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Topology, Algebraic Geometry, and Dynamics Seminar (TADS) Grothendieck-Springer resolutions and the Moore-Tachikawa conjecture

Feb 28, 2025, 1:30 - 2:30 PM

Exploratory Hall, Room 4208

 

Speaker: Peter Crooks, Utah State

Title: Grothendieck-Springer resolutions and the Moore-Tachikawa conjecture

Abstract: Let G be a complex semisimple group with Lie algebra g. Grothendieck-Springer resolutions are distinguished vector bundles over partial flag varieties of G. Each turns out to be an algebraic Poisson variety with a Hamiltonian action of G. The associated moment map to g can be regarded as a "partial resolution" of the Lie-Poisson structure. I will give a Lie-theoretic introduction to Grothendieck-Springer resolutions and their algebro-geometric features. All of the above-mentioned concepts will be defined in this process.  Particular attention will be paid to Grothendieck-Springer resolutions in Lie type A, and examples will be interspersed throughout the presentation. If time permits, I will outline joint work with Mayrand on new applications to the Moore-Tachikawa conjecture.

Date/Time: February 28, 1:30pm

Location: Exploratory Hall, Room 4208

 

 

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