EVENT DETAILS AND ABSTRACT

Title: Determinants, delooping and reciprocity
Speaker: Jesse Wolfson
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

The determinant line on the Sato Grassmanian of a Tate vector space plays a key role in the study of integrable hierarchies, loop groups and geometric Langlands. Given an idempotent complete exact category C, we construct a spectral determinant line on the Grassmanian of a Tate object in C. We explain how our construction realizes the K-theory of Tate objects as a delooping of the K-theory of C. We then connect it to the tame symbol in higher class field theory, and time permitting, we sketch a new proof of Kato reciprocity using the determinant. This is joint work with Oliver Braunling and Michael Groechenig.