From 3b8638858c865856ba3246a0fbb1ca370b0992e1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Germ=C3=A1n=20Correa?= Date: Thu, 2 Sep 2021 21:21:53 -0300 Subject: [PATCH] agrega

en abstracts completa sesion 2, cambia cartel de aviso de cierre de registro --- data/sesiones.yml | 57 +++++++++++++++++++------------------ templates/registration.html | 2 +- 2 files changed, 30 insertions(+), 29 deletions(-) diff --git a/data/sesiones.yml b/data/sesiones.yml index 78559ec..c66b70a 100644 --- a/data/sesiones.yml +++ b/data/sesiones.yml @@ -175,40 +175,41 @@ mail: carias0@unal.edu.co charlas: - titulo: Discretization of euclidean space ,vector calculus and 3D incompressible fluids - 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. + 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.

start: 2021-09-16T17:30 end: 2021-09-16T18:15 speaker: Dennis Sullivan (Stony Brook University and City University of New York Graduate Center, Estados Unidos) - titulo: Objective combinatorial bialgebras through decomposition spaces - 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. + 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.

start: 2021-09-16T16:45 end: 2021-09-16T17:30 speaker: Imma Gálvez-Carrillo (Universitat Politècnica de Catalunya, España) - titulo: Variants of the Waldhausen S-construction - 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. + 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.

start: 2021-09-17T16:45 end: 2021-09-17T17:30 speaker: Julie Bergner (University of Virginia, Estados Unidos) - titulo: Transfer systems and weak factorization systems - 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. + 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.

start: 2021-09-16T15:00 end: 2021-09-16T15:45 speaker: Angélica Osorno (Reed College, Estados Unidos) - titulo: Classifying stacky vector bundles - 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. + 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.

start: 2021-09-17T17:30 end: 2021-09-17T18:15 speaker: Matías del Hoyo (Universidade Federal Fluminense, Brasil) - titulo: Cut cotorsion pairs - 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. - This is a joint work with Mindy Huerta and Octavio Mendoza (Instituto de Matemáticas - Universidad Nacional Autónoma de México). + 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.

+

This is a joint work with Mindy Huerta and Octavio Mendoza (Instituto de Matemáticas - Universidad Nacional Autónoma de México).

start: 2021-09-17T15:45 end: 2021-09-17T16:30 speaker: Marco Perez (Universidad de la República, Uruguay) - titulo: Hopf and Bialgebras in Algebra, Topology and Physics abstract: | - 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. +

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: 2021-09-16T15:45 end: 2021-09-16T16:30 speaker: Ralph Kaufmann (Purdue University, Estados Unidos) @@ -645,13 +646,13 @@ 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 +

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 + 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 $$\mathcal{X}=\mathcal{O}_B= \{ UBU^* : \, U\quad\text{es unitaria}\}\,.$$ @@ -659,43 +660,43 @@ $$ \displaystyle{\bf{d}}_N(A,\mathcal{O}_B) =\inf_{C\in\mathcal{O}_B} {\bf{d}}_N(A,C)$$ 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. + 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: 2021-09-15T17:30 end: 2021-09-15T18:15 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. +

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: 2021-09-16T15:45 end: 2021-09-16T16:30 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. +

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: 2021-09-16T15:00 end: 2021-09-16T15:45 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. +

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: 2021-09-15T15:45 end: 2021-09-15T16:30 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 +

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 + 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 + 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. + 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: 2021-09-16T16:45 end: 2021-09-16T17:30 speaker: María José Benac (Universidad Nacional de Santiago del Estero, Argentina) @@ -707,9 +708,9 @@ 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. +

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: 2021-09-16T17:30 end: 2021-09-16T18:15 speaker: Nestor Guillen (Texas State University, Estados Unidos) diff --git a/templates/registration.html b/templates/registration.html index 8559146..8918862 100644 --- a/templates/registration.html +++ b/templates/registration.html @@ -22,7 +22,7 @@
- Inscripciones abiertas desde el domingo 20 de Junio al domingo 5 de Septiembre.
+ Inscripciones abiertas desde el domingo 20 de Junio al miércoles 8 de Septiembre.