Abstract：

The history of integrable systems is a story of deep mathematical structures emerging from physical problems. From classical mechanics to modern quantum theory, integrability continues to inspire new discoveries across mathematical physics. In the late 20th and early 21st centuries, algebraic geometry and representation theory became fundamental in advancing the study of integrable systems. However, only in recent years has it become possible to fully elucidate the connections and dualities between various integrable systems in purely geometric terms.

In this talk, I will introduce a novel geometric structure—an oper—that captures the phase spaces of a large family of many-body integrable systems as well as the spectra of quantum spin chains. Our approach establishes deep connections with various areas of mathematical physics, including representation theory, cluster algebras, quantum cohomology, and even quantum hydrodynamics.

Bio：

Dr. Peter Koroteev is an Assistant Professor at the Beijing Institute for MathematicalSciences and Applications (BIMSA). He earned BSc and MSc degrees in Mathematics and Physics from the Moscow Institute of Physics and Techno-logy and obtained his PhD from the University of Minnesota in 2012.His research is focused on the interaction between enumerative algebraic geometry, geometric representation theory and integrable systems.