Richard Rimanyi, UNC-Chapel Hill – Geometric Methods in Representation Theory

Title: Elliptic classes of Schubert varieties

Abstract: Assigning characteristic classes to singular varieties is an effective way of studying the enumerative properties of the singularities. Initially one wants to consider the so-called fundamental class in H, K, or Ell, but it turns out that in Ell such class is not well defined. However, a deformation of the notion of fundamental class (under the name of Chern-Schwartz-MacPherson class in H, motivic Chern class in K) extends to Ell, due to Borisov-Libgober. We will introduce a twisted version of the elliptic class, and show its relation to Tarasov-Varchenko weight functions and Okounkov’s stable envelopes. (Based on results with A. Weber, and on a work in progress with S. Kumar and A. Weber.)