[Binghamton Geometry Topology Seminar] Geometry and Topology seminar: David Mehrle

[Cary Malkiewich]

Hi everyone,

This week we are pleased to have David Mehrle (Cornell) speaking about
equivariant Hochschild homology, title and abstract below. This will be an *in
person* talk, on Thursday at 2:50pm in WH 100E. It looks like the weather
will be good, so we'll meet at 12pm on Thursday just outside WH 100E to
take the speaker to lunch, most likely eating outside. See you there!

Best,
Cary

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Title: Towards an equivariant Hochschild—Kostant—Rosenberg Theorem
Abstract: The Hochschild—Kostant—Rosenberg (HKR) theorem is a bridge
between algebra and geometry with applications in algebraic K-theory, Lie
theory, deformation theory, and other fields. For a smooth $k$-algebra $A$,
the HKR theorem gives an isomorphism between the Kähler differentials of
$A$ (a geometric object) and the Hochschild homology of $A$ (an algebraic
gadget). We conjecture that, when a finite group $G$ acts on $A$ by ring
homomorphisms, the HKR theorem becomes a $G$-equivariant isomorphism. In
this talk, I will share some progress towards proving this conjecture, and
discuss some of the obstacles that remain. This is joint work-in-progress
with J.D. Quigley and Michael Stahlhauer.
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