Power Operations and Central Maps

Seminar: 
Geometry, Symmetry and Physics
Event time: 
Tuesday, April 3, 2018 - 4:00pm to 5:00pm
Speaker: 
Augustus Lonergan
Speaker affiliation: 
MIT
Event description: 

Many interesting quantizations in representation theoryhave been observed to have a large center when reduced modulo p. This `p-center phenomenon' has been codified and successfully exploited by Bezrukavnikov and collaborators. In this talk, we explain that a large class of interesting quantizations (`quantum Coulomb branches' of Braverman-Finkelberg-Nakajima) exhibit the`p-center phenomenon'. The proof is by applying power operations (Steenrod operations) of algebraic topology to Beilinson-Drinfeld Grassmannians and related spaces. Time allowing, we will also discuss the related `multiplicative version' where reduction modulo pis replaced by setting the parameter q to a root of unity, and Steenrodoperations are replaced by Adams operations.