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Explore recent rigorous findings on topological expansion and phase diagrams in ensembles of random matrices with complex cubic and quartic potentials. Delve into proofs based on the Riemann–Hilbert approach to semiclassical asymptotics of non-Hermitian orthogonal polynomials and the theory of S-curves and quadratic differentials. This lecture, part of the Workshop on the Role of Integrable Systems dedicated to John Harnad, presents an ongoing project with collaborators Ahmad Barhoumi, Marco Bertola, Alfredo Dea˜no, Roozbeh Gharakhloo, Ken McLaughlin, Alex Tovbis, and Maxim Yattselev. Gain insights into advanced mathematical concepts and their applications in random matrix theory during this 65-minute presentation by Pavel M. Bleher at the Centre de recherches mathématiques (CRM).
