brought a multiplicity of theories in which these formal proofs are expressed. We propose to define these theories in a common logical framework, called Dedukti. Some axioms are common to the various theories and some others are specific, just like some axioms are common to all geometries and some others are specific. This logical framework extends predicate logic in several ways and we shall discuss why predicate logic must be extended to enable the expression of these theories.'
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speaker: Gilles Dowek (Institut de la Recherche en Informatique et Automatique, Francia)
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- titulo: Generalized Algebraic Theories and Categories with Families
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abstract: We give a new syntax independent definition of the notion of a finitely presented generalized algebraic theory as an initial object in a category of categories with families (cwfs) with extra structure. To this end we define inductively how to build a valid signature \(\Sigma\) for a generalized algebraic theory and the associated category \(\textrm{CwF}_{\Sigma}\) of cwfs with a \(\Sigma\)-structure and cwf-morphisms that preserve \(\Sigma\)-structure on the nose. Our definition refers to the purely semantic notions of uniform family of contexts, types, and terms. Furthermore, we show how to syntactically construct initial cwfs with \(\Sigma\)-structures. This result can be viewed as a generalization of Birkhoff’s completeness theorem for equational logic. It is obtained by extending Castellan, Clairambault, and Dybjer’s construction of an initial cwf. We provide examples of generalized algebraic theories for monoids, categories, categories with families, and categories with families with extra structure for some type formers of dependent type theory. The models of these are internal monoids, internal categories, and internal categories with families (with extra structure) in a category with families. Finally, we show how to extend our definition to some generalized algebraic theories that are not finitely presented, such as the theory of contextual categories with families.
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speaker: Peter Dybjer (Chalmers University of Technology, Suecia), joint with Marc Bezem, Thierry Coquand, and Martin Escardo
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- titulo: On the instability of the consistency operator
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abstract: We examine recursive monotonic functions on the Lindenbaum algebra of EA. We prove that no such function sends every consistent \(\varphi\), to a sentence with deductive strength strictly between \(\varphi\) and \(\textit{Con}(\varphi)\). We generalize this result to iterates of consistency into the effective transfinite. We then prove that for any recursive monotonic function \(f\), if there is an iterate of \(\textit{Con}\) that bounds \(f\) everywhere, then \(f\) must be somewhere equal to an iterate of \(\textit{Con}\).
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speaker: Antonio Montalbán (Berkeley University of California, Estados Unidos), joint work with James Walsh
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- titulo: Readers by name, presheaves by value
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abstract: Presheaves are an ubiquitary model construction used everywhere in logic, particularly in topos theory. It is therefore tempting to port them to the similar but slightly different context of type theory. Unfortunately, it turns out that there are subtle issues with the built-in computation rules of the latter, which we will expose. As an alternative, we will describe a new structure that is much better behaved in an intensional setting, but categorically equivalent to presheaves in an extensional one. Such a structure is motivated by considerations stemming from the study of generic side-effects in programming language theory, shedding a new light on the fundamental nature of such a well-known object.
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speaker: Pierre-Marie Pédrot (Institut de la Recherche en Informatique et Automatique, Francia)
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- titulo: Reversible computation and quantum control
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abstract: One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions of sequencing, conditionals, loops, and recursion are entirely classical. There is however, another notion of control flow, that is itself quantum. This purely quantum control flow is however not well-understood. In this talk, I will discuss how to retrieve some understanding of it with a detour through reversible computation. This will allow us to draw links with the logic \(\mu\)MALL, pointing towards a Curry-Howard isomorphism.
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speaker: Benoît Valiron (CentraleSupélec, Francia)
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- sesion: Algebraic and categorical structures in geometry and topology
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organizadores:
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- nombre: Manuel Rivera
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mail: manuelor@gmail.com
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- nombre: Camilo Arias Abad
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mail: carias0@unal.edu.co
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charlas:
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- titulo: Discretization of euclidean space ,vector calculus and 3D incompressible fluids
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abstract: Overlapping cubical decompositions admit hodge star dualities and analogues of Grassman algebra for differential forms and multivector fields with their exterior d and the divergence operator differentials del. For these operators there are hierarchies of deformation corrections to the first order derivation structure of exterior d and the second order derivation structure of the divergence operator. These suggest computer codes with surprising properties. There is a joint paper in the Atiyah Memorial Volume 2021 with Ruth Lawrence and Nissim Ranade describing this discretization with explicit calculations of the deformations.The computer studies are in progress.
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speaker: Dennis Sullivan (Stony Brook University and City University of New York Graduate Center, Estados Unidos)
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- titulo: Objective combinatorial bialgebras through decomposition spaces
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abstract: Decomposition spaces (also known as 2-Segal spaces) and the machinery of homotopy linear algebra allow us to realise objective combinatorial bialgebra structures, rendering classical combinatorial bialgebras once cardinalites are taken. In many cases such bialgebras are related, through CULF functors given by base change, Galois connection, duality, that descend to their numerical counterparts but provide deeper understanding of phenomena at the objective level. We will present a few important cases of such constructions, in particular relating to the bialgebras of Malvenuto-Reutenauner and of symmetric functions. Joint work in progress with Joachim Kock and Andrew Tonks.
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speaker: Imma Gálvez-Carrillo (Universitat Politècnica de Catalunya, España)
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- titulo: Variants of the Waldhausen S-construction
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abstract: The S-construction, first defined in the setting of cofibration categories by Waldhausen, gives a way to define the algebraic K-theory associated to certain kinds of categorical input. It was proved by Galvez-Carrillo, Kock, and Tonks that the result of applying this construction to an exact category is a decomposition space, also called a 2-Segal space, and Dyckerhoff and Kapranov independently proved the same result for the slightly more general input of proto-exact categories. In joint work with Osorno, Ozornova, Rovelli, and Scheimbauer, we proved that these results can be maximally generalized to the input of augmented stable double Segal spaces, so that the S-construction defines an equivalence of homotopy theories. In this talk, we'll review the S-construction and the reasoning behind these stages of generalization. Time permitting, we'll discuss attempts to characterize those augmented stable double Segal spaces that correspond to cyclic spaces, which is work in progress with Walker Stern.
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speaker: Julie Bergner (University of Virginia, Estados Unidos)
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- titulo: Transfer systems and weak factorization systems
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abstract: N∞ operads over a group G encode homotopy commutative operations together with a class of equivariant transfer (or norm) maps. Their homotopy theory is given by transfer systems, which are certain discrete objects that have a rich combinatorial structure defined in terms of the subgroup lattice of G. In this talk, we will show that when G is finite Abelian, transfer systems are in bijection with weak factorization systems on the poset category of subgroups of G. This leads to an involution on the lattice of transfer systems, generalizing the work of Balchin-Bearup-Pech-Roitzheim for cyclic groups of squarefree order. This is joint work with Evan Franchere, Usman Hafeez, Peter Marcus, Kyle Ormsby, Weihang Qin, and Riley Waugh.
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speaker: Angélica Osorno (Reed College, Estados Unidos)
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- titulo: Classifying stacky vector bundles
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abstract: Lie groupoids up to Morita equivalences serve as models for differentiable stacks, categorified spaces that generalize manifolds and orbifolds, and which are useful when dealing with singular quotients. Vector bundles over Lie groupoids have the tangent and cotangent constructions as prominent examples, and they admit a nice interpretation in terms of representations up to homotopy. In this talk, based on joint works with C. Ortiz, D. Stefani, and J. Desimoni, I will first discuss the Morita invariance of vector bundles, then describe the general linear 2-groupoid, and finally present a classification of stacky vector bundles by the resulting 2-Grassmannian.
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speaker: Matías del Hoyo (Universidade Federal Fluminense, Brasil)
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- titulo: Cut cotorsion pairs
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abstract: In this talk, I shall present the concept of cotorsion pairs cut along subcategories of an abelian category. This provides a generalization of complete cotorsion pairs, and represents a general framework to find approximations of objects restricted to certain subcategories. Several applications will be given in the settings of relative Gorenstein homological algebra and chain complexes, as well as to characterize some important results on the Finitistic Dimension Conjecture, the existence of right adjoints of quotient functors by Serre subcategories, and the description of cotorsion pairs in triangulated categories as co-t-structures.
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This is a joint work with Mindy Huerta and Octavio Mendoza (Instituto de Matemáticas - Universidad Nacional Autónoma de México).
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speaker: Marco Perez (Universidad de la República, Uruguay)
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- titulo: Hopf and Bialgebras in Algebra, Topology and Physics
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abstract: |
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Together with Imma Galvez-Carillo and Andy Tonks, we constructed Bi and Hopf-algebras from a three-fold hierarchy, simplicial objects, Co-operads with multiplication and Feynman categories. The common theme is that the co-product is a dualized composition product and the product iis an extra structure, which is free in the most prominent examples. These are the Hopf algebra of Baues in Topology, those of Goncharov and Brown in number theory, and those of Connes and Kreimer in mathematical physics. The natural structures are bi-algebras and the Hopf algebras appear as a connected quotient.
|
||
Together with Yang Mo, we introduced the notion of a path-like bi-algebra in order to better understand the relationship between the bialgebras and the Hopf algebras, which allowed us to complete the picture. The usual Quillen condition of being connected is replaced by the so-called Quillen-Takeushi filtration being exhaustive. This allows us to reduce the obstructions to having an antipode to (semi)-grouplike elements. This theory comprises all the examples above as well as those of May as special cases. Finally, quotients now appear naturally as the universal quotient spaces through which characters -with particular properties- factor. The characters take values in Rota-Baxter-algebras which are at the heart of the renormalization theory. This brings the theory full circle.
|
||
start:
|
||
end:
|
||
speaker: Ralph Kaufmann (Purdue University, Estados Unidos)
|
||
- sesion: 'Problemas inversos: desde la teoría a las aplicaciones'
|
||
organizadores:
|
||
- nombre: Adriano Dr Cezaro
|
||
mail: adrianocezaro@furg.br
|
||
- nombre: Alberto Mercado
|
||
mail: alberto.mercado@usm.cl
|
||
- nombre: Juan Pablo Agnelli
|
||
mail: agnelli@famaf.unc.edu.ar
|
||
charlas:
|
||
- titulo: Synergistic multi-spectral CT reconstruction with directional total variation
|
||
abstract: This work considers synergistic multi-spectral CT reconstruction where information from all available energy channels is combined to improve the reconstruction of each individual channel. We propose to fuse these available data (represented by a single sinogram) to obtain a polyenergetic image that keeps structural information shared by the energy channels with an increased signal-to-noise ratio. This new image is used as prior information during a channel-by-channel minimization process through the directional total variation. We analyze the use of directional total variation within variational regularization and iterative regularization. Our numerical results on simulated and experimental data show improvements in terms of image quality and in computational speed.
|
||
start:
|
||
end:
|
||
speaker: Evelyn Cueva (Escuela Politécnica Nacional, Ecuador)
|
||
- titulo: Bayesian Approach Helmholtz Inverse Problem
|
||
abstract: This work present an implementation for solving the Helmholtz inverse problem via Finite Element Methods and Bayesian inference theory. The solution of the inverse problem is a posterior distribution based on a number observation data sets, the forward problem governing the state solution, and a statistical prior distribution which describes the behavior of the uncertainty linked to the parameters.
|
||
start:
|
||
end:
|
||
speaker: Lilí Guadarrama (Centro de Investigación en Matemáticas, México)
|
||
- titulo: Partial data Photoacoustic Tomography in unbounded domains
|
||
abstract: |
|
||
Photoacoustic Tomography is a promising hybrid medical imaging modality that is able to generate high-resolution and high-contrast images, by exploiting the coupling of electromagnetic pulses (in the visible region) and ultrasound waves via de photoacoustic effect.
|
||
In this talk I will introduce the modality and focus on the ultrasound propagation part which is mathematically modeled as an inverse initial source problem for the wave equation. We will pose this problem in a setting consisting of an unbounded domain with boundary, with observation taking place in a subset of it. We will address the question of uniqueness, stability and reconstruction of the initial source of acoustic waves.
|
||
start:
|
||
end:
|
||
speaker: Benjamín Palacios (Pontificia Universidad Católica de Chile, Chile)
|
||
- titulo: Particle Source Estimation via Analytical Formulations of the Adjoint Flux
|
||
abstract: Numerous applications of research interest may benefit from the study and development of particle sources estimation methods, such as non-destructive material identification and nuclear safety. In such problems, we are concerned with estimating the spatial distribution and intensity of internal sources of neutral particles. In this context, we use the adjoint to the transport operator to derive a linear model that relates the absorption rate measurements of a series of internal particle detectors with the coefficients of the source expansion on a given basis. We consider both one-dimensional energy-dependent and two-dimensional (\(XY\)-geometry) monoenergetic transport problems. We use the adjoint version of the Analytical Discrete Ordinates (ADO) method to write spatially explicit solutions for the adjoint flux for one-dimensional problems. We consider a nodal version of the adjoint ADO method to writing similar explicit expressions for the \(x\) and \(y\) averaged adjoint fluxes for the two-dimensional case. In both cases, we use explicit expressions to derive closed-form formulas to the absorption rate. Then, we apply the iterated Tikhonov algorithm to estimate the sources from noisy measurements and a Bayesian approach through the Metropolis-Hastings algorithm. We successfully estimated one-dimensional polynomial and piecewise constant localized energy dependent sources and two-dimensional piecewise constant localized sources from noise measurements. In either case, the use of closed-form expressions allowed a relevant reduction in computational time.
|
||
start:
|
||
end:
|
||
speaker: Liliane Basso Barichello (Universidade Federal do Rio Grande do Sul, Brasil)
|
||
- titulo: Inverse scattering for the Jacobi system using input data containing transmission eigenvalues
|
||
abstract: |
|
||
The Jacobi system with the Dirichlet boundary condition is considered on a half-line lattice with real-valued coefficients including weight factors. The inverse problem of recovery of the coefficients is analyzed by using certain input data sets containing the transmission eigenvalues.
|
||
This is joint work with T. Aktosun of University of Texas at Arlington and V. G. Papanicolaou of National Technical University of Athens.
|
||
start:
|
||
end:
|
||
speaker: Abdon Choque Rivero (Universidad Michoacana de San Nicolás de Hidalgo, México)
|
||
- titulo: Identificación del coeficiente de velocidad local en un modelo bi-direccional para la propagación de ondas en la superficie de un canal con fondo variable
|
||
abstract: |
|
||
Un problema inverso es aquel donde se requiere determinar el valor de algunos parámetros de un modelo a partir de datos observados. El estudio de este tipo de problemas es de mucha importancia y aparece en diversas ramas de la ciencia y de las Matemáticas. En esta charla consideramos el problema inverso de identificación del coeficiente de velocidad lineal local en un sistema de tipo Boussinesq linealizado de tipo dispersivo deducido por Quintero y Muñoz (2004), a partir de las mediciones \(V_T(x), N_T(x)\) en un tiempo final \(T\), de la velocidad de las partículas en una profundidad fija y la amplitud de la onda, que se propaga en la superficie de un canal raso con fondo variable.
|
||
El problema inverso es reformulado como un problema de optimización con restricciones, donde la funcional objetivo es de tipo usado en métodos de mínimos cuadrados junto con una regularización del tipo introducido por Tikhonov (1963). El proceso de minimización del funcional Tikhonov adoptado se realiza utilizando el método iterativo quasi-Newton L-BFGS-B, introducido por Byrd et al. (1995). Se presentan simulaciones numéricas para mostrar la convergencia y robustez del método numérico propuesto, a\'un en el caso en que el coeficiente posee discontinuidades, o existe ruido en la medici\'on de los datos de entrada \(V_T(x), N_T(x)\).
|
||
Investigación realizada con el apoyo de la Universidad del Valle mediante proyecto C.I. 71235.
|
||
Referencias:
|
||
Tikhonov, A.N. (1963): Solution of incorrectly formulated problems and the regularization method. Soviet Math. Dokl. 4, 1035-1038.
|
||
Byrd, R.H., Lu, P., Nocedal, J. (1995): A limited memory algorithm for Bound Constrained Optimization. SIAM J. Sci. Stat. Comp. 16 (5): 1190-1208.
|
||
Quintero, J.R. , Muñoz, J.C. (2004): Existence and uniqueness for a Boussinesq system with a disordered forcing. Methods Appl. Anal., 11 (1): 015-032.
|
||
start:
|
||
end:
|
||
speaker: Juan Carlos Muñoz Grajales (Universidad del Valle, Colombia)
|
||
- titulo: Joint curvature-driven diffusion and weighted anisotropic total variation regularization for local inpainting
|
||
abstract: An image inpainting problem consists of restoring an image from a (possibly noisy) observation, in which data from one or more regions is missing. Several inpainting models to perform this task have been developed, and although some of them perform reasonably well in certain types of images, quite a few issues are yet to be sorted out. For instance, if the original image is expected to be smooth, inpainting can be performed with reasonably good results by modeling the solution as the result of a diffusion process using the heat equation. For non-smooth images, however, such an approach is far from being satisfactory. On the other hand, Total Variation (TV) inpainting models based on high order PDE diffusion equations can be used whenever edge restoration is a priority. More recently, the introduction of spatially variant conductivity coefficients on these models, such as in the case of Curvature-Driven Diffusions (CDD), has allowed inpainted images with well defined edges and enhanced object connectivity. The CDD approach, nonetheless, is not suitable wherever the image is smooth, as it tends to produce piecewise constant solutions. Based upon this, we propose using CDD to gather a-priori information used at a second step in a weighted anisotropic mixed Tikhonov plus total- variation model that allows for both edge preservation and object connectivity while precluding the staircasing effect that all pure TV-based methods entail. Comparisons between the results of the implemented models will be illustrated by several computed examples, along with performance measures.
|
||
start:
|
||
end:
|
||
speaker: Ruben D. Spies (Instituto de Matemática Aplicada del Litoral, Argentina)
|
||
- titulo: A Splitting Strategy for the Calibration of Jump-Diffusion Models
|
||
abstract: We present a splitting strategy to identify simultaneously the local-volatility surface and the jump-size distribution from quoted European prices. The underlying is a jump-diffusion driven asset with time and price dependent volatility. Our approach uses a forward partial-integro-differential equation for the option prices to produce a parameter-to-solution map. The corresponding inverse problem is then solved by Tikhonov-type regularization combined with a splitting strategy.
|
||
start:
|
||
end:
|
||
speaker: Vinicus V. Albani (Universidade Federal de Santa Catarina, Brasil)
|
||
- titulo: Lipschitz Stability for the Backward Heat Equation and its application to Lightsheet Fluorescence Microscopy
|
||
abstract: |
|
||
In this talk we will present a result about Lipschitz stability for the reconstruction of a compactly supported initial temperature for the heat equation in \(\mathbb{R}^n\), from measurements along a positive time interval and over an open set containing its support. We apply these results to deduce a Lipschitz stability inequality for the backwards heat equation problem in \(\mathbb{R}\) with measurements on a curve contained in \( \mathbb{R}\times[0,T]\), leading to stability estimates for an inverse problem arising in 2D Fluorescence Microscopy.
|
||
This is joint work with Pablo Arratia, Evelyn Cueva, Axel Osses and Benjamin Palacios.
|
||
start:
|
||
end:
|
||
speaker: Liliane Basso Barichello (Universidade Federal do Rio Grande do Sul, Brasil)
|
||
- titulo: Anatomical atlas of the upper part of the human head for electroencephalography and bioimpedance applications
|
||
abstract: |
|
||
Electrophysiology is the branch of physiology that investigates the electrical properties of biological tissues. Volume conductor problems in cerebral electrophysiology and bioimpedance do not have analytical solutions for nontrivial geometries and require a 3D model of the head and its electrical properties for solving the associated PDEs numerically.
|
||
Ideally, the model should be made with patient-specific information. In clinical practice, this is not always the case and an average head model is often used. Also, the electrical properties of the tissues might not be completely known due to natural variability.
|
||
A 4D (3D+T) statistical anatomical atlas of the electrical properties of the upper part of the human head for cerebral electrophysiology and bioimpedance applications is presented. The atlas is constructed based on MRI images of human individuals and comprises the electrical properties of the main internal structures and can be adjusted for specific electrical frequencies. The atlas also comprises a time-varying model of arterial brain circulation, based on the solution of the Navier-Stokes equations.
|
||
The atlas is an important tool for in silico studies on cerebral circulation and electrophysiology that require statistically consistent data, e.g., machine learning, sensitivity analyses, and as a benchmark to test inverse problem solvers. The atlas can also be used as statistical prior information for inverse problems in electrophysiology.
|
||
start:
|
||
end:
|
||
speaker: Moura da Silva (Universidade Federal do ABC, Brasil y University of Helsinki, Finlandia)
|
||
- sesion: Estadística Matemática
|
||
organizadores:
|
||
- nombre: Florencia Leonardi
|
||
mail: florencia@usp.br
|
||
- nombre: Pamela Llop
|
||
mail: lloppamela@gmail.com
|
||
- nombre: Daniela Rodriguez
|
||
mail: drodrig@dm.uba.ar
|
||
charlas:
|
||
- titulo: Differentially private inference via noisy optimization
|
||
abstract: We propose a general optimization-based framework for computing differentially private M-estimators and a new method for the construction of differentially private confidence regions. Firstly, we show that robust statistics can be used in conjunction with noisy gradient descent and noisy Newton methods in order to obtain optimal private estimators with global linear or quadratic convergence, respectively. We establish global convergence guarantees, under both local strong convexity and self-concordance, showing that our private estimators converge with high probability to a neighborhood of the non-private M-estimators. The radius of this neighborhood is nearly optimal in the sense it corresponds to the statistical minimax cost of differential privacy up to a logarithmic term. Secondly, we tackle the problem of parametric inference by constructing differentially private estimators of the asymptotic variance of our private M-estimators. This naturally leads to the use of approximate pivotal statistics for the construction of confidence regions and hypothesis testing. We demonstrate the effectiveness of a bias correction that leads to enhanced small-sample empirical performance in simulations.
|
||
start:
|
||
end:
|
||
speaker: Marco Avella Medina (Columbia University, Estados Unidos)
|
||
- titulo: Adaptive regression with Brownian path covariate
|
||
abstract: In this talk, we will study how to obtain optimal estimators in problems of non-parametric estimation. More specifically, we will present the Goldenshluger-Lepski (2011) method that allows one to obtain estimators that adapt to the smoothness of the function to be estimated. We will show how to extend this statistical procedure in regression with functional data when the regressor variable is a Wiener process \(W\). Using the Wiener-Ito decomposition of m(W), where \(m\) is the regression function, we will define a family of estimators that satisfy an oracle inequality, are proved to be adaptive and converge at polynomial rates over specific classes of functions.
|
||
start:
|
||
end:
|
||
speaker: Karine Bertin (Universidad de Valparaíso, Chile)
|
||
- titulo: 'Adjusting ROC curves for covariates: a robust approach'
|
||
abstract: |
|
||
ROC curves are a popular tool to describe the discriminating power of a binary classifier based on a continuous marker as the threshold is varied. They become an interesting strategy to evaluate how well an assignment rule based on a diagnostic test distinguishes one population from the other. Under certain circumstances the marker's discriminatory ability may be affected by certain covariates. In this situation, it seems sensible to include this information in the ROC analysis. This task can be accomplished either by the induced or the direct method.
|
||
In this talk we will focus on ROC curves in presence of covariates. We will show the impact of outliers on the conditional ROC curves and we will introduce a robust proposal. We follow a semiparametric approach where we combine robust parametric estimators with weighted empirical distribution estimators based on an adaptive procedure that downweights outliers.
|
||
We will discuss some aspects concerning consistency and through a Monte Carlo study we will compare the performance of the proposed estimators with the classical ones both, in clean and contaminated samples.
|
||
start:
|
||
end:
|
||
speaker: Ana M. Bianco (Universidad de Buenos Aires, Argentina)
|
||
- titulo: Least trimmed squares estimators for functional principal component analysis
|
||
abstract: 'Classical functional principal component analysis can yield erroneous approximations in presence of outliers. To reduce the influence of atypical data we propose two methods based on trimming: a multivariate least trimmed squares (LTS) estimator and its coordinatewise variant. The multivariate LTS minimizes the multivariate scale corresponding to \(h-\)subsets of curves while the coordinatewise version uses univariate LTS scale estimators. Consider a general setup in which observations are realizations of a random element on a separable Hilbert space \(\mathcal{H}\). For a fixed dimension \(q\), we aim to robustly estimate the \(q\) dimensional linear space in \(\mathcal{H}\) that gives the best approximation to the functional data. Our estimators use smoothing to first represent irregularly spaced curves in a high-dimensional space and then calculate the LTS solution on these multivariate data. The solution of the multivariate data is subsequently mapped back onto \(\mathcal{H}\). Poorly fitted observations can therefore be flagged as outliers. Simulations and real data applications show that our estimators yield competitive results when compared to existing methods when a minority of observations is contaminated. When a majority of the curves is contaminated at some positions along its trajectory coordinatewise methods like Coordinatewise LTS are preferred over multivariate LTS and other multivariate methods since they break down in this case.'
|
||
start:
|
||
end:
|
||
speaker: Holger Cevallos-Valdiviezo (Escuela Superior Politécnica del Litoral, Ecuador y Ghent University, Bélgica)
|
||
- titulo: A non-asymptotic analysis of certain high-dimensional estimators for the mean
|
||
abstract: Recent work in Statistics and Computer Science has considered the following problem. Given a distribution \(P\) over \({\bf R}^d\) and a fixed sample size \(n\), how well can one estimate the mean \(\mu = \bf E_{X\sim P} X\) from a sample \(X_1,\dots,X_n\stackrel{i.i.d.}{\sim}P\) while only requiring finite second moments and allowing for sample contamination? It turns out that the best estimators are not related to the sample mean. In this talk we present a new analysis of certain approaches to this problem, and reproduce or improve previous results by several authors.
|
||
start:
|
||
end:
|
||
speaker: Roberto Imbuzeiro Oliveira (Instituto de Matemática Pura e Aplicada, Brasil)
|
||
- titulo: Stick-breaking priors via dependent length variables
|
||
abstract: In this talk, we present new classes of Bayesian nonparametric prior distributions. By allowing length random variables, in stick-breaking constructions, to be exchangeable or Markovian, appealing models for discrete random probability measures appear. As a result, by tuning the stochastic dependence in such length variables allows to recover extreme families of random probability measures, i.e. Dirichlet and Geometric processes. As a byproduct, the ordering of the weights, in the species sampling representation, can be controlled and thus tuned for efficient MCMC implementations in density estimation or unsupervised classification problems. Various theoretical properties and illustrations will be presented.
|
||
start:
|
||
end:
|
||
speaker: Ramsés Mena Chávez (Universidad Nacional Autónoma de México, México)
|
||
- titulo: 'Modelling in pandemic times: using smart watch data for early detection of COVID-19'
|
||
abstract: |
|
||
The COVID-19 pandemic brought many challengers to statisticians and modelers across all quantitative disciplines. From accelerated clinical trials to modelling of epidemiological interventions at a feverish pace, to the study of the impact of the pandemic in mental health outcomes and racial disparities. In this talk, we would like to share our experience using classical statistical modelling and machine learning to use data obtained from wearable devices as digital biomarkers of COVID-19 infection.
|
||
Early in the pandemic, health care workers in the Mount Sinai Health System (New York city) were prospectively followed in an observational study using the custom Warrior Watch Study app, to collect weekly information about stress, symptoms and COVID-19 infection. Participants wore an Apple Watch for the duration of the study, measuring heart rate variability (HRV), a digital biomarker previously associated with infection in other settings, throughout the follow-up period.
|
||
The HRV data collected through the Apple Watch was characterized by a circadian pattern, with sparse sampling over a 24-hour period, and non-uniform timing across days and participants. These characteristics preclude us from using easily derived features (ie mean, maximum, CV etc) with Machine learning methods to develop a diagnostic tool. As such, suitable modelling of the non-uniform, sparsely sampled circadian rhythm data derived from wearable devices are an important step to advance the use of integrated wearable data for prediction of health outcomes.
|
||
To circumvent such limitations, we introduced the mixed-effects COSINOR model, where the daily circadian rhythm is express as a non-linear function with three rhythm characteristics: the rhythm-adjusted mean (MESOR), half the extent of variation within a cycle (amplitude), and an angle relating to the time at which peak values recur in each cycle (acrophase). The longitudinal changes in the circadian patterns can then be evaluated extending the COSINOR model to a mixed-effect model framework, allowing for random effects and interaction between COSINOR parameters and time-varying covariates. In this talk, we will discuss our model framework, boostrapped-based hypothesis testing and prediction approaches, as well as our evaluation of HRV measures as early biomarkers of COVID-19 diagnosis. To facilitate the future use of the mixed-effect COSINOR model, we implemented in an R package cosinoRmixedeffects.
|
||
start:
|
||
end:
|
||
speaker: Mayte Suarez-Farinas (Icahn School of Medicine at Mount Sinai, Estados Unidos)
|
||
- sesion: Teorı́a de bordismo y acciones de grupos finitos
|
||
organizadores:
|
||
- nombre: Andrés Ángel
|
||
mail: ja.angel908@uniandes.edu.co
|
||
- nombre: Ana González de los Santos
|
||
mail: anagon@fing.edu.uy
|
||
- nombre: Rita Jiménez Rolland
|
||
mail: rita@im.unam.mx csegovia@matem.unam.mx
|
||
- nombre: Carlos Segovia
|
||
mail: csegovia@matem.unam.mx
|
||
charlas:
|
||
- titulo: On the evenness conjecture for equivariant unitary bordism
|
||
abstract: The evenness conjecture for equivariant unitary bordism states that these homology groups are free modules of even degree with respect to the unitary bordism ring. This conjecture is known to be true for all finite abelian groups and some semidirect products of abelian groups. In this talk I will talk about some progress done with the group of quaternions of order 8, together with an approach of Eric Samperton and Carlos Segovia to construct a free action on a surface which does not bound equivariantly. This last construction might provide a counterexample of the evenness conjecture in dimension 2.
|
||
start:
|
||
end:
|
||
speaker: Bernardo Uribe (Universidad del Norte, Colombia)
|
||
- titulo: Extending free group action on surfaces
|
||
abstract: We are interested in the question of when a free action of a finite group on a closed oriented surface extends to a non-necessarily free action on a 3-manifold. We show the answer to this question is affirmative for abelian, dihedral, symmetric and alternating groups. We present also the proof for finite Coxeter groups.
|
||
start:
|
||
end:
|
||
speaker: Carlos Segovia (Universidad Nacional Autónoma de México, México)
|
||
- titulo: When does a free action of a finite group on a surface extend to a (possibly non-free) action on a 3-manifold?
|
||
abstract: Dominguez and Segovia recently asked the question in the title, and showed that the answer is “always” for many examples of finite groups, including symmetric groups, alternating groups and abelian. Surprisingly, in joint work with Segovia, we have found the first examples of finite groups that admit free actions on surfaces that do NOT extend to actions on 3-manifolds. Even more surprisingly, these groups are already known in algebraic geometry as counterexamples to the Noether conjecture over the complex numbers. In this talk, I will explain how to find these groups, and, more generally, how to decide algorithmically if any fixed finite group admits a non-extending action.
|
||
start:
|
||
end:
|
||
speaker: Eric G. Samperton (University of Illinois, Estados Unidos)
|
||
- titulo: The Loch Ness Monster as Homology Covers
|
||
abstract: The Loch Ness Monster (LNM) is, up to homeomorphisms, the unique orientable, second countable, connected and Hausdorff surface of infinite genus and exactly one end. In this talk I would like to discuss some properties on the LNM. In particular, we note that LNM is the homology cover of most of the surfaces and also it is the derived cover of uniformizations of Riemann surfaces (with some few exceptions). This is a joint work, in progress, with Ara Basmajian.
|
||
start:
|
||
end:
|
||
speaker: Rubén A. Hidalgo (Universidad de la Frontera, Chile)
|
||
- titulo: Diffeomorphisms of reducible three manifolds and bordisms of group actions on torus
|
||
abstract: I first talk about the joint work with K. Mann on certain rigidity results on group actions on torus. In particular, we show that if the torus action on itself extends to a \(C^0\) action on a three manifold \(M\) that bounds the torus, then \(M\) is homeomorphic to the solid torus. This also leads to the first example of a smooth action on the torus via diffeomorphisms that isotopic to the identity that is nontrivial in the bordisms of group actions. Time permitting, I will also talk about certain finiteness results about classifying space of reducible three manifolds which came out of the cohomological aspect of the above project.
|
||
start:
|
||
end:
|
||
speaker: Sam Nariman (Purdue University, Estados Unidos)
|
||
- titulo: Stolz' Positive scalar curvature surgery exact sequence and low dimensional group homology
|
||
abstract: We will show how positive knowledge about the Baum-Connes Conjecture for a group, together with a Pontrjagyn character and knowledge about the conjugacy classes of finite subgroups and their low dimensional homology provide an estimation of the degree of non rigidity of positive scalar curvature metrics of spin high dimensional manifolds with the given fundamental group.
|
||
start:
|
||
end:
|
||
speaker: Noé Bárcenas (Universidad Nacional Autónoma de México, México)
|
||
- titulo: Signature of manifold with single fixed point set of an abelian normal group
|
||
abstract: In this talk we will report progress made in the task of reducing the computation of the signature of a (possibly non compact) oriented smooth dimensional manifold with an orientation preserving co-compact smooth proper action of a discrete group with a single non empty fixed point submanifold of fixed dimension with respect to the action of a (finite) abelian normal subgroup. The aim of this reduction is to give a formula for the signature in terms of the signature of a manifold with free action and the signature of a disc neighborhood of its fixed-point set with quasi-free action. A necessary task in this reduction is the generalization of Novikov’s additivity to this context.
|
||
start:
|
||
end:
|
||
speaker: Quitzeh Morales (Universidad Pedagógica de Oaxaca, México)
|
||
- titulo: \(Z_p\)-bordism and the mod(\(p\))-Borsuk-Ulam Theorem
|
||
abstract: |
|
||
Crabb-Gonçalves-Libardi-Pergher classified for given integers \(m,n, \geq 1\) the bordism class of a closed smooth \(m\)-manifold \(X^m\) with a free smooth involution \(\tau\) with respect to the validity of the Borsuk-Ulam property that for every continuous map \(\varphi: X^m \to R^n\), there exists a point \(x \in X^m\) such that \(\varphi(x)= \varphi(\tau(x))\).
|
||
In this work together with Barbaresco-de Mattos-dos Santos-da Silva, we are considering the same problem for free \(Z_p\) action.
|
||
start:
|
||
end:
|
||
speaker: Alice Kimie Miwa Libardi (Universidad Estatal Paulista, Brasil)
|
||
- sesion: Ecuaciones de evolución no-lineales y su Dinámica
|
||
organizadores:
|
||
- nombre: Jaime Angulo Pava
|
||
mail: angulo@ime.usp.br
|
||
- nombre: Diego Chamorro
|
||
mail: diego.chamorro@univ-evry.fr
|
||
- nombre: Claudio Muñoz
|
||
mail: cmunoz@dim.uchile.cl
|
||
charlas:
|
||
- titulo: Regularity criteria for weak solutions to the three-dimensional MHD system
|
||
abstract: |
|
||
In this talk we will first review various known regularity criteria and partial regularity theory for 3D incompressible Navier-Stokes equations. I will then present two generalizations of partial regularity theory of Caffarelli, Kohn and Nirenberg to the weak solutions of MHD equations. The first one is based on the framework of parabolic Morrey spaces. We will show parabolic Hölder regularity for the "suitable weak solutions" to the MHD system in small neighborhoods. This type of parabolic generalization using Morrey spaces appears to be crucial when studying the role of the pressure in the regularity theory and makes it possible to weaken the hypotheses on the pressure. The second one is a regularity result relying on the notion of "dissipative solutions". By making use of the first result, we will show the regularity of the dissipative solutions to the MHD system with a weaker hypothesis on the pressure.
|
||
This is a joint work with Diego Chamorro (Université Paris-Saclay, site Evry).
|
||
start:
|
||
end:
|
||
speaker: Jiao He (Université Paris-Saclay, Francia)
|
||
- titulo: On the infinite energy weak solutions for the MHD equations
|
||
abstract: |
|
||
In this talk, we will consider the magneto-hydrodynamics (MHD) equations placed on the whole three-dimensional space. These equations write down as a nonlinear coupled system of two Navier-Stokes type equations, where the unknowns are the velocity field, the magnetic field and the pressure term. In the first part of this talk, within the framework of a kind of weighted L^2 spaces, we expose some new energy controls which allow us to prove the existence of global in time weak solutions. These solutions are also called the infinite energy weak solutions, in contrast with the classical theory of finite energy weak solutions in the L^2 space. The uniqueness of both finite energy and infinite energy weak solutions remains a very challenging open question. Thus, in the second part of this talk, we study a a priori condition, known as weak-strong uniqueness criterion, to ensure the uniqueness of the infinite energy weak solutions. This result is given in a fairly general multipliers type space, which contains some well-known functional spaces previously used to prove some weak-strong uniqueness criteria.
|
||
This is a joint work with Pedro Fernandez-Dalgo (Université Paris-Saclay).
|
||
start:
|
||
end:
|
||
speaker: Oscar Jarrín (Universidad de las Américas, Ecuador)
|
||
- titulo: Long-time asymptotics for a damped Navier-Stokes-Bardina model
|
||
abstract: We consider finite energy solutions for a damped Navier-Stokes-Bardina’s model and show that the corresponding dynamical system possesses a global attractor. We obtain upper bounds for its fractal dimension. Furthermore, we examine the long-term behavior of solutions of the damped Navier-Stokes-Bardina’s equation in the energy space.
|
||
start:
|
||
end:
|
||
speaker: Fernando Cortez (Escuela Politécnica Nacional, Ecuador)
|
||
- titulo: Compact embeddings of p-Sobolev-like cones of nuclear operators
|
||
abstract: We prove that a cone of nuclear operators, whose eigenfunctions belong to a p-Sobolev space and that have finite total energy, is compactly embedded in the trace norm. This result is analogous to the classical Sobolev embeddings but at operators level. In the path we prove regularity properties for the density function of any operator living in the cone. Also, departing from Lieb-Thirring type conditions, we obtain some Gagliardo-Nirenberg inequalities. By using the compactness property, several free-energy functionals for operators are shown to have a minimizer. The entropy term of these free-energy functionals is generated by a Casimir-class function related to the eigenvalue problem of the Schrödinger operator.
|
||
start:
|
||
end:
|
||
speaker: Juan Mayorga (Yachay Tech, Ecuador)
|
||
- titulo: Scattering for quadratic-type Schrödinger systems in dimension five without mass-resonance
|
||
abstract: In this talk we will discuss the scattering of non-radial solutions in the energy space to coupled system of nonlinear Schrödinger equations with quadratic-type growth interactions in dimension five without the mass-resonance condition. Our approach is based on the recent ideas introduced by Dodson and Murphy, which relies on an interaction Morawetz estimate.
|
||
start:
|
||
end:
|
||
speaker: Ademir Pastor (Universidade Estadual de Campinas, Brasil)
|
||
- titulo: Stability of smooth periodic traveling waves in the Camassa-Holm equation
|
||
abstract: |
|
||
Smooth periodic travelling waves in the Camassa–Holm (CH) equation are revisited in this talk. We show that these periodic waves can be characterized in two different ways by using two different Hamiltonian structures. The standard formulation, common to the Korteweg–de Vries (KdV) equation, has several disadvantages, e.g., the period function is not monotone and the quadratic energy form may have two rather than one negative eigenvalues. We explore the nonstandard formulation common to evolution equations of CH type and prove that the period function is monotone and the quadratic energy form has only one simple negative eigenvalue. We deduce a precise condition for the spectral and orbital stability of the smooth periodic travelling waves and show numerically that this condition is satisfied in the open region of three parameters where the smooth periodic waves exist.
|
||
This is a joint work with Dmitry E. Pelinovsky (McMaster University), AnnaGeyer (Delft University of Technology) and Renan H. Martins (State University of Maringa).
|
||
start:
|
||
end:
|
||
speaker: Fábio Natali (Universidade Estadual de Maringá, Brasil)
|
||
- titulo: Spectral stability of monotone traveling fronts for reaction diffusion-degenerate Nagumo equations
|
||
abstract: This talk addresses the spectral stability of monotone traveling front solutions for reaction diffusion equations where the reaction function is of Nagumo (or bistable) type and with diffusivities which are density dependent and degenerate at zero (one of the equilibrium points of the reaction). Spectral stability is understood as the property that the spectrum of the linearized operator around the wave, acting on an exponentially weighted space, is contained in the complex half plane with non-positive real part. The degenerate fronts studied in this paper travel with positive speed above a threshold value and connect the(diffusion-degenerate) zero state with the unstable equilibrium point of the reaction function. In this case, the degeneracy of the diffusion coefficient is responsible of the loss of hyperbolicity of the asymptotic coefficient matrices of the spectral problem at one of the end points, precluding the application of standard techniques to locate the essential spectrum. This difficulty is overcome with a suitable partition of the spectrum, a generalized convergence of operators technique, the analysis of singular (or Weyl) sequences and the use of energy estimates. The monotonicity of the fronts, as well as detailed descriptions of the decay structure of eigenfunctions on a case by case basis, are key ingredients to show that all traveling fronts under consideration are spectrally stable in a suitably chosen exponentially weighted L2 energy space.
|
||
start:
|
||
end:
|
||
speaker: Ramón G. Plaza (Universidad Nacional Autónoma de México, México)
|
||
- titulo: Blow-up solutions of the intercritical inhomogeneous NLS equation
|
||
abstract: |
|
||
We consider the inhomogeneous nonlinear Schrödinger (INLS) equation
|
||
$$i u_t +\Delta u+|x|^{-b}|u|^{2\sigma} u = 0, \,\,\, x\in \mathbb{R}^N,$$
|
||
with \(N\geq 3\) and \(0<b<\min\{\frac{N}{2},2\}\). We focus on the intercritical case, where the scaling invariant Sobolev index \(s_c=\frac{N}{2}-\frac{2-b}{2\sigma}\) satisfies \(0<s_c<1\). In this talk, for initial data in \(\dot H^{s_c}\cap \dot H^1\), we discuss the existence of blow-up solutions and also a lower bound for the blow-up rate in the radial and non-radial settings.
|
||
This is a joint work with Mykael Cardoso (Universidade Federal do Piauí, Brasil).
|
||
start:
|
||
end:
|
||
speaker: Luiz Gustavo Farah (Universidade Federal de Minas Gerais, Brasil).
|
||
- titulo: A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models
|
||
abstract: |
|
||
In this talk I will discuss stability properties of kinks for the (1+1)-dimensional nonlinear scalar field theory models \(\partial_t2\phi -\partial_x2\phi + W'(\phi) = 0, \quad (t,x)\in\R\times\R\). The orbital stability of kinks under general assumptions on the potential \(W\) is a consequence of energy arguments. The main result I will present is the derivation of a simple and explicit sufficient condition on the potential \(W\) for the asymptotic stability of a given kink. This condition applies to any static or moving kink, in particular no symmetry assumption is required. Applications of the criterion to the \(P(\phi)_2\) theories and the double sine-Gordon theory will be discussed.
|
||
This is a joint work with Y. Martel, C. Muñoz and H. Van Den Bosch.
|
||
start:
|
||
end:
|
||
speaker: Michal Kowalczyk (Universidad de Chile, Chile)
|
||
- titulo: Korteweg de-Vries limit for the Fermi-Pasta-Ulam System
|
||
abstract: In this talk, we are going to discuss dispersive properties for the Fermi-Pasta-Ulam (FPU) system with infinitely many oscillators. Precisely, we see that FPU systems are reformulated and their solutions satisfies Strichartz, local smoothing, and maximal function estimates in comparison with linear Korteweg–de Vries (KdV) flows. With these properties, we finally show that the infinite FPU system can be approximated by counter-propagating waves governed by the KdV equation as the lattice spacing approaches zero.
|
||
start:
|
||
end:
|
||
speaker: Chulkwang Kwak (Ehwa Womans University, Corea del Sur)
|
||
- titulo: TBA
|
||
abstract: TBA
|
||
start:
|
||
end:
|
||
speaker: Hanne Van Den Bosch (Universidad de Chile, Chile)
|
||
- sesion: Combinatoria
|
||
organizadores:
|
||
- nombre: Celina Miraglia Herrera de Figueiredo
|
||
mail: celina@cos.ufrj.br
|
||
- nombre: Flavia Bonomo
|
||
mail: fbonomo@dc.uba.ar
|
||
- nombre: Lucia Moura
|
||
mail: lmoura@uottawa.ca
|
||
charlas:
|
||
- titulo: Complete colorings on circulant graphs and digraphs
|
||
abstract: |
|
||
A <em>complete</em> \(k\)-vertex-coloring of a graph \(G\) is a vertex-coloring of \(G\) using \(k\) colors such that for every pair of colors there is at least two incident vertices in \(G\) colored with this pair of colors. The \emph{chromatic} \(\chi(G)\) and \emph{achromatic} \(\alpha(G)\) numbers of \(G\) are the smallest and the largest number of colors in a complete proper \(k\)-vertex-coloring of \(G\), therefore \(\chi(G)\leq\alpha(G)\).
|
||
The dichromatic number and the diachromatic number, generalice the concepts of chromatic number and achromatic number. An <em>acyclic</em> \(k\)-vertex-coloring of a digraph \(D\) is vertex coloring using \(k\) colors such that \(D\) has no monochromatic cycles and a \emph{complete} \(k\)-vertex-coloring of a digraph \(D\) is a vertex coloring using \(k\) colors such that for every ordered pair \((i,j)\) of different colors, there is at least one arc \((u,v)\) such that \(u\) has color \(i\) and \(v\) has color \(j\). The dichromatic number \(dc(D)\) and diachromatic number \(dac(D)\) of \(D\) are the smallest and the largest number of colors in a complete proper \(k\)-vertex-coloring of \(D\), therefore \(dc(D)\leq dac(D)\).
|
||
We determine the achromatic and diachromatic numbers of some specific circulant graphs and digraphs and give general bounds for these two parameters on these graphs and digraphs. Also, we determine the achromatic index for circulant graphs of order \(q^2+q+1\) using projective planes.
|
||
Joint work with: Juan José Montellano-Ballesteros, Mika Olsen and Christian Rubio-Montiel.
|
||
start:
|
||
end:
|
||
speaker: Gabriela Araujo-Pardo (Universidad Nacional Autónoma de México, México)
|
||
- titulo: Fault Localization via Combinatorial Testing
|
||
abstract: |
|
||
In this talk, we explore combinatorial arrays that are useful in identifying faulty interactions in complex engineered systems. A {\sl separating hash family} ${\sf SHF}_\lambda(N; k,v,\{w_1,\dots,w_s\})$ is an $N \times k$ array on $v$ symbols, with the property that no matter how disjoint sets $C_1, \dots, C_s$ of columns with $|C_i| = w_i$ are chosen, there are at least $\lambda$ rows in which, for every $1 \leq i < j \leq s$, no entry in a column of $C_i$ equals that in a column of $C_j$. (That is, there are $\lambda$ rows in which sets $\{C_1,\dots,C_s\}$ are {\sl separated}.) Separating hash families have numerous applications in combinatorial cryptography and in the construction of various combinatorial arrays; typically, one only considers whether two symbols are the same or different. We instead employ symbols that have algebraic significance.
|
||
We consider an ${\sf SHF}_\lambda(N; k,q^s,\{w_1,\dots,w_s\})$ whose symbols are column vectors from ${\mathbb F}_q^s$. The entry in row $r$ and column $c$ of the ${\sf SHF}$ is denoted by ${\bf v}_{r,c}$. Suppose that $C_1, \dots, C_s$ is a set of disjoint sets of columns. Row $r$ is {\sl covering} for $\{C_1, \dots, C_s\}$ if, whenever we choose $s$ columns $\{ \gamma_i \in C_i : 1 \leq i \leq s\}$, the $s \times s$ matrix $[ {\bf v}_{r,\gamma_1} \cdots {\bf v}_{r,\gamma_s} ]$ is nonsingular over ${\mathbb F}_q$. Then the ${\sf SHF}_\lambda(N; k,q^s,\{w_1,\dots,w_s\})$ is {\sl covering} if, for every way to choose $\{C_1, \dots, C_s\}$, there are at least $\lambda$ covering rows.
|
||
We establish that covering separating hash families of type $1^t d^1$ give an effective construction for detecting arrays, which are useful in screening complex systems to find interactions among $t$ or fewer factors without being masked by $d$ or fewer other interactions. This connection easily accommodates outlier and missing responses in the screening. We explore asymptotic existence results and explicit constructions using finite geometries for covering separating hash families. We develop randomized and derandomized construction algorithms and discuss consequences for detecting arrays. This is joint work with Violet R. Syrotiuk (ASU).
|
||
start:
|
||
end:
|
||
speaker: Charles J. Colbourn (Arizona State University, Estados Unidos)
|
||
- titulo: On the \(\Delta\)-interval and \(\Delta\)-convexity numbers of graphs and graph products
|
||
abstract: |
|
||
Given a graph \(G\) and a set \(S \subseteq V(G)\), the \(\Delta\)-interval of \(S\), \([S]_{\Delta}\), is the set formed by the vertices of \(S\) and every \(w \in V(G)\) forming a triangle with two vertices of \(S\). If \([S]_\Delta = S\), then \(S\) is \(\Delta\)-convex of \(G\); if \([S]_{\Delta} = V(G)\), then \(S\) is a \(\Delta\)-interval set of \(G\). The \(\Delta\)-interval number of \(G\) is the minimum cardinality of a \(\Delta\)-interval set and the \(\Delta\)-convexity number of \(G\) is the maximum cardinality of a proper \(\Delta\)-convex subset of \(V(G)\). In this work, we show that the problem of computing the \(\Delta\)-convexity number is {\sf W}[1]-hard and {\sf NP}-hard to approximate within a factor \(O(n^{1-\varepsilon})\) for any constant \(\varepsilon > 0\) even for graphs with diameter \(2\) and that the problem of computing the \(\Delta\)-interval number is {\sf NP}-complete for general graphs. For the positive side, we present characterizations that lead to polynomial-time algorithms for computing the \(\Delta\)-convexity number of chordal graphs and for computing the \(\Delta\)-interval number of block graphs. We also present results on the \(\Delta\)-hull, \(\Delta\)-interval and \(\Delta\)-convexity numbers concerning the three standard graph products, namely, the Cartesian, strong and lexicographic products, in function of these and well-studied parameters of the operands.
|
||
Joint work with: Bijo S. Anand, Prasanth G. Narasimha-Shenoi, and Sabeer S. Ramla.
|
||
start:
|
||
end:
|
||
speaker: Mitre Dourado (Universidade Federal do Rio de Janeiro, Brasil)
|
||
- titulo: Unavoidable patterns
|
||
abstract: Ramsey's theorem states that, for any integer \(t\), if \(n\) is a sufficiently large integer, then every \(2\)-edge-coloring of a complete graph \(K_n\) contains a monochromatic \(K_t\). On the other hand, Turán's theorem says that, if a graph has sufficiently many edges, then it contains a \(K_t\) as a subgraph. In relation to these two types of problems, we study which \(2\)-colored patterns are forced to appear in differently saturated \(2\)-edge-colorings of the complete graph \(K_n\) provided \(n\) is large enough. This is a joint work with Yair Caro and Amanda Montejano.
|
||
start:
|
||
end:
|
||
speaker: Adriana Hansberg (Universidad Nacional Autónoma de México, México)
|
||
- titulo: Approximating graph eigenvalues using tree decompositions
|
||
abstract: |
|
||
Spectral graph theory aims to extract structural information about graphs from spectra of different types of matrices associated with them, such as the adjacency matrix, Laplacian matrices, and many others. A basic step in any such application consists of computing or approximating the spectrum or some prescribed subset of eigenvalues. One strategy for this is to compute diagonal matrices that are congruent to the original matrices, which can be done quite efficiently if we have a graph decompositions such as the tree decomposition with bounded width. To be precise, let \(M=(m_{ij})\) be a symmetric matrix of order \(n\) whose elements lie in an arbitrary field \(\mathbb{F}\), and let \(G\) be the graph with vertex set \(\{1,\ldots,n\}\) such that distinct vertices \(i\) and \(j\) are adjacent if and only if \(m_{ij} \neq 0\). We present an algorithm that finds a diagonal matrix that is congruent to \(M\) in time \(O(k^2 n)\), provided that we are given a suitable tree decomposition of \(G\) with width \(k\). In addition to the above applications, this allows one to compute the determinant and to find the rank of a symmetric matrix in time \(O(k^2 n)\).
|
||
This is joint work with M. FŸrer (Pennsylvannia State University) and Vilmar Trevisan (Universidade Federal do Rio Grande do Sul).
|
||
start:
|
||
end:
|
||
speaker: Carlos Hoppen (Universidade Federal do Rio Grande do Sul, Brasil)
|
||
- titulo: Fault tolerance in cryptography using cover-free families
|
||
abstract: |
|
||
Cover-free families (CFFs) have been investigated under different names and as a solution to many problems related to combinatorial group testing. A \(d\)-cover-free family \(d\)-CFF\((t, n)\) is a set system with n subsets of a \(t\)-set, where the union of any d subsets does not contain any other. A \(d\)-CFF\((t, n)\) allows for the identification of up to \(d\) defective elements in a set of \(n\) elements by performing only \(t\) tests (typically \(t \ll n\)).
|
||
We explore different aspects of cover-free families in order to achieve fault tolerance in cryptography. For instance, while CFFs are used as a solution to many problems in this area, we note that some of those problems require CFFs with increasing \(n\). In this context, we investigate new infinite families and their constructions in order to better approach fault tolerance in cryptography. This is joint work with Lucia Moura.
|
||
[1] IDALINO, T. B.; MOURA, L., Nested cover-free families for unbounded fault-tolerant aggregate signatures. Theoretical Computer Science, 854 (2021), 116--130.
|
||
[2] IDALINO, T. B.; MOURA, L., Embedding cover-free families and cryptographical applications. Advances in Mathematics of Communications, 13 (2019), 629--643.
|
||
start:
|
||
end:
|
||
speaker: Thais Bardini Idalino (Universidade Federal de Santa Catarina, Brasil)
|
||
- titulo: Perfect sequence covering arrays
|
||
abstract: |
|
||
An \((n,k,\lambda)\) perfect sequence covering array is a subset of the \(n!\) permutations of the sequence \((1, 2, \dots, n)\) whose elements collectively contain each ordered \(k\)-subsequence exactly \(\lambda\) times. The central question is: for given \(n\) and \(k\), what is the smallest value of \(\lambda\) (denoted \(g(n,k)\)) for which such a configuration exists? We interpret the sequences of a perfect sequence covering array as elements of the symmetric group \(S_n\), and constrain its structure to be a union of cosets of a prescribed subgroup of \(S_n\). By adapting a search algorithm due to Mathon and van Trung for finding spreads, we obtain highly structured examples of perfect sequence covering arrays. In particular, we determine that \(g(6,3) = g(7,3) = g(7,4) = 2\) and that \(g(8,3)\) is either 2 or 3.
|
||
This is joint work with Jingzhou Na.
|
||
start:
|
||
end:
|
||
speaker: Jonathan Jedwab (Simon Fraser University, Canada)
|
||
- titulo: The status of the \((r, l)\) well-covered graph sandwich problem
|
||
abstract: |
|
||
An \((r, l)\)-partition of a graph \(G\) is a partition of its vertex set into \(r\) independent sets and \(l\) cliques. A graph is \((r,l)\) if it admits an \((r, l)\)-partition. A graph is well-covered if every maximal independent set is also maximum. A graph is \((r,l)\)-well-covered if it is both \((r,l)\) and well-covered. We have proved the full classification of the decision problem \((r,l)\)-Well-Covered Graph problem, where we are given a graph \(G\), and the question is whether \(G\) is an \((r, l)\)-well-covered graph. We have shown that this problem is polynomial only in the cases \((0, 1)\), \((0, 2)\), \((1, 0)\), \((1, 1)\), \((1, 2)\), and \((2, 0)\) and hard otherwise. The Sandwich Problem for the Property \(\pi\) has as an instance a pair of graphs \(G1 = (V, E_1)\) and \(G2 = (V, E_2)\) with \(E_1 \subset E_2\), plus the question whether there is a graph \(G=(V,E)\) with \(E_1 \subset E\subset E_2\), such that \(G\) has the property \(\pi\). When a recognition problem for a property \(\pi\) is hard, we can consider the sets \(E_1 = E_2\) to obtain that the sandwich problem for the property \(\pi\) reduces to the recognition and so also hard. Hence, the only cases where the \((r, l)\)-well-covered sandwich problem can be no longer hard are in the \(6\) polynomial cases. In this talk we prove that \((r, l)\)-well-covered sandwich problem is polynomial in the cases that \((r, l) = (0, 1), (1, 0), (1, 1)\) or \((0, 2)\), and NP-complete if we consider the property of being \((1, 2)\)-well-covered.
|
||
This work was done with the collaboration of Sancrey Rodrigues Alves (FAETEC), Fernanda Couto (UFRRJ), Luerbio Faria (UERJ), Sylvain Gravier (CNRS), and Uéverton S. Souza (UFF).
|
||
start:
|
||
end:
|
||
speaker: Sulamita Klein (Universidade Federal do Rio de Janeiro, Brasil)
|
||
- titulo: Counting Segment, Rays, Lines in Quasimetric spaces
|
||
abstract: In the Euclidean plane, it is a well-known result that a set of n points defines exactly \(n(n-1)/2\) distinct segments, at least \(2(n-1)-1\) different rays and, when the points are not collinear, at least \(n\) different lines. Segments, rays and lines can be define in any quasimetric space by using its quasimetric. In this talk we survey recent results concerning the generalization of the above mentioned properties of the Euclidean plane, specially those of lines, to finite quasimetric spaces, mainly those defined by connected graphs and strongly connected digraphs.
|
||
start:
|
||
end:
|
||
speaker: Martín Matamala (Universidad de Chile, Chile)
|
||
- titulo: Uniformly Optimally-Reliable Graphs
|
||
abstract: |
|
||
The reliability polynomial of a simple graph G represents the probability that G will remain connected given a fixed probability \(1-p\) of each edge failing. A graph \(G\) is uniformly most reliable if its reliability polynomial is greater than or equal to the reliability polynomial of all other graphs with the same number of nodes and edges for all \(p \in [0, 1]\).
|
||
Which is the most-reliable graph with n nodes and m edges?
|
||
This problem has several variants, according to the notion of optimality (in a local or uniform sense), failure type (either nodes or edges), or reliability model (all-terminal connectedness, source-terminal or general multi-terminal setting).
|
||
This presentation shows a summary of the multiple proposals to attack the problem, together with recent trends and important conjectures proposed decades ago which require further research.
|
||
Particularly, we will present recently proved conjectures regarding UMGR (Uniformly Most-Reliable Graphs) as well as new evaluation techniques for this property.
|
||
Keywords: uniformly most-reliable graph, uniformly least-reliable graph, all-terminal reliability, source-terminal reliability, failure-type, graph theory.
|
||
start:
|
||
end:
|
||
speaker: Franco Robledo (Universidad de la Republica, Uruguay)
|
||
- titulo: Circularly compatible ones, \(D\)-circularity, and proper circular-arc bigraphs
|
||
abstract: In 1969, Tucker characterized proper circular-arc graphs as those graphs whose augmented adjacency matrices have the circularly compatible ones property. Moreover, he also found a polynomial-time algorithm for deciding whether any given augmented adjacency matrix has the circularly compatible ones property. These results led to the first polynomial-time recognition algorithm for proper circular-arc graphs. However, as remarked there, this work did not solve the problems of finding a structure theorem and an efficient recognition algorithm for the circularly compatible ones property in arbitrary matrices (i.e., not restricted to augmented adjacency matrices only). We solve these problems. More precisely, we give a minimal forbidden submatrix characterization for the circularly compatible ones property in arbitrary matrices and a linear-time recognition algorithm for the same property. We derive these results from analogous ones for the related \(D\)-circular property. Interestingly, these results lead to a minimal forbidden induced subgraph characterization and a linear-time recognition algorithm for proper circular-arc bigraphs, solving a problem first posed by Basu et al. [J. Graph Theory, 73 (2013), pp. 361--376]. Our findings generalize some known results about \(D\)-interval hypergraphs and proper interval bigraphs.
|
||
start:
|
||
end:
|
||
speaker: Martín Safe, (Universidad Nacional del Sur, Argentina)
|
||
- titulo: Active clustering
|
||
abstract: |
|
||
Given a set (known to us), and a partition of this set, unknown to us, consider the following task. We have to determine the partition by making successive queries about pairs of elements, each time querying whether the pair belong to the same class or not. Later queries are allowed to depend on the outcome of earlier queries. There is a natural way to assign a graph to each step of the querying process, by starting with an edgeless graph where each vertex represents an element of the set, and after queries identifying vertices for a yes-answer and adding edges for no-answers. We prove the at first sight surprising result that the partitioning algorithms reaching the minimal average number of queries are exactly those that keep these graphs chordal. (The average is taken over all possible partitions of the base set.) The optimal algorithms even share the same distribution on the number of queries, which we characterize. We also analyse a related model where the number of partition classes is fixed, and each element of the base set chooses its partition class randomly.
|
||
This is joint work with Élie de Panafieu, Quentin Lutz and Alex Scott.
|
||
start:
|
||
end:
|
||
speaker: Maya Stein (Universidad de Chile, Chile)
|
||
- sesion: Análisis Numérico
|
||
organizadores:
|
||
- nombre: Gabriel Acosta
|
||
mail: gacosta@dm.uba.ar
|
||
- nombre: Pedro Morin
|
||
mail: pmorin@fiq.unl.edu.ar
|
||
- nombre: Rodolfo Rodríguez
|
||
mail: rodolfo@ing-mat.udec.cl
|
||
charlas:
|
||
- titulo: Aproximación unificada del problema acoplado de Stokes-Darcy
|
||
abstract: |
|
||
En esta charla nos abocaremos al análisis y la resolución numérica, por elementos finitos mixtos, del problema acoplado de Stokes-Darcy en el plano. Introduciremos una formulación modificada del problema con el propósito de permitir el uso de la misma familia de elementos, en el sector del dominio gobernado por la ecuación de Stokes y en la porción del dominio gobernada por la ecuación de Darcy.
|
||
En primer lugar consideraremos el caso de que el dominio sea poligonal, donde presentaremos resultados tanto teóricos como numéricos de la resolución del problema utilizando MINI-elements, los cuales son uno de los más sencillos de implementar. También, aprovechando las ventajas de nuestra formulación, mostraremos la buena performance de la aplicación de otros elementos como los P2-P1 o P1-P1 estabilizados.
|
||
Luego trataremos el problema en dominios curvos, incluso con la posibilidad de tener interfase curva, haciendo uso de triángulos curvos. Con este enfoque obtendremos también estimaciones de error de orden óptimo, extendiendo así los resultados obtenidos para el caso poligonal. Por último presentaremos experimentos numéricos que confirman la buena performance del método propuesto.
|
||
Trabajo en colaboración con María Lorena Stockdale. Departamento de Matematica, FCEyN, Universidad de Buenos Aires.
|
||
start:
|
||
end:
|
||
speaker: Gabriela Armentano (Universidad de Buenos Aires, Argentina)
|
||
- titulo: 'Transversally-Enriched Pipe Element Method: an efficient approach for computational hemodynamics'
|
||
abstract: The development of novel numerical and computational strategies for the simulation of blood flow in complex patient-specific vasculatures has gained strong attention in the scientific community aiming both theoretical and applied research. The need for fast, yet accurate methods is at the core of any translational research enterprise. In this talk, we will introduce a middle fidelity numerical approach to tackle the demanding blood-flow simulation in deformable arteries. This strategy can be placed in-between oversimplified (low-fidelity) reduced 1D models and expensive (high-fidelity) full 3D models. The main feature of the method is the discretization of the pipe-like domain in which the fluid flow problem is addressed. This pipe-oriented discretization is exploited by placing a differentiated polynomial approximation for cross-sectional and longitudinal directions. We will show the basic idea of the method, a numerical study of its convergence properties and applications for patient-specific blood flow modeling in large branching arterial geometries.
|
||
start:
|
||
end:
|
||
speaker: Pablo Blanco (Laboratório Nacional de Computação Científica, Brasil) joint with Alonso M. Alvarez, Raúl A. Feijóo
|
||
- titulo: Local error estimates for nonlocal problems
|
||
abstract: |
|
||
The integral fractional Laplacian of order \(s \in (0,1)\) is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary singularity regardless of the domain regularity. This, in turn, deteriorates the global regularity of solutions and as a result the global convergence rate of the numerical solutions.
|
||
In this talk we shall discuss regularity of solutions on bounded Lipschitz domains. For finite element discretizations, we derive local error estimates in the \(H^s\)-seminorm and show optimal convergence rates in the interior of the domain by only assuming meshes to be shape-regular. These estimates quantify the fact that the reduced approximation error is concentrated near the boundary of the domain. We illustrate our theoretical results with several numerical examples.
|
||
The talk is based on joint work with Dmitriy Leykekhman (University of Connecticut) and Ricardo Nochetto (University of Maryland).
|
||
start:
|
||
end:
|
||
speaker: Juan Pablo Borthagaray (Universidad de la República, Uruguay)
|
||
- titulo: A priori and a posteriori error analysis of a momentum conservative mixed-FEM for the stationary Navier-Stokes problem
|
||
abstract: |
|
||
In this talk we present a new conforming mixed finite element method for the Navier-Stokes problem posed on non-standard Banach spaces, where a pseudostress tensor and the velocity are the main unknowns of the system. The associated Galerkin scheme can be defined by employing Raviart-Thomas elements of degree k for the pseudostress and discontinuous piecewise polynomials of degree k for the velocity. Next, by extending standard techniques commonly used on Hilbert spaces to the case of Banach spaces we derive a reliable and efficient residual-based a posteriori error estimator for the corresponding mixed scheme.
|
||
Joint work with S. Caucao (Universidad Católica de la Santísima Concepción, Chile), C. Garcia (Pontificia Universidad Católica de Chile), R. Oyarzúa (Universidad del Bío Bío, Chile) and S. Villa (Universidad del Bío Bío, Chile).
|
||
start:
|
||
end:
|
||
speaker: Jessika Camaño (Universidad Católica de la Santísima Concepción, Concepción, Chile)
|
||
- titulo: A fully discrete adaptive scheme for parabolic equations
|
||
abstract: |
|
||
We present an adaptive algorithm for solving linear parabolic equations using hierarchical B-splines and the implicit Euler method for the spatial and time discretizations, respectively.
|
||
Our development improves upon one from 2018 by Gaspoz and collaborators, where fully discrete adaptive schemes have been analyzed within the framework of classical finite elements. Our approach is based on an a posteriori error estimation that essentially consists of four indicators: a time and a consistency error indicator that dictate the time-step size adaptation, and coarsening and a space error indicator that are used to obtain suitably adapted hierarchical meshes (at different time steps). Even though we use hierarchical B-splines for the space discretization, a straightforward generalization to other methods, such as FEM, is possible. The algorithm is guaranteed to reach the final time within a finite number of operations, and keep the space-time error below a prescribed tolerance. Some numerical tests document the practical performance of the proposed adaptive algorithm.
|
||
start:
|
||
end:
|
||
speaker: Eduardo Garau (Universidad Nacional del Litoral, Santa Fe, Argentina)
|
||
- titulo: LSD for multiscale problems
|
||
abstract: |
|
||
The Localized Spectral Decomposition finite element method is based on a hybrid formulation of elliptic partial differential equations, that is then transformed via a FETI-like space decomposition. Such decomposition make the formulation embarrassingly parallel and efficient, in particular in the presence of multiscale coefficients. It differs from most of the methods out there since it requires solution's minimum regularity. The major novelty is that we base our decomposition in local spectral problems, resulting in methods that are robust with respect to high contrast coefficients.
|
||
This is a joint work with Marcus Sarkis, of WPI (Worcester Polytechnic Institute).
|
||
start:
|
||
end:
|
||
speaker: Alexandre Madureira (Laboratório Nacional de Computação Científica, Brasil)
|
||
- titulo: Virtual Element Spectral Analysis for the Transmission Eigenvalue Problem.
|
||
abstract: The aim of this talk is to analyze a C1 Virtual Element Method (VEM) on polygonal meshes for solving a quadratic and non-selfadjoint fourth-order eigenvalue problem derived from the transmission eigenvalue problem. Optimal order error estimates for the eigenfunctions and a double order for the eigenvalues are obtained. Numerical experiments will be provided to verify the theoretical error estimates.
|
||
start:
|
||
end:
|
||
speaker: David Mora (Universidad del Bio-Bio, Concepción, Chile)
|
||
- titulo: Analysis and approximation of fluids under singular forcing
|
||
abstract: We present a well-posedness theory for Newtonian and some non-Newtonian fluids under singular forcing in Lipschitz domains and in convex polytopes. The main idea, that allows us to deal with such forces, is that we study the fluid problems in suitably weighted Sobolev spaces. We develop an a priori approximation theory, which requires the development of the stability of the Stokes projection over weighted spaces. We conclude by presenting existence results for a singular Bousinessq system and, in the case that the forcing is a linear combination of Dirac deltas, we also present an a posteriori error estimator.
|
||
start:
|
||
end:
|
||
speaker: Enrique Otárola (Universidad Técnica Federico Santamaría, Valparaíso, Chile)
|
||
- sesion: Análisis Funcional y Geometría
|
||
organizadores:
|
||
- nombre: Esteban Andruchow
|
||
mail: eandruch@ungs.edu.ar
|
||
- nombre: Pedro Massey
|
||
mail: massey@mate.unlp.edu.ar
|
||
- nombre: Lázaro Recht
|
||
mail: recht@usb.ve
|
||
charlas:
|
||
- titulo: Mínimos locales de problemas tipo Procusto en la variedad de matrices positivas
|
||
abstract: |
|
||
Sea\(\mathcal{M}_d(\mathbb{C})\)el espacio de matrices (cuadradas) de dimensión\(d\)y\(\mathcal{X}\subset \mathcal{M}_d(\mathbb{C})\) Consideremos una matriz\(A\in\mathcal{M}_d(\mathbb{C})\)(fija) y una métrica en\(\mathcal{M}_d(\mathbb{C})\)dada por una distancia\(\rm {\textbf d}\)
|
||
Un típico problema de aproximación de matrices (o de tipo Procusto) es estudiar la distancia mínima
|
||
$$\rm {\textbf d}(A,\mathcal{X}):= \inf\{ \rm {\textbf d}(A,C):\,C \in \mathcal{X}\}\,,$$
|
||
y en caso de que se alcance, estudiar el conjunto de mejores aproximantes de\(A\)en\(\mathcal{X}\)
|
||
$$\mathcal{A}^{\rm op}(A,\mathcal{X}) =\{C\in\mathcal{X}:\,\rm {\textbf d}(A,C)= \rm {\textbf d}(A,\mathcal{X})\}\,.$$
|
||
Algunas de las elecciones clásicas de \(\mathcal{X}\subset \mathcal{M}_d(\mathbb{C})\)son las matrices autoadjuntas, las semidefinidas positivas, los proyectores ortogonales, etc, y la métrica suele ser la inducida por la norma Frobenius, pero también podría provenir de cualquier otra norma, por ejemplo, de alguna que sea unitariamente invariante (nui).
|
||
El problema del que nos ocuparemos en esta charla es el siguiente: dada\(N\)una nui (estrictamente convexa) en\(\mathcal{M}_d(\mathbb{C})\) definimos en el cono de matrices positivas\(\mathcal{P}_d(\mathbb{C})\) la distancia
|
||
$$ {\bf{d}}_N(A,B):=N(\log(A^{-1/2} B A^{-1/2})) \quad \text{para } A,B\in\mathcal{P}_d(\mathbb{C}). $$
|
||
Entonces, si fijamos\(A,B\in \mathcal{P}_d(\mathbb{C})\)podemos considerar
|
||
$$\mathcal{X}=\mathcal{O}_B= \{ UBU^* : \, U\quad\text{es unitaria}\}\,.$$
|
||
Luego, el problema de Procusto asociado es el de estudiar la distancia
|
||
$$ \displaystyle{\bf{d}}_N(A,\mathcal{O}_B) =\inf_{C\in\mathcal{O}_B} {\bf{d}}_N(A,C)$$
|
||
y (en caso de ser posible) los mejores aproximantes de\(A\)en\(\mathcal{O}_B\) En 2019, Bhatia y Congedo probaron que esa distancia se alcanza en matrices de\(\mathcal{O}_B\)que conmutan con\(A\) Como\(\mathcal{O}_B\)es un espacio métrico con la métrica inducida por la norma usual de operadores, lo que proponemos en esta charla es estudiar los minimizadores globales la función\(F_{(N,A,B)}= F_N:\mathcal{O}_B \to \mathbb{R}_{>0}\)dada por
|
||
$$F_N(C)=N (\log (A^{-1/2}CA^{-1/2}))$$
|
||
para \(C\in \mathcal{O}_B\) En particular, vamos a dar una caracterización espectral de los minimizadores locales de\(F_N\)en \(\mathcal{O}_B\)(cuando\(N\)es una nui estrictamente convexa) utilizando técnicas geométricas aplicadas al caso de igualdad en la desigualdad de Lidskii (multiplicativa) y probaremos que los minimizadores locales son globales, independientemente de la nui estrictamente convexa elegida. La charla está basada en un trabajo en co-autoría con Pablo Calderón y Mariano Ruiz.
|
||
start:
|
||
end:
|
||
speaker: Noelia Belén Rios (Universidad Nacional de La Plata, Argentina)
|
||
- titulo: On \(\lambda\)-Rings of Pseudo-differential Operators
|
||
abstract: |
|
||
The theory of\(\lambda\)Rings goes back to the work of Grothendieck on Chern classes in algebraic topology, it is a suitable axiomatization of the algebraic properties of exterior powers operations on vector bundles;\(\lambda\)rings were also used by Atiyah and coworkers in the study of representations of groups and\(K\)Theory. During this talk we will present recent results on the\(\lambda\)ring structure in algebras of pseudo-differential operators and their use in index theory.
|
||
start:
|
||
end:
|
||
speaker: Alexander Cardona (Universidad de los Andes, Colombia)
|
||
- titulo: El cuarto problema de Hilbert para analistas
|
||
abstract: |
|
||
El cuarto problema de Hilbert pide construir y estudiar las distancias continuas (aunque no necesariamente simétricas) en abiertos convexos de espacios proyectivos para las cuales las rectas son lineas geodésicas. En dimensión dos, y para distancias simétricas, la solución de Busemann y Pogorelov es de una maravillosa simplicidad. Sin embargo, en dimensiones mayores a dos y para distancias no simétricas podemos seguir considerando el problema como abierto. Después de una breve reseña de la solución bidimensional de Busemann y Pogorelov y de varios resultados parciales en dimensión superior, la charla se centrará en la formulación de problemas relacionados a la transformada de Fourier y a otras transformadas integrales que llevarían a una solución o a un mejor entendimiento del problema de Hilbert.
|
||
start:
|
||
end:
|
||
speaker: Juan Carlos Alvarez-Paiva (Université Lille 1, Francia)
|
||
- titulo: Productos de operadores positivos
|
||
abstract: |
|
||
La charla se basa en un trabajo en colaboración con Maximiliano Contino, Michael Dritschel y Stefania Marcantognini sobre el conjunto de operadores en un espacio de Hilbert separable que pueden escribirse como el producto de dos operadores lineales, acotados y positivos. En espacios de dimensión finita, es fácil ver que un operador es el producto de dos operadores positivos si y sólo si es similar a un operador positivo, es decir si y sólo si es un operador escalar con espectro positivo. La estructura de este conjunto en espacios de dimensión infinita es mucho más rica y compleja. La factorization de un elemento del conjunto no es única pero existen factorizaciones distinguidas. La pertenencia a este conjunto se vincula con la cuasi-similaridad y cuasi afinidad a un operador positivo aunque no es equivalente. Estudiamos también las propiedades espectrales de los elementos del conjunto y describimos varios ejemplos.
|
||
start:
|
||
end:
|
||
speaker: Alejandra Maestripieri (Universidad de Buenos Aires, Argentina)
|
||
- titulo: Diseño óptimo de multicompletaciones con restricciones de norma
|
||
abstract: |
|
||
Consideremos una sucesión finita de números reales positivos\(\alpha=(\alpha_i)_{i=1}^n\) y una sucesión de números enteros positivos\(\mathbf d=(d_j)_{j=1}^m\), ambas ordenadas en forma no-creciente.
|
||
Un\((\alpha,\mathbf d)-\)diseño es una familia\(\Phi=(\mathcal F_j)_{j=1}^m\) tal que:\(\mathcal F_j=\{f_{ij}\}_{i=1}^n \in (\mathbb C^{d_j})^n\) de forma que se verifican las restricciones $$\sum_{j=1}^m\|f_{ij}\|^2=\alpha_i\,,\ i=1,\ldots,n.$$ Denotaremos con\(\mathcal D(\alpha,\mathbf d)\) al conjunto de todos los\((\alpha,\mathbf d)-\)diseños.
|
||
Sea\(\Phi^0 =(\mathcal F^0_j)_{j=1}^m\) tal que\(\mathcal F^0_j=\{f^0_{ij}\}_{i=1}^k\in (\mathbb C^{d_j})^k\) con\(j=1,\ldots,m\). Una\((\alpha,\mathbf d)-\){ \it multicompletación} de\(\Phi^0\) es
|
||
$$(\Phi^0,\Phi)=(\mathcal F^0_j,\mathcal F_j)_{j=1}^m \,\text{ con }\, \Phi\in \mathcal D(\alpha,\mathbf d)\,,$$
|
||
donde\((\mathcal F^0_j, \mathcal F_j)\in (\mathbb C^{d_j})^{k+n}\), para\(j=1, \ldots, m\). Dadas\((\Phi^0,\Phi)\) una\((\alpha,\mathbf d)-\)multicompletación y una función\(\varphi:\mathbb R_{\geq 0}\to \mathbb R_{\geq 0}\) estrictamente convexa, consideramos el potencial conjunto inducido por\(\varphi\), dado por:
|
||
$$\Psi_{\varphi}(\Phi)= \rm P_{\varphi}(\Phi^0,\Phi)=\sum_{j=1}^m \text{tr}(\varphi[S_{(\mathcal F^0_j , \mathcal F_j)}]),$$
|
||
donde\(S_{(\mathcal F^0_j, \mathcal F_j)}=S_{\mathcal F^0_j}+S_{ \mathcal F_j}\) denota el operador de marco de\((\mathcal F^0_j, \mathcal F_j)\in (\mathbb C^{d_j})^{k+n}\), para\(j=1, \ldots, m\). Es bien sabido que los mínimos de potenciales convexos (bajo restricciones en las normas de los vectores) dan lugar a sistemas de reconstrucción más estables: cuanto menor es el potencial, más estable es el sistema.
|
||
En esta charla consideraremos el problema de la existencia de\((\alpha,\mathbf d)-\)multicompletaciones\((\Phi^0,\Phi^{\text{op}})\) óptimas dentro de la clase de todas las\((\alpha,\mathbf d)-\)multicompletaciones, es decir, tales que
|
||
$$\rm P_{\varphi}(\Phi^0,\Phi^{\text{op}})\leq \rm P_{\varphi}(\Phi^0,\Phi),$$
|
||
para toda\((\alpha,\mathbf d)-\)multicompletación\((\Phi^0,\Phi)\) y para toda\(\varphi\).
|
||
Si\(m=1\) y\(\mathcal F_1^0\) es una sucesión inicial fija, entonces el problema anterior se reduce a hallar las completaciones óptimas de\(\mathcal F_1^0\) con normas predeterminadas por\(\alpha\) (este caso fue probado por P. Massey, N. Ríos y D. Stojanoff en 2018), que a su vez contiene el problema de diseño óptimo con normas predeterminadas i.e.\(\mathcal F_1^0=\{0\}\) (probado por M.B; P. Massey, M. Ruiz y D. Stojanoff en 2020). La charla está basada en un trabajo en co-autoría con P. Massey, M. Ruiz y D. Stojanoff.
|
||
start:
|
||
end:
|
||
speaker: María José Benac (Universidad Nacional de Santiago del Estero, Argentina)
|
||
- titulo: From closures of unitary group actions to groupoid actions
|
||
abstract: |
|
||
The set of all normal operators on a Hilbert space is naturally acted on both by the group of unitary operators and by the groupoid of partial isometries. We show that the norm closures of these group orbits are related to the above groupoid orbits, and this relation allows one to study the differentiable structures of these orbit closures. Some of the earlier results on closed unitary orbits are recovered in the natural degree of generality in our framework. This presentation is based on joint work with Gabriel Larotonda.
|
||
start:
|
||
end:
|
||
speaker: Daniel Beltita (Institute of Mathematics of the Romanian Academy, Rumania)
|
||
- titulo: A nonlocal Jacobian equation?
|
||
abstract: |
|
||
We study an operator that assigns to each function\(u:\mathbb{R}^d\to\mathbb{R}\) a mapping\(G_u:\mathbb{R}^d \to C_*(\mathbb{R}^d)\),
|
||
$$G_u(x)(h) := u(x+h)-u(x)\;\forall h \in \mathbb{R}^d.$$
|
||
This map\(G_u(x)\) has some similarities with the gradient map\(\nabla u(x)\), which is a central object of study in the theory of the Monge-Ampère equation and Jacobian equations in general. The image of the map\(G_u\) will be, in general, a\(d\)-dimensional submanifold inside the Banach space\(C_*(\mathbb{R}^d)\) (the space of continuous, bounded functions which vanish at the origin). Our goal is to find a relation, at least for some broad class of functions\(u\), between the oscillation of the function\(u\) in a compact domain\(D\) and the\(d\)-dimensional measure of the set\(G_u(D)\). Such a relation would be analogous to Aleksandrov's estimate for convex functions, a fundamental estimate in the theory of elliptic equations which can be traced back to the reverse Blaschke-Santaló inequality. The validity of an integro-differential version of this estimate would have significant implications for the study of nonlinear integro-differential equations. In this talk I will review this background and discuss some preliminary results about the map\(G_u\). This is work in progress.
|
||
start:
|
||
end:
|
||
speaker: Nestor Guillen (Texas State University, Estados Unidos)
|
||
- titulo: Constant scalar curvature, scalar flat, and Einstein metrics
|
||
abstract: |
|
||
Let\((M^n,g)\) be a closed Riemannian manifold of dimension\(n\). Then:
|
||
<ul>
|
||
<li> If\(n=1\),\(g\) is flat.</li>
|
||
<li> If\(n=2\),\(g\) is Einstein if, and only if,\(g\) has constant scalar curvature. Generically, the scalar curvature is negative.</li>
|
||
<li> If\(n\geq 3\), then\(g\) has constant scalar curvature if, and only if,\(g\) is a critical point of the scale invariant normalized total scalar curvature (or Yamabe functional) in its conformal class. A metric of constant nonpositive scalar curvature is a Yamabe metric in its conformal class, while if\(g\) has positive scalar curvature and\((M,g)\) admits an isometric minimal embedding into the standard sphere, then\(g\) is Yamabe in its conformal class. Over the space of metrics of fixed volume, a metric\(g\) is Einstein if, and only if, it is critical point of the total scalar curvature, while a metric is scalar flat or Einstein if, and only if, it is a critical point of the squared\(L^2\) norm of the scalar curvature functional.</li>
|
||
</ul>
|
||
start:
|
||
end:
|
||
speaker: Santiago Simanca (the results of this talk were obtained during his stay at Courant Institute of Mathematical Sciences until 2020)
|
||
- sesion: Geometría, Mecánica, Control y sus interconexiones
|
||
organizadores:
|
||
- nombre: Viviana Alejandra Díaz
|
||
mail: viviana.diaz@uns.edu.ar
|
||
- nombre: Edith Padrón Fernandez
|
||
mail: mepadron@ull.es
|
||
charlas:
|
||
- titulo: Conserved quantities and the existence of (twisted) Poisson brackets in nonholonomic mechanics
|
||
abstract: |
|
||
In this talk, I will start by explaining the nonhamiltonian nature of nonholonomic systems, and then we will study the "hamiltonization problem" from a geometric standpoint. By making use of symmetries and suitable first integrals of the system, we will explicitly define a new bracket on the reduced space codifying the nonholonomic dynamics that, in many examples, is a genuine Poisson bracket making the system hamiltonian (in general, the new bracket carries an almost symplectic foliation determined by the first integrals). This is a joint work with Luis Yapu-Quispe.
|
||
start:
|
||
end:
|
||
speaker: Paula Balseiro (Universidad Federal Fluminense, Brasil)
|
||
- titulo: From retraction maps to geometric integrators for optimal control problems
|
||
abstract: |
|
||
Retraction maps are used in many research fields such as approximation of trajectories of differential equations, optimization theory, interpolation theory etc. In this talk we will review the concept of retraction map in differentiable manifolds to generalize it to obtain an extended retraction map from the tangent bundle of the configuration manifold to two copies of this manifold. After suitably lifting the new retraction map to the cotangent bundle, the typical phase space for Hamiltonian mechanical systems, we will be able to define geometric integrators for optimal control problems. This is a joint work with David Martín de Diego.
|
||
start:
|
||
end:
|
||
speaker: María Barbero Liñán (Universidad Politécnica de Madrid, España)
|
||
- titulo: Relación entre la teoría de campos de Chern-Simons y relatividad general en dimensión \(3\), desde el punto de vista de los problemas variacionales de Griffiths
|
||
abstract: |
|
||
La teoría de campos de Chern-Simons es una teoría de campos topológica, y puede formularse sobre cualquier fibrado principal cuyo grupo de estructura admita una forma bilineal invariante. Consideremos un fibrado principal \(\pi:P\to M\) con grupo de estructura \(G\) y sea \(K\subset G\) un subgrupo; tomemos la familia de problemas variacionales de Chern-Simons sobre todos los subfibrados de \(P\) con fibra \(K\). En la presente charla explicaremos cómo esta familia de problemas variacionales puede codificarse mediante un único principio variacional de tipo Griffiths. Finalmente, utilizaremos el problema variacional construído para entender desde un punto de vista geométrico la correspondencia entre gravedad en dimensión \(2+1\) y la teoría de Chern-Simons.
|
||
start:
|
||
end:
|
||
speaker: Santiago Capriotti (Universidad Nacional del Sur, Argentina)
|
||
- titulo: Lie group's exponential curves and the Hamilton-Jacobi theory
|
||
abstract: |
|
||
In this talk we present an extended version of the Hamilton-Jacobi equation (HJE), valid for general dynamical systems defined by vector fields (not only by the Hamiltonian ones), and a result which ensures that, if we have a complete solution of the HJE for a given dynamical system, inside a certain subclass of systems, then such a system can be integrated up to quadratures. Then we apply this result to show that the exponential curves \(\exp\left(\eta\,t\right)\) of any Lie group, which are the integral curves of the left invariant vector fields in the group, can be constructed up to quadratures (unless for certain elements \(\eta\) inside its corresponding Lie algebra). This gives rise to an alternative concrete expression of \(\exp\left(\eta\,t\right)\), different to those that appears in the literature for matrix Lie groups.
|
||
start:
|
||
end:
|
||
speaker: Sergio Grillo (Centro Atómico Bariloche, Argentina)
|
||
- titulo: Null hyperpolygons and quasi-parabolic Higgs bundles
|
||
abstract: |
|
||
Hyperpolygons spaces are a family of hyperkähler manifolds that can be obtained from coadjoint orbits by hyperkähler reduction. Jointly with L. Godinho, we showed that these spaces are isomorphic to certain families of parabolic Higgs bundles, when a suitable condition between the parabolic weights and the spectra of the coadjoint orbits is satisfied. In analogy to this construction, we introduce two moduli spaces: the moduli spaces of quasi-parabolic \(SL(2,\mathbb{C})\)-Higgs bundles over \(\mathbb{C}\mathbb{P}^1\) on one hand and the null hyperpolygon spaces on the other, and establish an isomorphism between them. Finally we describe the fixed loci of natural involutions defined on these spaces and relate them to the moduli space of null hyperpolygons in the Minkowski 3-space. This is based on joint works with Leonor Godinho.
|
||
start:
|
||
end:
|
||
speaker: Alessia Mandini (Pontifícia Universidade Católica do Rio de Janeiro, Brasil)
|
||
- titulo: Kinetic nonholonomic dynamics is neither Hamiltonian nor variational and however...
|
||
abstract: |
|
||
It is well-known that kinetic nonholonomic dynamics is neither Hamiltonian nor variational. However, in this talk, after introducing a geometrical description of nonholonomic dynamics, I will present a result which is a little surprising. Namely, for a kinetic nonholonomic system and a given point \(q\) of the configuration space \(Q\), one may define:
|
||
<ul>
|
||
<li> A submanifold \({\mathcal M}^{nh}_q\) of \(Q\), which contains to the point \(q\) and whose dimension is equal to the rank of the constraint distribution, and</li>
|
||
<li> A family of Riemannian metrics on \({\mathcal M}^{nh}_q\) such that the geodesics of every one of these metrics with starting point \(q\) are just the nonholonomic trajectories with the same starting point \(q\).</li>
|
||
</ul>
|
||
In particular, the previous facts imply that the kinetic nonholonomic trajectories with starting point \(q\), for sufficiently small times, minimize length in \({\mathcal M}^{nh}_q\)!
|
||
start:
|
||
end:
|
||
speaker: Juan Carlos Marrero (Universidad de La Laguna, España)
|
||
- titulo: Discrete variational calculus and accelerated methods in optimization
|
||
abstract: |
|
||
Many of the new developments in machine learning are connected with gradient-based optimization methods. Recently, these methods have been studied using a variational perspective. This has opened up the possibility of introducing variational and symplectic integration methods using geometric integrators. In particular, in thistle, we introduce variational integrators which allows us to derive different methods for optimization. However, since the systems are explicitly time-dependent, the preservation of the symplecticity property occurs solely on the fibers. Finally, using discrete Lagrange-d'Alembert principle we produce optimization methods whose behavior is similar to the classical Nesterov method reducing the oscillations of typical momentum methods. Joint work with Cédric M. Campos and Alejandro Mahillo.
|
||
start:
|
||
end:
|
||
speaker: David Martín de Diego (Instituto de Ciencias Matemática, España)
|
||
- titulo: Sobre sistemas mecánicos discretos forzados y la reducción de Routh discreta
|
||
abstract: |
|
||
Los sistemas lagrangianos y hamiltonianos con fuerzas aparecen en distintos contextos tales como sistemas con fuerzas de control o sistemas con fuerzas de disipación y fricción. También es usual que los sistemas dinámicos que se obtienen al reducir una simetría de un sistema mecánico sean sistemas forzados. En los casos en los que las fuerzas no puedan ser absorbidas por el lagrangiano o el hamiltoniano como parte de un potencial, se realiza una descripción variacional alternativa del caso sin fuerzas. Como en el caso continuo, cuando se realiza un proceso de reducción de una simetría de un sistema mecánico discreto, es usual que el sistema dinámico reducido presentes términos que se pueden interpretar como fuerzas. Entre otras razones, esto hace que resulte interesante estudiar las características de los sistemas discretos forzados. Un caso particularmente interesante de reducción de simetrías de un sistema mecánico es el que se basa en el uso de sus cantidades conservadas. Cuando se considera un sistema mecánico discreto que admite una aplicación momento que se conserva sobre las trayectorias del sistema, se aplica el proceso conocido como la reducción de Routh discreta que da lugar a un sistema forzado. En esta charla se consideran sistemas mecánicos discretos forzados. A partir de su dinámica definida por un principio de Lagrange d'Alembert discreto que se define modificando convenientemente el principio variacional usual, se estudia la existencia de estructuras simplécticas y su posible conservación por la evolución del sistema. En particular, se considera el proceso de reducción de Routh discreta para una simetría no necesariamente abeliana de un sistema mecánico discreto como un caso particular de un proceso de reducción de simetrías más general. También se analizan la existencia y la conservación de estructuras simplécticas sobre el espacio reducido en el marco de los sistemas forzados teniendo en cuenta las características propias de este caso especial.
|
||
start:
|
||
end:
|
||
speaker: Marcela Zuccalli (Universidad Nacional de La Plata, Argentina)
|
||
- sesion: Teoría de códigos y temas afines
|
||
organizadores:
|
||
- nombre: Ricardo Podestá
|
||
mail: podesta@famaf.unc.edu.ar
|
||
- nombre: Claudio Qureshi
|
||
mail: cqureshi@gmail.com
|
||
charlas:
|
||
- titulo: The conorm code of an AG-code
|
||
abstract: |
|
||
Let \(\mathbb{F}_q\) be a finite field with \(q\) elements. For a given trascendental element \(x\) over \(\mathbb{F}_q\), the field of fractions of the ring \(\mathbb{F}_q[x]\) is denoted as \(\mathbb{F}_q(x)\) and it is called a rational function field over \(\mathbb{F}_q\). An (algebraic) function field \(F\) of one variable over \(\mathbb{F}_q\) is a field extension \(F/\mathbb{F}_q(x)\) of finite degree. The \textit{Riemann-Roch space} associated to a divisor \(G\) of \(F\) is the vector space over \(\mathbb{F}_q\) defined as
|
||
$$\mathcal{L}(G)=\{x\in F\,:\, (x)\geq G\}\cup \{0\},$$
|
||
where \((x)\) denotes the principal divisor of \(x\). It turns out that \(\mathcal{L}(G)\) is a finite dimensional vector space over \(\mathbb{F}_q\) for any divisor \(G\) of \(F\). Given disjoint divisors \(D=P_1+\cdots+P_n\) and \(G\) of \(F/\mathbb{F}_q\), where \(P_1,\ldots,P_n\) are different rational places, the \textit{algebraic geometry code} (AG-code for short) associated to \(D\) and \(G\) is defined as
|
||
$$C_\mathcal{L}^F (D,G) = \{(x(P_1),\ldots, x(P_n))\,:\,x\in \mathcal{L}(G)\}\subseteq (\mathbb{F}_q)^n,$$
|
||
where \(x(P_i)\) denotes the residue class of \(x\) modulo \(P_i\) for \(i=1,\ldots,n\).
|
||
In this talk the concept of the <em>conorm code,/em> associated to an AG-code will be introduced. We will show some interesting properties of this new code since some well known families of codes such as repetition codes, Hermitian codes and Reed-Solomon codes can be obtained as conorm codes from other more basic codes. We will see that in some particular cases over geometric Galois extensions of function fields, the conorm code and the original code are different representations of the same algebraic geometry code.
|
||
start:
|
||
end:
|
||
speaker: María Chara (Universidad Nacional del Litoral, Argentina)
|
||
- titulo: Códigos Reticulados
|
||
abstract: |
|
||
Reticulados são subconjuntos discretos do espaço euclidiano n dimensional gerados por combinações inteiras de um conjunto de vetores independentes. Reticulados vem sendo usados em processos de codificação para transmissão de sinais particularmente para comunicações do tipo MIMO (multiple-input/multiple-output) e também em esquemas criptográficos na recente área da chamada criptografia pós-quântica. Nesta apresentação faremos uma abordagem geral deste tema e apresentaremos de forma resumida alguns resultados recentes sobre códigos reticulados perfeitos em diferentes métricas, constelações de Voronoi em reticulados construídos a partir de códigos em anéis finitos e uma extensão do problema ``Ring-LWE'' de criptografia baseada em reticulados que inclui uma classe mais geral de reticulados algébricos.
|
||
start:
|
||
end:
|
||
speaker: Sueli I. R. Costa (Universidade Estadual de Campinas, Brasil)
|
||
- titulo: The Generalized Covering Radii of Codes
|
||
abstract: |
|
||
The <em>generalized covering-radius hierarchy</em> of a linear code is a new property of codes which was motivated by an application to database linear querying, such as private information-retrieval protocols. It characterizes the trade-off between storage amount, latency, and access complexity, in such database systems.
|
||
In this work, we introduce and discuss three definitions for the generalized covering radius of a code, highlighting the combinatorial, geometric, and algebraic properties of this concept and prove them to be equivalent. We also discuss a connection between the generalized covering radii and the generalized Hamming weights of codes by showing that the latter is in fact a packing problem with some rank relaxation.
|
||
Other contributions to the subject include bounds relating various parameters of codes to the generalized covering radii and an asymptotic upper bound (for particular parameters) which shows that the generalized covering radii improves the naive approach.
|
||
Joint work with Dor Elimelech and Moshe Schwartz (Ben-Gurion University/Israel).
|
||
start:
|
||
end:
|
||
speaker: Marcelo Firer (Universidade Estadual de Campinas, Brasil)
|
||
- titulo: A novel version of group codes
|
||
abstract: |
|
||
Let \(G\) be a finite abelian group, with \(G=\prod_{i=1}^n \langle g_{i} \rangle \) where \(|\langle g_{i} \rangle|=m_{i}\). Then every element in \(G\) can be uniquely written as \(\prod_{i=1}^n g_i^{\epsilon_i}\) where \(0\leq \epsilon_i \leq m_{i}-1 \). To determine a measure of the separation between two elements of \(G\) we use the \texttt{Minkowski distance \(l_1\)}, which is given by
|
||
$$l_{1}\Big(\prod_{i=1}^n g_i^{\epsilon_i}, \prod_{i=1}^n g_i^{\delta_i}\Big) = \sum_{i=1}^n |\epsilon_i-\delta_i|.$$
|
||
A <em>grid code</em> \(\codeC\) is a subset of \(G\), if \(\codeC\) is subgroup of \(G\), then it is said that \(\codeC\) is a \texttt{group code}. The elements of \(\codeC\) are called \texttt{codewords}. The \texttt{minimum distance} \(d\) of a code \(\codeC\) is defined as usually, that is, as the smallest distance between any two different elements of \(\codeC\). Let \(\codeC\) be a code of \(G\) with minimum distance \(d\). Then we say that \(\codeC\) is a \((n,|\codeC|,d)\)-code over \(G\) and \((n,|\codeC|,d)\) are its parameters.
|
||
In this talk, we consider such codes, and we prove some classical results on block codes, like Singleton Bound and others.
|
||
start:
|
||
end:
|
||
speaker: Ismael Gutiérrez (Universidad del Norte, Colombia)
|
||
- titulo: Direct sum of Barnes-Wall lattices via totally real number fields
|
||
abstract: |
|
||
Let \(\mathbb{K}\) be a number field of degree \(n\), \(\mathcal O_{\mathbb{K}}\) its ring of integers and \(\alpha \in \mathcal O_{\mathbb{K}}\) a totally real and totally positive element. In 1999, Eva Bayer-Fluckiger introduced a twisted embedding \(\sigma_{\alpha}:\mathbb{K} \rightarrow \mathbb{R}^{n}\) such that if \(\mathcal I \subseteq \mathcal O_{\mathbb{K}}\) is a free \(\mathbb{Z}\)-module of rank \(n\), then \(\sigma_{\alpha}(\mathcal I)\) is a lattice in \(\mathbb{R}^{n}\). It was shown that if \(\mathbb{K}\) is a totally real number field, then \(\sigma_{\alpha}(\mathcal I)\) is a full diversity lattice. In this talk we will approach constructions of direct sum of Barnes-Wall lattices \(BW_n\) for \(n=4,8\) and \(16\) via ideals of the ring of the integers \(\mathbb{Z}[\zeta_{2^{r}q} + \zeta_{2^{r}q}^{-1}]\) for \(q = 3, 5\) and \(15\). Our focus is on totally real number fields since the associated lattices have full diversity and then may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. The minimum product distances of such constructions are also presented here. This is a joint work with Jo\~{a}o E. Strapasson, Agnaldo J. Ferrari and Sueli I. R. Costa and it was partially supported by Fapesp 2013/25977-7, 2014/14449-2 and 2015/17167-0 and CNPq 432735/2016-0 and 429346/2018-2.
|
||
start:
|
||
end:
|
||
speaker: Grasiele C. Jorge (Universidade Federal de São Paulo, Brasil)
|
||
- titulo: AG codes, bases of Riemann-Roch spaces and Weierstrass semigroups
|
||
abstract: |
|
||
In this talk we are going to discuss some results on the explicit construction of bases of Riemann-Roch spaces, weierstrass semigroups and the floor of certain divisors. We also will apply these results to get AG codes with good parameters.
|
||
start:
|
||
end:
|
||
speaker: Horacio Navarro (Universidad del Valle, Colombia)
|
||
- titulo: The weight distribution of irreducible cyclic codes associated with decomposable generalized Paley graphs
|
||
abstract: |
|
||
We use known characterizations of generalized Paley graphs which are Cartesian decomposable to explicitly compute the spectra of the corresponding associated irreducible cyclic codes. As applications, we give reduction formulas for the number of rational points in Artin-Schreier curves defined over extension fields. This talk is based on a recent joint work with Ricardo Podestá.
|
||
start:
|
||
end:
|
||
speaker: Denis Videla (Universidad Nacional de Córdoba, Argentina)
|
||
- titulo: A Decoding Algorithm of MDS Array Codes
|
||
abstract: |
|
||
This work aims to present a construction of MDS (Maximum Distance Separable) array codes constructed by using superregular matrices, in particular Vandermonde matrices and Cauchy matrices, and the Frobenius companion matrix obtained through a primitive polynomial over \(\mathbb{F}_q[x]\). Array codes are two-dimensional error correction codes whose main characteristic is the ability to correct burst of errors, that is, errors that occur in consecutive bits. MDS codes are codes in which the minimum distance is the maximum possible. This characteristic is important because, in coding theory, the minimum distance is related to the error correction capacity of the code in addition to providing maximum protection against failures of a device for a given amount of redundancy. Based on this construction, a decoding algorithm is presented to correct up to two bursts of errors in MDS array codes with parameters \([m + k, k, m + 1]\) over \(\mathbb{F}_q^b\), for all \(m \geq 4\), where \(b\) refers to the length of the error. In addition, some examples are presented to correct three bursts of errors. This is a joint work with Débora Beatriz Claro Zanitti, São Paulo State University (UNESP).
|
||
start:
|
||
end:
|
||
speaker: Cintya Wink de Oliveira Benedito (Universidade Estadual Paulista, Brasil)
|
||
- sesion: Análisis no lineal en espacios de Banach
|
||
organizadores:
|
||
- nombre: Gerardo Botelho
|
||
mail: botelho@ufu.br
|
||
- nombre: Daniel Carando
|
||
mail: dcarando@dm.uba.ar
|
||
- nombre: Maite Fenández Unzueta
|
||
mail: maite@cimat.mx
|
||
- sesion: Ecuaciones diferenciales y estructuras geométricas
|
||
organizadores:
|
||
- nombre: John Alexander Arredondo García
|
||
mail: alexander.arredondo@konradlorenz.edu.co
|
||
- nombre: Ronaldo Alves García
|
||
mail: ragarcia@ufg.br
|
||
- nombre: Mikhail Malakhaltsev
|
||
mail: mikarm@uniandes.edu.co
|
||
- nombre: Jesús Muciño Raymundo
|
||
mail: muciray@matmor.unam.mx
|
||
- sesion: Quantum symmetries
|
||
organizadores:
|
||
- nombre: César Galindo
|
||
mail: cn.galindo1116@uniandes.edu.co
|
||
- nombre: Julia Plavnik
|
||
mail: jplavnik@iu.edu
|
||
- nombre: Leandro Vendramin
|
||
mail: lvendramin@dm.uba.ar
|
||
- sesion: Sistemas Dinámicos y Teoría Ergódica
|
||
organizadores:
|
||
- nombre: Jairo Bochi
|
||
mail: jairo.bochi@mat.uc.cl
|
||
- nombre: Katrin Gelfert
|
||
mail: gelfert@im.ufrj.br
|
||
- nombre: Rafael Potrie
|
||
mail: rpotrie@cmat.edu.uy
|
||
- sesion: Funciones especiales, polinomios ortogonales y teoría de aproximación
|
||
organizadores:
|
||
- nombre: Manuel Domínguez de la Iglesia
|
||
mail: mdi29@im.unam.mx
|
||
- nombre: Pablo Manuel Román
|
||
mail: roman@famaf.unc.edu.ar
|
||
- sesion: Teoría algebraica de formas cuadráticas sobre anillos
|
||
organizadores:
|
||
- nombre: Hugo L. Mariano
|
||
mail: hugomar@ime.usp.br
|
||
- nombre: Alejandro Petrovich
|
||
mail: apetrov@dm.uba.ar
|
||
- sesion: Lógica matemática
|
||
organizadores:
|
||
- nombre: Manuela Busaniche
|
||
mail: mbusaniche@santafe-conicet.gov.ar
|
||
- nombre: Marcelo Esteban Coniglio
|
||
mail: coniglio@cle.unicamp.br
|
||
- sesion: Operator Algebras
|
||
organizadores:
|
||
- nombre: Fernando Abadie
|
||
mail: fabadie@cmat.edu.uy
|
||
- nombre: Alcides Buss
|
||
mail: alcides.buss@ufsc.br
|
||
- nombre: Damián Ferraro
|
||
mail: damian@cmat.edu.uy
|
||
- sesion: Teoría de Números
|
||
organizadores:
|
||
- nombre: María de los Ángeles Chara
|
||
mail: charamaria@gmail.com
|
||
- nombre: Guillermo Mantilla
|
||
mail: guillermoa.mantillas@konradlorenz.edu.co
|
||
- nombre: Amalia Pizarro
|
||
mail: amalia.pizarro@uv.cl
|
||
- sesion: Dinámica de grupos
|
||
organizadores:
|
||
- nombre: Juan Alonso
|
||
mail: juan@cmat.edu.uy
|
||
- nombre: Nancy Guelman
|
||
mail: nguelman@fing.edu.uy
|
||
- nombre: Sebastián Hurtado
|
||
mail: shurtados@uchicago.edu
|
||
- nombre: Cristóbal Rivas
|
||
mail: cristobal.rivas@usach.cl
|
||
- sesion: Functional Differential Equations and its Applications
|
||
organizadores:
|
||
- nombre: Pablo Amster
|
||
mail: pamster@dm.uba.ar
|
||
- nombre: Gonzalo Robledo
|
||
mail: grobledo@uchile.cl
|
||
- sesion: Problemas Variacionales y Ecuaciones Diferenciales Parciales
|
||
organizadores:
|
||
- nombre: Judith Campos Cordero
|
||
mail: judith@ciencias.unam.mx
|
||
- nombre: Duvan Henao Manrique
|
||
mail: dhenao@mat.puc.cl
|
||
- nombre: Dora Cecilia Salazar Lozano
|
||
mail: dcsalazarl@unal.edu.co
|
||
- sesion: Stochastic processes and applications
|
||
organizadores:
|
||
- nombre: Joaquín Fontbona
|
||
mail: fontbona@dim.uchile.cl
|
||
- nombre: Juan Carlos Pardo
|
||
mail: jcpardo@cimat.mx
|
||
- nombre: Daniel Remenik
|
||
mail: dremenik@dim.uchile.cl
|
||
- nombre: Víctor Rivero
|
||
mail: rivero@cimat.mx
|
||
- sesion: Large Stochastic systems
|
||
organizadores:
|
||
- nombre: Claudio Landim
|
||
mail: landim@impa.br
|
||
- nombre: Pablo Ferrari
|
||
mail: pferrari@dm.uba.ar
|
||
- sesion: Geometría Algebraica computacional
|
||
organizadores:
|
||
- nombre: Gregorio Malajovich
|
||
mail: gregorio.malajovich@gmail.com
|
||
- nombre: Diego Armentano
|
||
mail: diego@cmat.edu.uy
|
||
- sesion: Análisis wavelet y aplicaciones
|
||
organizadores:
|
||
- nombre: Victoria Vampa
|
||
mail: victoriavampa@gmail.com
|
||
- nombre: Liliam Alvarez Díaz
|
||
mail: lilliam@ceniai.inf.cu
|
||
- nombre: María Teresa Martín
|
||
mail: mtmartin@fisica.unlp.edu.ar
|
||
- sesion: Geometría Algebraica
|
||
organizadores:
|
||
- nombre: Álvaro Rittatore
|
||
mail: alvaro@cmat.edu.uy
|
||
- nombre: Pedro Luis del Ángel R.
|
||
mail: luis@cimat.mx
|
||
- sesion: K-teoría
|
||
organizadores:
|
||
- nombre: Noé Bárcenas
|
||
mail: barcenas@matmor.unam.mx
|
||
- nombre: Eugenia Ellis
|
||
mail: eellis@fing.edu.uy
|
||
- sesion: Stochastic analysis and stochastic processes
|
||
organizadores:
|
||
- nombre: Paavo Salminen
|
||
mail: paavo.salminen@abo.fi
|
||
- nombre: Antoine Lejay
|
||
mail: Antoine.Lejay@univ-lorraine.fr
|
||
- nombre: Ernesto Mordecki
|
||
mail: mordecki@cmat.edu.uy
|
||
- sesion: Control and Stabilization for Partial Differential Equations
|
||
organizadores:
|
||
- nombre: Fágner D. Araruna
|
||
mail: fagner@mat.ufpb.br
|
||
- nombre: Eduardo Cerpa
|
||
mail: eduardo.cerpa@usm.cl
|
||
- nombre: Luz de Teresa
|
||
mail: deteresa@matem.unam.mx
|
||
- sesion: Geometría Diferencial
|
||
organizadores:
|
||
- nombre: Romina Arroyo
|
||
mail: romina.melisa.arroyo@unc.edu.ar
|
||
- nombre: Viviana del Barco
|
||
mail: delbarc@ime.unicamp.br
|
||
- nombre: Silvio Reggiani
|
||
mail: reggiani@fceia.unr.edu.ar
|
||
- sesion: Comunicación de las matemáticas en América Latina
|
||
organizadores:
|
||
- nombre: Javier Elizondo
|
||
mail: javier@im.unam.mx
|
||
- nombre: Eduardo Sáenz de Cabezón
|
||
mail: eduardo.saenz-de-cabezon@unirioja.es
|