Speaker
Christian Korff: University of Glasgow
Abstract
“The study of quantum cohomology and quantum K-theory rings of flag manifolds has been closely linked to quantum integrable systems and lattice models in mathematical physics since the pioneering work of Givental, Kim, and Givental–Lee. More recently, a different perspective has emerged from the work of Maulik and Okounkov, which connects the direct sum of the quantum cohomology and quantum K-theory rings of Nakajima varieties to solutions of the quantum Yang–Baxter equation and quantum groups. Prototypical examples are provided by the cotangent bundles of flag varieties. Although, in principle, one can recover the corresponding structures on the base varieties by taking an appropriate limit, this procedure is technically difficult and leads to a highly degenerate quantum group structure.
In this talk, I present an explicit geometric construction of the quantum group associated with Grassmannians in terms of a Yang–Baxter algebra defined via concrete convolution operators. This yields a non-degenerate quantum group structure directly on the Grassmannian and provides a geometric framework linking quantum Schubert calculus with quantum integrability. The talk is based on joint work with Vassily Gorbounov and Leonardo Mihalcea.”