Geometric Analysis and Topology Seminar

Mod 2 volume polynomials, Parseval-Rayleigh identities and a cute application

Speaker: Karim Adiprasito, Hebrew University of Jerusalem

Location: Warren Weaver Hall 512

Date: Friday, March 10, 2023, 11 a.m.

Synopsis:

Volume polynomials are a tremendously useful tool in convex geometry, describing the geometry off a convex polytope and forming the fundamental class for the associated valuation algebra. They are also central in the study of toric varieties. I will survey them.

 

Then I will consider them in characteristic two.

 

Then, when you already think I am crazy, I will describe a Rayleigh-Parseval identity for them.

 

Then, when you already have called the nearest sanatorium to pick me up, I will use these to resolve some classical conjectures of Hibi and Stanley.