Barcelona Algebraic Topology Group

Friday June 7th, 2013, CRM (Aula petita):

12:00 Dietrich Notbohm : Depth and homology decompositions

Abstract:  Homology decomposition techniques are
a powerful tool used in the analysis of the homotopy theory of (classifying)
spaces. The associated Bousfield-Kan spectral sequences involve higher
derived limits of the inverse limit functor. We study the impact of
depth conditions on the vanishing of these higher limits and apply our theory
in several cases,. In particular we will dicuss our theory in the context of group cohomology and  of polynomial invariants.

Check the calendar for upcoming events

Past seminars

May 10th, 2013, CRM (Aula petita), :

12:00 Nora Seeliger (Univ. Paris 13-CRM):  String topology of highly connected manifolds

Abstract: We compute the homology of the free loop space of highly connected manifolds as a module and parts of the Chas Sullivan product and the BV operator.

May 3rd, 2013, CRM (Aula petita), :

12:00 Jesper Møller (Univ. de Copenhague): Chromatic polynomials of simplicial complexes.

Abstract: Have a look at : http://arxiv.org/abs/1212.0305

April 26th, 2013, CRM (Aula petita), double session!

11h00: Frank Neumann (University of Leicester) :  Etale homotopy theory of Deligne-Mumford stacks

Abstract: We will give an overview on étale homotopy theory à la
Artin-Mazur of Deligne-Mumford stacks and discuss several examples including moduli stacks
of algebraic curves and principally polarised abelian varieties. These
examples and their compactifications encode interesting arithmetic
information on absolute Galois group Gal(Q̅ /Q). Joint work with
Paola Frediani (Pavia).

12:00 Ignasi Mundet  Riera(UB) : Accions de grups finits en varietats sense cohomologia senar.

Abstract: Sigui M una varietat compacta, possiblement amb vora, amb la
cohomologia lliure de torsió i suportada en graus parells. Demostrarem
que existeix una constant C amb la propietat que si un grup finit G actua
diferenciablement i de manera efectiva a M, i tots els primers que divideixen
l'ordre de G són més grans que C, aleshores G és abelià i existeixen punts
de M fixats per tots els elements de G.

March 15th, 2013, 12h00, CRM (Aula petita)

Abdó Roig-Meranges (UPC) : Infinit-categories de feixos i descens per blow-ups.

Abstract:  El teorema d'extensió de Guillén-Navarro dóna un criteri per a l'extensió de
functors cohomològics definits sobre varietats algebraiques llises, a la
categoria de totes les varietats algebraiques, possiblement singulars.

En aquesta xerrada descriuré una formulació infinit-categòrica de la
teoria d'homotopia de feixos (Lurie), i explicaré com es pot fer servir
per donar una demostració senzilla del teorema d'extensió de
Guillén-Navarro.

March 1st, 2013, 12h00, CRM (Aula petita)

Joachim Kock (UAB) : Homotopy Type Theory II

Abstract: This is the second part of the talk given on February, 1st.

February, 22nd, 2013, 12h00, CRM (Aula petita)

Natàlia Castellana (UAB): Teorema d'Artin generalitzat per sistemes de fusió
(amb I. Gálvez i A. Tonks)

Abstract: El teorema d'Artin en teoria de representacions és un resulta local
en el sentit en que descriu un objecte global, l'anell de representacions complexes d'un grup
finit, en termes dels anells de representacions d'una família de subgrups i les
seves relacions de conjugació. En aquest treball estudiem com aquest resultat és cert
per sistemes de fusió així com la seva generalització a teories de cohomologia
en el sentit de Hopkins-Kuhn-Ravenel.

February 1st, 2013, 12h00, CRM (Aula petita)

Joachim Kock (UAB): "Homotopy Type Theory"

Abstract: I will give an introduction to the interactions discovered recently between constructive type theory and
abstract homotopy theory, following Awodey and Voevodsky.  In type theory one has types, and the types have terms: this is on
one hand analogous to how sets have elements, but it also corresponds to the way propositions have proofs.  There are many
syntactic rules for how new types can be introduced and eliminated.  For example there are type constructors called
dependent sums and dependent products.  These can be modeled by locally cartesian closed categories such as Set.  More
importantly there is something called identity types: the identity type of a type A is a new type whose terms parametrise
all the ways in which the terms of A can be considered identical.  Saying that a proposition is true amounts to saying
just that the type is inhabited by some term (some proof).  The corresponding identity type then parametrises the possible
equivalences between proofs.  The statement that two proofs are equivalent in turn needs a proof, and so on.  This mechanism,
which goes on forever, has no analogue in the Set interpretation of type theory, since elements are either equal or not, but it
can be interpreted in homotopy theory: "identity is homotopy" (and higher identities are higher homotopies).  In my talk I
will try to be more precise, and also try to explain what people are up to do with all this, and why it is interesting...

November 9th, 2012, 12h00, CRM (Aula petita)

Santiago López de Medrano (UNAM): " Cuádricas y el Functor Producto Poliedral".

Abstract: Durante algunos años he estudiado la topología de las intersecciones genéricas de varias cuádricas en Rⁿ de la forma

Σ a_i x_i² ,a_i en R, i=1 . . . n

y de la variedad Z que se obtiene intersecando además con la esfera unitaria. En los años 80 pude describir la topología de Z para dos cuádricas y con ciertas restricciones. Un primer paso fue el cálculo de su homología mediante un procedimiento que es válido sin restricciones y para cualquier número de cuádricas. Este procedimiento utiliza básicamente la acción natural del grupo Z₂ⁿ en la variedad cuyo cociente es un politopo convexo.

En la primera parte de la charla detallaré este cálculo. En la segunda mencionaré una construcción muy general (el functor Producto Poliedral ) de espacios topológicos (conocidos como Complejos Angulo-Momento Gen- eralizados) a partir de un complejo simplicial y parejas de espacios (X_i, A_i). Trataré de mostrar como esta construcción incluye a las variedades Z como caso muy particular y como permite entender y calcular su homología y la de otras variedades relacionadas de una manera unificada. Pero también que el cálculo concreto original sigue teniendo algunas ventajas interesantes sobre su versión abstracta general.

Referencias: Bahri,A.,Bendersky,M.,Cohen,F.R.,Gitler,S.:The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces, Advances in Mathematics Volume 225 (2010), 1634-1668.

Gitler,S.,López de Medrano,S.: Intersections of Quadrics, Moment-Angle Manifolds and Connected Sums, arXiv:0901.2580v4, 2012.

López de Medrano,S.:Topology of the intersection of quadrics in Rⁿ, in Algebraic Topology (Arcata Ca, 1986), Springer Verlag LNM 1370(1989), 280-292.

October 26th, 2012, 12:00, CRM (Aula petita).

Wolfgang Pitsch (UAB), "Point-free reconstruction of Schemes: the affine case"

Abstract: I will report on an on-going project with J. Kock on the reconstruction of Schemes from its category of quasi-coherent scheves, concentrating on the affine case. I will show in particular how one can reconstruct Spec R out of D(R) without having to bother about the points in the space and why it is not the Zariski toplogy but rather its Hochster dual that naturally pops-out.

October 19th, 2012, 12:00, CRM (Aula petita).

Joachim Kock (UAB), "Data types with symmetries and polynomial functors over groupoid".

October 5th, 2012, 12h00, CRM (Aula petita).

Carlos Andrés Giraldo Hernández (UAB), "Classification of Diagrams of Fibrations".

September 6th, 2012, 15:30, C3b-158.

Toke Nørgård-Sørensen (University of Copenhagen), "Homotopy representations of p-compact groups."

Abstract: I will introduce the definition of homotopy representations and talk a bit about my own results. Then I will shift focus to connected compact Lie groups and explain how one can analyze the homotopy representations in this case. I will illustrate the methods by using as example the group Sp(1).