Geometry, Statistical Mechanics, and Integrability - IPAM at UCLA Spring 2024 Program

Explore the cutting-edge intersections of probability theory, statistical mechanics, geometry, and integrable systems in this 34-minute video presentation about IPAM's Spring 2024 long program at UCLA. Delve into the revitalization of these fields through the introduction of tools from conformal geometry, discrete analyticity, algebraic geometry, and integrable systems. Discover recent connections between classical and discrete geometric structures on surfaces and combinatorial models like the dimer model, Ising model, and Tutte polynomial. Examine links to hyperbolic geometry, polyhedra, knot theory, Lorentzian geometry, and symplectic geometry. Investigate the combinatorics of totally nonnegative Grassmannians and their relations to various mathematical models. Explore connections between statistical mechanics models and representation theory, including Young diagrams, Gelfand-Tsetlin patterns, and Littlewood-Richardson coefficients. Learn about the Bethe Ansatz and Yang-Baxter equation as fundamental tools in combinatorial representation theory. Gain insight into this diverse realm of ideas unified by the underlying themes of geometry and statistical mechanics.