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- titulo: Set Theory and its Interactions
  organizadores:
  - nombre: Carlos Di Prisco
    mail: ca.di@uniandes.edu.co
  - nombre: Christina Brech
    mail: brech@ime.usp.br
  charlas:
  - titulo: Around (*)
    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)
  - titulo: Group operations and universal minimal flows
    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)
  - titulo: Preservation of some covering properties by elementary submodels
    abstract: |
      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.
      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.
      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
  - titulo: The Katetov order on MAD families
    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)
  - titulo: Hereditary interval algebras and cardinal characteristics of the continuum
    abstract: | 
      An interval algebra is a Boolean algebra which is isomorphic to the algebra of finite
      unions of half-open intervals, of a linearly ordered set. An interval algebra is hereditary
      if every subalgebra is an interval algebra. We answer a question of M. Bekkali and S.
      Todorcevic, by showing that it is consistent that every $\sigma$-centered interval algebra of size
      \(\mathfrak{b}\)  is hereditary. We also show that there is, in ZFC, an hereditary interval algebra of
      cardinality \(\aleph_1\).
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    speaker: Carlos Martinez-Ranero (Universidad de Concepción, Chile)
  - titulo: Groups definable in partial differential fields with an automorphism
    abstract: |
      Model theory is a branch of mathematical logic with strong interactions with other branches of mathematics, including algebra, geometry and number theory.
      
      In this talk we are interested in differential and difference fields from the model-theoretic point of view. 
      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.

      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, 
      Tracey McGrail showed that the theory of differential fields of characteristic zero
      with \(m\) commuting derivations has a model companion called \(DCF\).  This theory is complete, \(\omega\)-stable and eliminates quantifiers and imaginaries.

      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.
      
      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. 
      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         
  - titulo: Some lessons after the formalization of the ctm approach to forcing
    abstract: |
      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.

      To achieve this, we worked in the proof assistant Isabelle, basing our development on the theory Isabelle/ZF by L. Paulson and others.

      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.

      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
  - titulo: On non-classical models of ZFC
    abstract: |
      In this talk we present recent developments in the study of non-classical models of ZFC. 
      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.
      
      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 \(\mathbf{V}^{\mathbb{A}}   \vDash \varphi \land \neg \varphi\).
      
      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. 
      
      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      
- titulo: Combinatoria algebraica de funciones simétricas, cuasisimétricas y sus generalizaciones
  organizadores:
  - nombre: Rafael S. González D'León
    mail: rafael.gonzalezl@usa.edu.co
  - nombre: Yannic Vargas Lozada
    mail: yannicmath@gmail.com
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- titulo: Lógica y Computación
  organizadores:
  - nombre: Alexandre Miquel
    mail: amiquel@fing.edu.uy
  - nombre: Martin Hyland
    mail: M.Hyland@dpmms.cam.ac.uk
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- titulo: Algebraic and categorical structures in geometry and topology
  organizadores:
  - nombre: Manuel Rivera
    mail: manuelor@gmail.com
  - nombre: Camilo Arias Abad
    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.
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    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.
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    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.
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    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.
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    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.
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    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).
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    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.
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    speaker: Ralph Kaufmann (Purdue University, Estados Unidos)      
- titulo: '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
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- titulo: 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
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- titulo: 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
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- titulo: 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
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- titulo: 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
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- titulo: 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
- titulo: 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
- titulo: 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
- titulo: Teoría de códigos y temas afines
  organizadores:
  - nombre: Ricardo Podestá
    mail: podesta@famaf.unc.edu.ar	
  - nombre: Claudio Qureshi
    mail: cqureshi@gmail.com
- titulo: 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
- titulo: 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
- titulo: 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
- titulo: 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
- titulo: 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
- titulo: 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
- titulo: Lógica matemática
  organizadores:
  - nombre: Manuela Busaniche
    mail: mbusaniche@santafe-conicet.gov.ar	
  - nombre: Marcelo Esteban Coniglio
    mail: coniglio@cle.unicamp.br
- titulo: 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
- titulo: 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
- titulo: 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
- titulo: Functional Differential Equations and its Applications
  organizadores:
  - nombre: Pablo Amster
    mail: pamster@dm.uba.ar	
  - nombre: Gonzalo Robledo
    mail: grobledo@uchile.cl
- titulo: 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
- titulo: 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
- titulo: Large Stochastic systems
  organizadores:
  - nombre: Claudio Landim
    mail: landim@impa.br	
  - nombre: Pablo Ferrari
    mail: pferrari@dm.uba.ar
- titulo: Geometría Algebraica computacional
  organizadores:
  - nombre: Gregorio Malajovich
    mail: gregorio.malajovich@gmail.com	
  - nombre: Diego Armentano
    mail: diego@cmat.edu.uy
- titulo: 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
- titulo: Geometría Algebraica
  organizadores:
  - nombre: Álvaro Rittatore
    mail: alvaro@cmat.edu.uy	
  - nombre: Pedro Luis del Ángel R.
    mail: luis@cimat.mx
- titulo: K-teoría
  organizadores:
  - nombre: Noé Bárcenas
    mail: barcenas@matmor.unam.mx	
  - nombre: Eugenia Ellis
    mail: eellis@fing.edu.uy	  
- titulo: 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
- titulo: 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
- titulo: 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
- titulo: 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