Friday's Topology Seminar 20172018 
Speaker: Sune Precht Reeh (UAB) 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) 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 pgroup 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) 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) 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 plocal compact group is stratified. Speaker: Joachim Kock (UAB) Abstract: Lurie's infinityoperads are defined as certain Gammaspaces, in the spirit of MayThomason. 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 infinityoperads, 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 infinitycategory of analytic monads is equivalent to the infinitycategory of dendroidal Segal spaces. This is joint work with David Gepner and Rune Haugseng. Speaker: Albert Ruiz (UAB) Title: On the classification of plocal compact groups over a fixed discrete ptoral group.
