### On the motivic class of the commuting variety and related problems

Bryan, J *(British Columbia)*

Friday 15 April 2011, 11:00-12:00

Seminar Room 1, Newton Institute

#### Abstract

In 1960, Feit and Fine found a beautiful formula for the number of commuting n by n matrices over the finite field F_q. Their result can be reinterpreted as a formula for the motivic class of the commuting variety in the Grothendieck group. We will describe a simple new proof of their formula which allows us to generalize the result to several other settings with applications to motivic Donaldson-Thomas theory.

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