Barcelona Algebraic Topology Group

Speaker: Nitu Kitchloo (Johns Hopkins University)
Title: Stability for Kac-Moody Groups
Place: C3b/158
Date: 20th July at 12:00

Abstract: In the class of Kac-Moody groups, one can extend all the exceptional families of compact Lie groups yielding infinite families, as well as other infinite families. We will show that these exceptional families stabilize in a homotopical sense and that the (co)homology of their classifying spaces is torsion free for all but a finite set of primes that is determined by the family (and not the individual groups in the family).

See the calendar for upcoming events.

Speaker: Marithania Silvero (BGSMath-UB)
Title: Strongly quasipositive links and Conway polynomial
Place: Seminari C3b/158
Date: 20th July at 10:45

Abstract: Strongly quasipositive links are those links which can be seen as closures of positive braids in terms of band generators. We give a necessary condition for a link with braid index 3 to be strongly quasipositive, by proving that they have positive Conway polynomial (that is, all its coefficients are non-negative). We also show that this result cannot be extended to a higher number of strands, as we provide a strongly quasipositive braid on 5 strands whose closure has non-positive Conway polynomial.

Speaker: Rémi Molinier (Université de Grénoble)
Title: Cohomology with twisted coefficients of linking systems and stable elements
Place: Seminari C3b/158
Date: 8st June at 12:00

Abstract: A theorem of Boto, Levi and Oliver describes the cohomology of the geometric realization of a linking system, with trivial coefficients, as the submodule of stable elements in the cohomology of the Sylow. When we are looking at twisted coefficients, the formula can not be true in general as pointed out by Levi and Ragnarsson but we can try to understand under which condition it holds. In this talk we will see some conditions under which we can express the cohomology of a linking system as stable elements.

Speaker: Thomas Wasserman (Oxford)
Title:A Reduced Tensor Product of Braided Fusion Categories containing a Symmetric Fusion Category
Place: Seminari C3b/158
Date: 1st June at 12:00

Abstract:
In this talk I will construct a reduced tensor product of braided fusion categories containing a symmetric fusion category $\mathcal{A}$. This tensor product takes into account the relative braiding with respect to objects of $\mathcal{A}$ in these braided fusion categories. The resulting category is again a braided fusion category containing $\mathcal{A}$. This tensor product is inspired by the tensor product of $G$-equivariant once-extended three-dimensional quantum field theories, for a finite group $G$.

Speaker: Mark Weber
Title: Feynman categories as operads
Place: Seminari C3b/158
Date: 23th May at 15:00

Abstract:
(Joint work with Michael Batanin and Joachim Kock,
TAC 33 (2018), 148-192 [http://www.tac.mta.ca/tac/volumes/33/7/33-07.pdf])

In various papers of Kaufmann and Ward, the notion of "Feynman category" is introduced as a generalisation of "coloured symmetric operad", and then developed further.  In this talk it will be explained that in fact Feynman categories and colouredsymmetric operads are the same things, in that one can set up a biequivalence between 2-categories whose objects are these structures.  Moreover, this biequivalence induces equivalences between the corresponding categories of algebras.  Thus Feynman categories are not really "new", but rather are an interesting alternative point of view on coloured symmetric operads.

Speaker: Jérôme Los (Université de Marseille)
Title: Sequences in the mapping class group: some convergence/
divergence questions
Place: Seminari C3b/158
Date: 23th May at 16:00

Speaker: Bob Oliver (Université Paris 13)
Title: Recent constructions and theorems on fusion systems due to Michael Aschbacher
Place: Seminari C3b/158
Date: 23th February at 12:00

Abstract: Fix a prime p. The fusion system of a finite group G with respect to a Sylow subgroup S ∈ Syl_p(G) is the category F_S(G) whose objects are the subgroups of S, and whose morphisms are the homomorphisms induced by conjugation in G. More generally, an abstract fusion system over a p-group S is a category whose objects are the subgroups of S and whose morphisms are injective homomorphisms between the subgroups that satisfy certain axioms formulated by Lluis Puig and motivated by the Sylow theorems for finite groups.

Starting 10–15 years ago, Michael Aschbacher and some other finite group theorists became interested in fusion systems, hoping that they can be used to help shorten some parts of the proof of the classification of finite simple groups. This has led to many new structures and results such as generalized Fitting subsystems of fusion systems, as well as intersections, central products, and centralizers of normal fusion subsystems. In many cases, these are analogs of basic, elementary structures or operations in finite groups, but are surprisingly difficult to define in the context of fusion systems.

Speaker: Alex Cebrian (UAB)
Title: A simplicial groupoid for plethystic substitution
Place: Seminari C3b/158
Date: 2nd March at 12:00

Abstract: We give a simple combinatorial model for plethystic substitution: precisely, the plethystic bialgebra is realised as the homotopy cardinality of the incidence bialgebra of a simplicial groupoid, obtained from surjections by a construction reminiscent of Waldhausen S and Quillen Q-construction.

Speaker: Sune Precht Reeh (UAB)

Title: Constructing a transporter infinity category for fusion systems
Place: CRM, Aula petita
Date: 21th February at 12:10

Abstract: In this research talk, I will give a tour of the progress I have made in the last two weeks on constructing an infinity category that is supposed to model the transporter category for a fusion system (when given a choice of locality/linking system).

Speaker: Jesper M. Møller (University of Copenhagen)
Title: The Alperin weight conjecture, the Knörr-Robinson conjecture, and equivariant Euler characteristics
Place: Seminari C3b/158
Date: 16th February at 12:00

Abstract: A topologically biased amateur marvels at the Alperin weight conjecture from different angles without getting anywhere near a solution.

See the calendar for upcoming events.

Speaker: Natàlia Castellana (UAB)
Title: Stratification for homotopical groups
Place: Seminari C3b/158
Date: 24th November at 12:00

Abstract: Joint work with Tobias Barthel, Drew Heard and Gabriel Valenzuela. In this project we show that the category of module spectra over C^*(BG;F_p) where G is a p-local compact group is stratified.

Speaker: Joachim Kock (UAB)
Title: Infinity-operads as polynomial monads
Place: Seminari C3b/158
Date: 22th September at 12:00

Abstract: Lurie's infinity-operads are defined as certain Gamma-spaces, in the spirit of May-Thomason.  A different approach to infinity- operads is due to Cisinski and Moerdijk in terms of dendroidal Segal spaces.  After outlining these approaches, I will explain a new model for infinity-operads, given in terms of polynomial monads.  This provides an infinity version of the classical viewpoint that operads are monoids in the monoidal category of species/analytic functors under the substitution product. Leaving out the technical details, I will explain the ideas behind the proof that the infinity-category of analytic monads is equivalent to the infinity-category of dendroidal Segal spaces.  This is joint work with David Gepner and Rune Haugseng.

Speaker: Albert Ruiz (UAB)

Title: On the classification of p-local compact groups over a fixed discrete p-toral group.
Place: Seminari C1/366
Date: 15th September at 12:00
Abstract: p-local finite groups where defined by Broto-Levi-Oliver as a generalization of finite groups studied at a prime p. Later on, the same authors, defined p-local compact groups as a generalization of compact Lie Groups at a prime p and p-compact groups.
Examples of p-local finite groups which do not correspond to finite groups are known for every prime number p. In the infinite case, very few cases which do not correspond to p-compact groups have been studied. In this talk we will see a classification of p-local compact groups over some special discrete p-toral groups (joint work with Bob Oliver) which include a family of p-local compact groups which are not p-compact groups (joint work with Alex González and Toni Lozano).