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Explore a quantum field theory approach to Selberg-Dyson integrals with a large number of variables on Jordan curves in this 44-minute conference talk. Delve into an ensemble of particles with logarithmic repulsive interaction on a Jordan curve, which represents a geometric deformation of the celebrated Dyson-Selberg integral. Discover how in the limit of a large number of variables, the integral converges to the spectral determinant of the Neumann jump operator defined on the curve. Learn about the emergent conformal covariance exhibited by the Dyson-Selberg integral and examine a probabilistic version of Fekete's theory of finite-dimensional approximation of conformal maps. Gain insights into advanced mathematical physics concepts that bridge quantum field theory, probability theory, and geometric analysis through this research presentation delivered at IPAM's New Interactions Between Probability and Geometry Workshop.
