# Algebra Seminar

Date:

02/20/2019 - 2:00pm to 3:00pm

Location:

745 POT

Speaker(s) / Presenter(s):

Oliver Pechenik, University of Michigan

**Title**: Degenerations of cohomology rings

**Abstract**: An associative algebra is encoded by its structure constants, describing how to multiply elements in a distinguished basis and expand in that basis. Such algebras are rigid in the sense that you can't generally maintain associativity while modifying some of the structure constants. Motivated by analogues of Horn's problem on eigenvalues of sums of Hermitian matrices, Belkale and Kumar (2006) nonetheless obtained important new associative algebras from the cohomology of generalized flag varieties by setting various structure constants equal to zero. The existence of this degeneration was originally established via geometric invariant theory; another proof was supplied by Graham and Evens (2013) using relative Lie algebra cohomology. We give an elementary proof. This leads us to an additional degeneration, which we interpret geometrically. (Joint work with Dominic Searles.)

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