Abstracts

Jaume Aguadé

Title:

Abstract:

Natàlia Castellana

Title: A view of Carles's garden from my kitchen

Abstract: We will see (joint fusion cuisine adventure with Tobi, Drew and Gabriel).

Antonio Díaz Ramos

Title: Fusion systems for profinite groups

Abstract: For both finite groups and compact Lie groups, there exist algebraic structures that encode their fusion patterns as well as their classifying spaces at a given prime. In this talk, I will introduce similar ideas for profinite groups and, in particular, for compact p-adic analytic groups. Then we will study classifying spaces and stable elements theorem for continuous cohomology. We will provide some concrete continuous cohomology computations. This is an ongoing joint work with O. Garaialde, N. Mazza and S. Park.

Oihana Garayalde Ocaña

Title: From the mod-p cohomology of finite abelian p-groups to Carlson's conjecture

Abstract: Let p be a prime number and let G be a finite p-group of size p^n and nilpotency class m. Then, G has coclass c=n-m. In 2005, J.F. Carlson conjectured that for fixed p and c, there are only finitely many isomorphism types of mod-p cohomology rings for all the (infinitely many) finite p-groups of coclass c.

For p=2, the above conjecture was proved by Carlson himself providing explicit isomorphisms between certain mod-2 cohomology rings. For the p odd case, a stronger result has been recently proven by P. Symonds from which the conjecture is obtained.

In this talk, we will report on a different partial proof of the aforementioned conjecture which- similar to Carlson- provides a more explicit description for the mod-p cohomology ring isomorphisms.

This is a joint work with Antonio Díaz Ramos and Jon González-Sánchez.

Jesper Grodal

Title: String topology of finite groups of Lie type

Abstract: Finite groups of Lie type, such as SL_n(F_q), Sp_n(F_q)..., are ubiquitous in mathematics, and calculating their cohomology has been a central theme over the years. Without any structural reasons as to why, it has calculationally been observed that, when calculable, their mod ell cohomology agree with the mod ell cohomology of LBG(C), the free loop space on BG(C), the classifying space of the corresponding complex algebraic group G(C), as long as q is congruent to 1 mod ell. This despite that LBG(C) and BG(F_q) are vastly different spaces, also at a prime ell, ruling out some space-level equivalence. In recent joint work with Anssi Lahtinen, that combines ell–compact groups with string topology à la Chas–Sullivan, we give a general structural relationship between these two cohomologies, which, suitably formulated, even works without any congruence condition on q, as long as it is prime to ell. We use this to prove structured versions of previous calculations, and establish isomorphism in new cases. The isomorphism conjecture in general hinges on the fate of a single cohomology class in exceptional Lie groups at small primes. My talk will begin to tell this story, as we know it so far...

Ran Levi

Title: On the topology of complexes of injective words

Abstract: An ordered simplicial complex is a collection of finite ordered sets that is closed under inclusion. Ordered simplicial complexes arose recently in applications of algebraic topology to neuroscience, and are of independent interest in topology, combinatorics and cohomology of groups. In this article we mainly study uniform ordered complexes, i.e., ordered simplicial complexes that are obtained as a finite union of ordered simplices of the same dimension. In particular, we determine the homotopy type of the union of two ordered simplices. We prove that the stable homotopy type of any finite simplicial complex is realizable by a uniform ordered complex. We also discuss homotopy decompositions for complexes of injective words, related to work of Randal-Williams and Wahl. Time permitting we discuss probabilistic aspects of this construction and some open problems.

Jesper M. Møller

Title: Dowling lattices for beginners

Abstract: The partition lattice of a finite set S consists of all set partitions of S ordered by refinement. Similarly, for a finite group G and a finite free G-set S, the Dowling lattice consists of all free G-partitions of S ordered by refinement. I'd like to introduce Dowling posets (also in a more general context) and present some basic facts and discuss some conjectures about them.

Bob Oliver

Title: Simple fusion systems over finite p-groups with weakly closed abelian subgroup

Abstract: Find it here