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Cohomology of Spaltenstein varieties

SPEAKER: Jonathan Brundan

TITLE: Cohomology of Spaltenstein varieties

ABSTRACT Many of you remember Nick Spaltenstein, who was once a faculty member here (Spaltenstein cap Brundan = 1 year). But perhaps you don’t remember his varieties. They are the generalizations of the Springer variety (full flags fixed by a nilpotent endomorphism) that you get by replacing full flags by partial flags. In the talk I’ll describe an explicit presentation for the cohomology algebra of a Spaltenstein variety which extends the presentation for cohomology of Springer varieties found by De Concini, Procesi and Tanisaki in the early 1980’s. A key step in the argument was worked out by Victor Ostrik, and these cohomology algebras also play a role in some recent work of Nick Proudfoot, so this is really a Eugene subject!