Petr Pushkar (Columbia), * Quantum K-theory of quiver varieties and quantum integrable systems *

In this talk I will define the quantum K-theory of Nakajima quiver varieties and show its connection to representation theory of quantum groups and quantum integrable systems on the examples of the Grassmannian and the flag variety. In particular, the Baxter operator will be identified with operators of quantum multiplication by quantum tautological classes via Bethe equations. Quantum tautological classes will also be constructed and, time permitting, an explicit universal combinatorial formula for them will be shown. Based on joint works with P.Koroteev, A.Smirnov and A.Zeitlin