The non-abelian localization theorem and the Verlinde formula for Higgs bundles
-- Daniel Halpern-Leistner, December 9, 2016

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The Verlinde formula is a celebrated explicit computation of
the dimension of the space of sections of certain positive line
bundles over the moduli space of semistable vector bundles over an
algebraic curve. I will describe a recent generalization of this
formula in which the moduli of vector bundles is replaced by the
moduli of semistable Higgs bundles, a moduli space of great interest
in geometric representation theory. A key part of the proof is a new
"virtual non-abelian localization formula" in K-theory, which has
broader applications in enumerative geometry. The localization formula
is an application of the nascent theory of Theta-stratifications, and
it serves as a new source of applications of derived algebraic
geometry to more classical questions.