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Attend a 48-minute lecture on "Introduction to Equivariant K-theory" by Dave Anderson from the Institute for Advanced Study, scheduled for March 5, 2025, as part of the Special Year Seminar I series. Explore the foundations of K-theory, which emerged in the 1950s from Grothendieck's work on the Riemann-Roch theorem, and its equivariant extension for varieties and vector bundles with group actions. The lecture focuses particularly on the case where G=T is a torus, complementing Bill Graham's previous lectures on equivariant cohomology. Learn about the localization theorem, K-theoretic equivariant multiplicity, and applications to flag varieties and toric varieties. Discover how these concepts lead to the Weyl character formula for irreducible representations of semisimple Lie groups and Brion's formula for lattice points in polytopes. The presentation will also cover the equivariant Riemann-Roch theorem connecting equivariant K-theory to equivariant cohomology and Chow groups, concluding with positivity theorems for Schubert decompositions. The lecture takes place at 2:00pm in Simonyi 101.
