Title: Quantum difference equations for quiver varieties Abstract: Let QH(X) be a quantum cohomology ring of some variety X. The operation of quantum multiplication defines a flat connection on H^2(X) also known as quantum differential equation. In this talk I … Read more
Title: Power structures over the Grothendieck ring of varieties and Macdonald type equations. Abstract: One has a simple formula due to I. Macdonald for the generating series of the Euler characteristics of the symmetric powers of a topological space $X$: \sum_{n=0}^\infty … Read more
Title: Flag varieties, Hilbert schemes on C^2 and link homology Abstract: This is a joint work with A. Oblomkov. We construct a categorical action of an ordinary and affine braid group on matrix factorizations over varieties constructed out of Hilbert … Read more
Title: New feature of the Schubert calculus Abstract: In the talk we will describe a new feature of the Schubert calculus in the equivariant cohomology or K theory which holds for all types of the classical Lie groups. As the main … Read more
Title: Conformal bootstrap and integrability Abstract: I will review the idea of conformal bootstrap. In the last years it was revived by remarkable progress in calculating critical exponents for theories in space- times of dimension >2. The following relation of … Read more
Title: Link homology and Hilbert schemes Abstract: Khovanov and Rozansky defined a link invariant called triply graded homology. It is conjectured by Gorsky, Negut and Rasmussen that this invariant can be expressed geometrically by a functor from complexes of Soergel … Read more
Title: Knot invariants from A-branes Abstract: We propose a categorification of Chern-Simons invariants of knots in Euclidean 3d space associated to a simple Lie algebra, based on category of A-branes in finite dimensional Landau-Ginzburg (LG) models. The category of A-branes in … Read more
Title: Cyclotomic Double affine Hecke algebras Abstract: I'll show that the partially spherical cyclotomic rational Cherednik algebra (obtained from the full rational Cherednik algebra by averaging out the cyclotomic part of the underlying reflection group) has four other descriptions: (1) … Read more
Title: "Hidden algebraic structures in topology" Abstract: The goal of this talk is to give an exposition, from several different angles, of new connections that seem to emerge between low-dimensional topology and abstract algebra. While the general picture for such connections --- … Read more
Title: The 2-leg vertex in K-theoretic DT theory Abstract: K-theoretic Donaldson-Thomas counts of curves in toric and many related threefolds can be computed in terms of a certain canonical 3-valent tensor, the K-theoretic equivariant vertex. In the talk I will derive a … Read more
Title: Supersymmetric quantum spin chains Abstract: We will consider quantum spin chains, in particular nonhomogeneous Gaudin models and XXX spin chains associated to Lie superalgebra gl(m|n). The Hamiltonians of these models are given by the coefficients of quantum Berezinian of the … Read more
Title: q-opers, QQ-systems, and q-Langlands correspondence. Abstract: The well-known relation between a certain class of connections (opers) with regular singularities on projective line without monodromy and the Bethe equations for Gaudin models serves as an example of geometric Langlands correspondence. … Read more
