REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: Kazhdan-Lusztig polynomials for Coxeter groups were introduced in the 1970s, attracting a great deal of research in geometric representation theory, and providing deep relationships among representation theory, topology, and combinatorics.  In 2016, Ben Elias, Nicholas Proudfoot, and Max Wakefield defined an analogous polynomial in the setting of matroids.  In this talk, I will define these polynomials and give examples of them, focusing everywhere on the analogy with the classical Coxeter group setting.  I will also discuss some on-going joint work with Tom Braden and Nicholas Proudfoot concerning the structure of these polynomials and a conjectural definition of intersection cohomologyfor matroids.