Department of Mathematics

Indian Institute of Science

Bangalore 560 012

 

SEMINAR

 

Speaker

:

Ajay Ramadoss, Indiana University
Affiliation : Indiana University

Subject Area

:

Mathematics

 

Venue

:

Department of Mathematics, Lecture Hall I

 

Time

:

11:15 am.

 

Date  

:

July 27, 2016 (Wednesday)

Title

:

"Representation homology"
Abstract

:

The n-dimensional matrix representations of a group or an associative algebra A form a space (algebraic variety) Rep(A,n) called the n-th representation variety of A. This is a classical geometric invariant that plays a role in many areas of mathematics. The construction of Rep(A,n) is natural (functorial) in A, but it is not `exact' in the sense of homological algebra. In this talk, we will explain how to refine Rep(A,n) by constructing a derived representation variety DRep(A,n), which is an example of a derived moduli space in algebraic geometry. For an application, we will look at the classical varieties of commuting matrices, and present a series of combinatorial conjectures extending the famous Macdonald conjectures in representation theory.