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 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) 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 Qconstruction.
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