Friday's Topology Seminar 20172018 
Speaker: Marithania Silvero (BGSMathUB) 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 nonnegative). 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 nonpositive Conway polynomial. Speaker: Nitu Kitchloo (Johns Hopkins University) Abstract: In the class of KacMoody 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: Rémi Molinier (Université de Grénoble) 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) Abstract: Speaker: Mark Weber 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 2categories 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: 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. Speaker: Alex Cebrian (UAB) 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 Qconstruction.
Speaker: Sune Precht Reeh (UAB) Title: Constructing a transporter infinity category for fusion systems 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: 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.
