|Date: Wednesday, November 06, 2019
Location: 4096 East Hall (4:00 PM to 5:20 PM)
Title: Schubert calculus in equivariant elliptic cohomology
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 a 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. To make sense of the Borisov-Libgober class for a wider class of singularities we introduce a version of it, which now necessarily depends on new ('dynamical' or 'Kahler') variables. We obtain that this elliptic class of Schubert varieties satisfies two different recursions (Bott-Samelson, and R-matrix recursions). The second one relates elliptic Schubert calculus with Felder-Tarasov-Varchenko weight functions, and Aganagic-Okounkov stable envelopes. The duality between the two recursions is an incarnation of 3d mirror symmetry (and symplectic duality). Joint work with A. Weber.
Speaker: Richard Rimanyi
Institution: University of North Carolina