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Barcelona Algebraic Topology Group

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Friday's Topology Seminar 2017-2018

Speaker: Sune Precht Reeh (UAB)
Title: Constructing a transporter infinity category for fusion systems
Place: CRM, Aula petita
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).

I will explain the construction itself as a category enriched in Kan complexes. I will talk about the results obtained so far, with details as time permits, and I will explain the open problems that I am still working on, including how to adapt this transporter category into a working orbit category.


Speaker: Bob Oliver (Université Paris 13)
Title: Recent constructions and theorems on fusion systems due to Michael Aschbacher
Place: Seminari C3b/158
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 ∈ Sylp(G) is the category FS(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.

See the calendar for upcoming events.


Speaker: Jesper M. Møller (University of Copenhagen)
Title: The Alperin weight conjecture, the Knörr-Robinson conjecture, and equivariant Euler characteristics
Place: Seminari C3b/158
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
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
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
15th September at 12:00
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).