|
There are no translations available.
Date and place: July 18, 2014. 12am. CRM, small lecture room.
Speaker : Shizuo Kaji (Yamaguchi U)
Title: A product in equivariant homology for compact Lie group actions
Abstract: The Tate cohomology for a finite group integrates group homology and cohomology into one theory. It is equipped with a cup product, which coincides with the usual one on cohomology and gives a ring structure on homology. A few attempts have been made to generalise this product structure on homology. We follow the line of Kreck and Tene. Kreck defined a product on H_*(BG;Z) for a compact Lie group G based on his geometric homology theory and Tene showed it coincides with the cup product on the Tate cohomology when G is finite. We will generalise this product to one on the equivariant homology of a manifold with a nice action of a Lie group. Our construction is simple and purely homotopy theoretical. This is a joint work with Haggai Tene.
Date and place: June 20, 2014. 12am. CRM, small lecture room.
Speaker : Conchita Martínez (U Zaragoza)
Title: On dimension invariants for groups admitting a cocompact model for proper actions.
Date and place: May 9, 2014. 12am. CRM, small lecture room.
Speaker : Enric Ventura (UPC)
Title: Inverting automorphisms of the free group
Abstract: We introduce a complexity function α (resp. β) to measure the maximal possible gap between the norm of an automorphism (resp. an outer automorphism) of a finitely generated group G, and the norm of its inverse. We shall concentrate in the case of free groups Fr and prove some results about the growth of these functions αr and βr for rank r=2, α2 is quadratic and β2 is linear; and for higher rank, we will give polynomial lower bounds for both functions, and a polynomial upper bound for βr (the lower bounds use just manipulation of automorphisms and counting techniques, while the proof of the upper bound makes use of a recent result by Algom-Kfir and Bestvina about the asymetry of the metric in the Outer Space). This is joint work with P. Silva and M. Ladra.
Date and place: April 25, 2014. 12am. CRM, small lecture room.
Speaker : Peter Symonds (University of Manchester)
Title: Finite subgroups of the Nottingham group and Katz-Gabber covers
Date and place: TBA.
Speaker : Carles Broto (UAB)
Title: Sistemes de fusió de grups finits simples de tipus Lie, VII
Abstract: Els grups finits simples de tipus Lie formen la família més gran de grups finits simples. En aquesta sèrie de xerrades s'introdueixen els conceptes més importants involucrats en la descripció del sistema de fusió d'aquests grups en un primer p, és a dir, l'estructura del p-subgrup de Sylow i de la fusió dintre d'aquest. (La fusió determina i és determinada per la p-compleció de l'espai classificador del grup) I. Grups algebraics lineals II. Sistemes d'arrels. III: Classificació de grups algebraics lineals semisimples. IV: Els grups finits tipus Lie. V: Sistemes de Tits. VI i VII: Sistemes de Fusió.
Date and place: April 4, 2014. 12am. CRM, small lecture room.
Speaker : Carles Broto (UAB)
Title: Sistemes de fusió de grups finits simples de tipus Lie, VI
Abstract: Els grups finits simples de tipus Lie formen la família més gran de grups finits simples. En aquesta sèrie de xerrades s'introdueixen els conceptes més importants involucrats en la descripció del sistema de fusió d'aquests grups en un primer p, és a dir, l'estructura del p-subgrup de Sylow i de la fusió dintre d'aquest. (La fusió determina i és determinada per la p-compleció de l'espai classificador del grup) I. Grups algebraics lineals II. Sistemes d'arrels. III: Classificació de grups algebraics lineals semisimples. IV: Els grups finits tipus Lie. V: Sistemes de Tits. VI: Sistemes de Fusió.
Date and place: March 28, 2014. 12am. CRM, small lecture room.
Speaker: Akihiro Ohsita (Osaka University of Economics)
Title: KO-theory of the exceptional flag manifolds
Abstract: For a compact simple Lie group $G$, I here use the word flag manifold to mean $G/T$, where $T$ is a maximal torus. The $KO$-theory of the flag manifolds has been calculated by several authors such as Kishimoto, Kono, Ohsita, Yagita, and Zibrowius. The last two use some algebraic geometry and i heard recently Zibowius showed a type-independent method. In the seminar I explain a way to compute it in a manner of algebraic topology, especially for exceptional group cases.
Date and place: March 21, 2014. 12am. CRM, small lecture room.
Speaker: Jesper Michael Møller (University of Copenhagen)
Title: 2-chromatic numbers of surfaces and Steiner triple systems
Abstract: 2-chromatic numbers are for surfaces what (1-)chromatic numbers are for graphs. The 1-chromatic number of the circle is 3. It follows from the 4-color theorem that the 2-chromatic number of the 2-sphere is 2. What are the 2-chromatic numbers of the other compact surfaces? It is probably very difficult to find the answer to this question. Let us be more modest and just try to find a concrete example of a combinatorial surface with 2-chromatic number equal to 3,4 or 5. Even this turns out not to be easy and this is where Steiner triple systems come into the picture.
Date and place: March 14, 2014. 12am. CRM, small lecture room.
Speaker: José Luis Rodríguez (Universidad de Almería)
Title: Symmetric patterns in string art
Abstract: Some geometric figures can be extremely beautiful to our eyes, due to their highly symmetry and homogeneity. Like islamic patterns and tilings, whose beauty is based on crystallographic group symmetries, the beauty of (semi) regular polytopes, is based on their symmetries which can be easily described by root systems.
This discussion is illustrated with some string works done by students of maths at the University of Almería, and other string works done by the author. Among these, we show the Petrie projection of E8, which has a rotational symmetry of order 30, another projection of E8 of order 6, suggested by Tom Ruen, and some string work based on tilings from the Alhambra of Granada, and the Alcazar of Seville.
Date and place: March 7, 2014. 12am. CRM, small lecture room.
Speaker: Vladimir Vershinine (Université Montpellier 2)
Title: Braids: Topology and Algebra
Abstract: We start with definition of braids pointing out their connections with topology. After reviewing their basic topological and algebraical properties we give a small survey of generalisations of braids. The cohomology of braids will be presented as well as connections with loop spaces. At the end we shall give the results on Brunnian braids and their connection with homotopy groups of spheres.
Title: Fusion systems over finite 2-groups
Speaker: Bob Oliver (Université Paris 13)
Date and Place: February 28, 2014. 12am. CRM, small lecture room.
Date and place: February 21, 2014. 12am. CRM, small lecture room.
Speaker: Ran Levi (University of Aberdeen)
Title: Neuro-Topology: The topology of neural systems
Abstract: This talk is a report on an ongoing project that aims to contribute to the understanding of certain aspects of brain activity. The project is carried out jointly with Kathryn Hess, and Sophie Raynor, in collaboration with the Blue Brain Project in EPFL, and as a part of the Human Brain Project. The brain, or possibly any part of it, can be viewed as a graph in several ways, the simplest of which is by regarding the neurons as vertices with an edge between two vertices if they are connected to each other by a synapse. One naturally regards this graph as oriented, as the connections in a neural system are directional, but for some purposes ignoring orientation is also interesting. Experimental data will impose restrictions on the nature of such a graph, for instance on the number and strength of connections between any given vertex and other vertices. Once a graphical description is the basic concept one deals with, a variety of mathematical structures that may be biologically relevant emerge. In this talk I will discuss a number of ideas that we have been investigating, ranging from the application of basic techniques of algebraic topology to the study of state of the art simulated neural systems, to a category theoretic model of neural systems which encodes not only their structure, but also the activity within them and their ever changing states.
Date and place: February 14, 2014. 12am. CRM, small lecture room.
Speaker : María Ronco (Universidad de Talca, Chile)
Title: Triples de operads y descripción de objetos libres
Abstract: Dado un espacio vectorial equipado de cierta estructura de álgebra y cierta estructura de coálgebra, más una ley distributiva entre esas estructuras, se trata de estudiar las estructuras del espacio de primitivos. El caso más simple es cuando se tiene una biálgebra H, esto es un álgebra asociativa equipada de un coproducto coasociativo que es un morfismo de álgebras, el espacio de elementos primitivos Prim(H) tiene una estructura natural de álgebra de Lie. En el caso de ser H coconmutativa y conilpotente, el Teorema de Cartier-Milnor-Moore prueba que esta álgebra de Lie determina toda la estructura de biálgebra de H. Daremos varios ejemplos de este tipo para el caso no-conmutativo, como las biálgebras dendriformes, las biálgebras 2-asociativas y las biálgebras asociativas compatibles.Finalmente mostraremos la existencia de este tipo de estructuras en el complejo de cadenas singulares de un H-espacio asociativo.
Date and place: February 7, 2014. 12am. CRM, small lecture room.
Speaker : Carles Broto (UAB)
Title: Sistemes de fusió de grups finits simples de tipus Lie, V: Sistemes de Tits
Abstract: Els grups finits simples de tipus Lie formen la família més gran de grups finits simples. En aquesta sèrie de xerrades s'introdueixen els conceptes més importants involucrats en la descripció del sistema de fusió d'aquests grups en un primer p, és a dir, l'estructura del p-subgrup de Sylow i de la fusió dintre d'aquest. (La fusió determina i és determinada per la p-compleció de l'espai classificador del grup) I. Grups algebraics lineals II. Sistemes d'arrels. III: Classificació de grups algebraics lineals semisimples. IV: Els grups finits tipus Lie. V: Sistemes de Tits.
Date and place: January 31, 2014. 12am. CRM, small lecture room.
Speaker : Carles Broto (UAB)
Title: Sistemes de fusió de grups finits simples de tipus Lie, IV: Els grups finits tipus Lie (continuació)
Abstract: Els grups finits simples de tipus Lie formen la família més gran de grups finits simples. En aquesta sèrie de xerrades s'introdueixen els conceptes més importants involucrats en la descripció del sistema de fusió d'aquests grups en un primer p, és a dir, l'estructura del p-subgrup de Sylow i de la fusió dintre d'aquest. (La fusió determina i és determinada per la p-compleció de l'espai classificador del grup) I. Grups algebraics lineals II. Sistemes d'arrels. III: Classificació de grups algebraics lineals semisimples. IV: Els grups finits tipus Lie.
Date and place: January 24th, 2014. 12am. CRM, small lecture room.
Speaker : Carles Broto (UAB)
Title: Sistemes de fusió de grups finits simples de tipus Lie, IV: Finite groups of Lie type (continuated)
Abstract: Els grups finits simples de tipus Lie formen la família més gran de grups finits simples. En aquesta sèrie de xerrades s'introdueixen els conceptes més importants involucrats en la descripció del sistema de fusió d'aquests grups en un primer p, és a dir, l'estructura del p-subgrup de Sylow i de la fusió dintre d'aquest. (La fusió determina i és determinada per la p-compleció de l'espai classificador del grup) I. Grups algebraics lineals II. Sistemes d'arrels. III: Classificació de grups algebraics lineals semisimples. IV: Finite groups of Lie type.
Date and place: January 10th, 2014. 12am. CRM, small lecture room.
Speaker : Àlex González (Kansas State University, Manhattan, KS)
Title: La classificació dels grups p-locals compactes de rang 1
Abstract: En aquesta xerrada proposem una definició de connectivitat per grups p-locals compactes, i classifiquem tots els grups p-locals compactes de rang 1 respecte a aquesta noció. Aprofitarem aquesta classificació per fer una discussió del cas general.
Date and place: January 7th, 2014. 11am. CRM A2, C3b/-104.
Speaker : Simona Paoli (University of Leicester)
Title: Bicategories and weakly globular double categories
Abstract: Several notions of weak 2-categories exist in the literature. Among these are the classical notion of bicategory as well as that of Tamsamani weak 2-category, which have been shown to be suitably equivalent by Lack and Paoli. We introduce a new notion of weak 2-category as a subcategory of double categories, which we call weakly globular. We then show that weakly globular double categories are suitably equivalent to Tamsamani weak 2-categories and thus to bicategories. This affords a new type of rigidification of a bicategory. This is joint work with Dorette Pronk.
Date and place: December 20th, 2013. 12am. CRM, small lecture room.
Speaker : Carles Broto (UAB)
Title: Sistemes de fusió de grups finits simples de tipus Lie, IV: Finite groups of Lie type.
Abstract: Els grups finits simples de tipus Lie formen la família més gran de grups finits simples. En aquesta sèrie de xerrades s'introdueixen els conceptes més importants involucrats en la descripció del sistema de fusió d'aquests grups en un primer p, és a dir, l'estructura del p-subgrup de Sylow i de la fusió dintre d'aquest. (La fusió determina i és determinada per la p-compleció de l'espai classificador del grup) I. Grups algebraics lineals II. Sistemes d'arrels. III: Classificació de grups algebraics lineals semisimples. IV: Finite groups of Lie type.
Date and place: November 29th, 2013. 12am. CRM, small lecture room.
Speaker : Carles Broto (UAB)
Title: Sistemes de fusió de grups finits simples de tipus Lie, III: Classificació de grups algebraics lineals semisimples.
Abstract: Els grups finits simples de tipus Lie formen la família més gran de grups finits simples. En aquesta sèrie de xerrades s'introdueixen els conceptes més importants involucrats en la descripció del sistema de fusió d'aquests grups en un primer p, és a dir, l'estructura del p-subgrup de Sylow i de la fusió dintre d'aquest. (La fusió determina i és determinada per la p-compleció de l'espai classificador del grup) I. Grups algebraics lineals II. Sistemes d'arrels. III: Classificació de grups algebraics lineals semisimples.
Date and place: November 22nd, 2013. 12 am at the CRM, C1/028 small lecture room.
Speaker : Antonio Díaz (Universidad de Málaga)
Title: Mackey functors and fusion systems.
Abstract: fusion systems are algebraic models for certain spaces called p-local finite groups whose homotopy is similar to that of p-completions of classifying spaces of finite groups. In this talk we develop the machinery of Mackey functors in the setup of fusion systems. Then we use these tools to construct a Lyndon-Hochschild-Serre(LHSss)-type spectral sequence and to study sharpness for fusion systems. The new spectral sequence coincides with the classical LHSss. in the case of an extension of groups but it might be applied in situations where the LHSss cannot. For instance, to compute the cohomology of the finite simple groups which possess a strongly closed subgroup. Sharpness is a vanishing of higher limits condition that ensures simplified formulas for the cohomology of a p-local finite group. These formulas appear when reconstructing a p-local finite group from the classifying spaces of its p-subgroups. In the group case it was proven to hold by Dwyer (1998). Here we prove it for some exotic p-local finite groups by means of Mackey technology. This is partly joint work with Sejong Park.
Date and place: November 22nd, 2013. 11 am at the CRM, C1/028 small lecture room.
Speaker : Eduardo Hoefel (Universidade Federal do Paraná, Curitiba / Paris 13)
Title: Homotopy Representations and Open-Closed structures.
Abstract: In this talk we study the homotopy representations of associative and Lie algebras in connection with the several algebraic structures that appear in the study of the Swiss-cheese operad. We refer to this class of algebraic structures as "Open-Closed Structures", which naturally include the OCHAs discovered by Kajiura and Stasheff. This talk is based on joint work with Muriel Livernet.
Date and place: November 15th, 2013. CRM, small lecture room.
Speaker : Matías del Hoyo (Utrech / IMPA)
Title: Lax functors and homotopy.
Abstract: The theory of classifying spaces associates geometric objects to categorical structures, and has become a useful tool originally in K-theory but also in areas such as algebra and geometric topology. When moving to higher categories the notion of lax functors arises naturally, they only preserve the structure up to certain homotopies or 2-cells, and in many situations they are more appropiate than the strict functors. In this talk I will discuss the behaviour of lax functors under the construction of classifying spaces, use a rectification construction to establish a lax version of Quillen's Theorem A, and discuss as an application the loop spaces of 2-categories
Date and place: October 25th, 2013. 12am. CRM, small lecture room.
Speaker : Toni Lozano (UAB)
Title: Sistemes de fusió de grups finits simples de tipus Lie, II: Sistemes d'arrels.
Abstract: Els grups finits simples de tipus Lie formen la família més gran de grups finits simples. En aquesta sèrie de xerrades s'introdueixen els conceptes més importants involucrats en la descripció del sistema de fusió d'aquests grups en un primer p, és a dir, l'estructura del p-subgrup de Sylow i de la fusió dintre d'aquest. (La fusió determina i és determinada per la p-compleció de l'espai classificador del grup) I. Grups algebraics lineals II. Sistemes d'arrels
Date and place: October 4th, 2013. CRM, small lecture room.
Speaker : George Raptis ( Universität Osnabrück)
Title: The moduli space of topological realizations of an unstable coalgebra.
Abstract: The mod p homology of a space is an unstable coalgebra over the Steenrod algebra at the prime p. This talk will be about the problem of realizing an unstable coalgebra as the homology of a space. More generally, one can consider a moduli space of all such topological realizations and ask for a description of its homotopy type. I will present a description of this realization space in terms of the André-Quillen cohomology of the unstable coalgebra. This description readily yields obstruction theories for the existence and uniqueness of topological realizations recovering and extending results of Blanc, Bousfield and others. This is joint work with G. Biedermann and M. Stelzer.
Date and place: September 27th, 2013. 12am. CRM, small lecture room.
Speaker : Saïd Zarati (Université de Tunis El Manar)
Title: Invariants of finite p-group actions on finite complexes.
Abstract: This is report on recent joint work with J. Lannes and L. Schwartz.
|
