A.Smirnov - Geometric methods in theory of integrable spin chains - I

Trainer: Andrey Smirnov
Title: Geometric methods in theory of integrable spin chains
Abstract: In this lecture series I overview an approach to the integrable systems of spin chains using equivariant enumerative geometry of quiver varieties. In this approach the Hilbert space of a spin chain is realized as the equivariant cohomology or K-theory of a quiver variety and the Hamiltonians of the spin chain feature as operators of quantum multiplication in these rings.
I will start the lectures by reviewing the most classical sl(2) XXX spin chain. Then I will introduce quiver varieties of type A, overview their basic properties and their equivariant cohomology/K-theory rings. After this, I will talk about equivariant counts of rational curves in quiver varieties, associated quantum difference equations and explain connections with the spin chains and Bethe ansatz.