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### Quantum difference equations for Nakajima varieties

**Algebra & Discrete Mathematics**

Speaker: | Andrey Smirnov, U.C. Berkeley |

Location: | 2112 Mathematics |

Start time: | Mon, Jan 23 2017, 4:10PM |

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 will discuss the generalization of this picture to the quantum K-theory of X given by a quiver variety. The corresponding differential equation is now substituted by a difference equation, which can be considered as a "flat difference connection" on a lattice ( Picard group of X ). I will explain the relation of this difference connection with K-theoretic J-function of Givental, qKZ-equations, monodromy problem (for the quantum connection), and dynamical Weyl group.