Title: Quantum equivariant K-theory and integrability

Abstract: I will talk about relationship between the theory of quantum integrable systems and the quantum geometry of Nakajima varieties, which was explored by many physicists and mathematicians. The main goal of the talk is the geometric description of the so-called XXZ spin chain in the context of quantum equivariant K-theory on the cotangent bundle of the Grassmannian. If time allows I will talk about more recent results about the description of the quantum K-theory ring of flag varieties via Ruijsenaars-Schneider/relativistic Toda integrable systems.