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 socalled 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 ChernSchwartzMacPherson class in H, motivic Chern class in K) extends to Ell, due to BorisovLibgober. To make sense of the BorisovLibgober 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 (BottSamelson, and Rmatrix recursions). The second one relates elliptic Schubert calculus with FelderTarasovVarchenko weight functions, and AganagicOkounkov stable envelopes. The duality between the two recursions is an incarnation of 3d mirror symmetry (and symplectic duality). Joint work with A. Weber.
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Speaker: Richard Rimanyi
Institution: University of North Carolina
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