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 Events
MIT
Wed 3 May 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Character maps, free loops, and fusion systems
ESB 4133 (PIMS Lounge)
Wed 3 May 2017, 3:15pm-4:15pm

Abstract

A saturated fusion system associated to a finite group G encodes the p-structure of the group as the Sylow p-subgroup enriched with additional conjugation. The fusion system contains just the right amount of algebraic information to for instance reconstruct the p-completion of BG, but not BG itself. Abstract saturated fusion systems F without ambient groups exist, and these have (p-completed) classifying spaces BF as well.

In a joint project with Tomer Schlank and Nat Stapleton, we combine the theory of abstract fusion systems with the work by Hopkins-Kuhn-Ravenel and Stapleton on transchromatic character maps, and we generalize several results from finite groups to fusion systems.

A main ingredient of this project is studying the free loop spaces L(BG) and L(BF) for groups and fusion systems, and constructing transfer maps from L(BG) to L(BH) when H is a subgroup of G.
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Harvard University
Thu 4 May 2017, 3:15pm SPECIAL
Topology and related seminars
Nonconnective simplicial commutative rings
Thu 4 May 2017, 3:15pm-4:15pm

Abstract

 Simplicial commutative rings are one of the first steps into "derived" rings that one can take. Many constructions for general E_infty-ring spectra or even Z-algebras are simpler in the world of simplicial commutative rings; however, from a purely homotopy-theoretic or categorical picture they are slightly mysterious. I will explain ongoing work with Bhargav Bhatt on an extended theory of "generalized rings" which extends this category to allow nonconnective objects. Many "equational" constructions which cannot work with E_infty-rings extend well to generalized rings.
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