Geometric Aspects of Integrable Systems
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Title:
Geometric Aspects of Integrable Systems
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.
Colloquium tea will be served in the Math Commons Room at 3:00pm