Tue, 25 Oct 2022
14:00
L6

Sums of squares in group algebras and vanishing of cohomology

Piotr Nowak
(Institute of Mathematics - Polish Academy of Sciences)
Abstract

I will discuss algebraic conditions that for a given group guarantee or characterize the vanishing of cohomology in a given degree with coefficients in any unitary representation. These conditions will be expressed in terms positivity of certain elements over group algebras, where positivity is meant as being a sum of hermitian squares. I will explain how conditions like this can be used to give computer-assisted proofs of vanishing of cohomology. 

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