Quantum Algebras and Spectral R-matrices from Equivariant Affine Grassmannians - Part 1

This lecture features Wenjun Niu from Perimeter Institute presenting the first part of a two-part series on quantum algebras and spectral R-matrices derived from equivariant affine Grassmannians, delivered on April 9, 2025, at the M-Seminar at Kansas State University. Explore joint work with R. Abedin that constructs new quantum algebras and spectral solutions of quantum Yang-Baxter equations, focusing on quantizations of Yang's r matrix associated with the cotangent Lie algebra d=T^*g. Learn about the geometric foundations based on equivariant affine Grassmannians and their connection to holomorphic-topological twist of 4d N=2 gauge theories. The presentation includes a review of Costello-Witten-Yamazaki's work on gauge-theoretic origins of spectral solutions to Yang-Baxter equations, followed by explanations of results related to equivariant affine Grassmannian geometry. If time permits, discover how the quantum algebra can be dynamically twisted over formal neighborhoods of the moduli space of G-bundles to obtain dynamical R-matrices.