### Counting conjectures for fusion systems

Algebra Seminar

1st June 2022, 2:30 pm – 3:30 pm

Fry Building, Room 2.04

An ℓ-compact group is a homotopical analogue of a compact Lie group whose homotopy fixed point spaces are classifying spaces of fusion systems of finite groups of Lie type. After motivating the study of weights for fusion systems, I will report on the first part of ongoing joint work with Gunter Malle and Radha Kessar investigating weights associated to homotopy fixed point spaces of ℓ-compact groups. We showed that certain equations predicted by local-global conjectures in the modular representation theory of finite groups of Lie type continue to hold in the ℓ-compact setting. If time permits, I will show these equations hold even more generally in the category of ℓ-local compact groups, pointing towards some yet unknown structural explanation for them purely in the framework of fusion systems.

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