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Explore advanced topics in quantum geometry through this comprehensive workshop featuring 14 expert lectures from leading researchers at the Institut des Hautes Etudes Scientifiques. Delve into cutting-edge mathematical concepts including Gromov-Witten theory of complete intersections, quantizations of complex Lagrangian fibrations, and Donaldson-Thomas invariants of toric quivers. Examine the intersection of algebraic geometry, mathematical physics, and quantum field theory through presentations on Argyres-Douglas theories, isomonodromy, topological recursion, and Jeffrey-Kirwan localization for quiver varieties. Investigate moduli spaces of irregular singular connections, their quantization and braiding properties, while exploring integrable systems on multiplicative quiver varieties. Study the quantisation of spectral curves of arbitrary rank and genus, combinatorial quantisation of supergroup Chern-Simons theory, and the negative aspects of Witten's conjecture. Gain insights into length partitions of random multi-geodesics on large genus hyperbolic surfaces and discover the invariant properties of the center of small quantum groups, providing a comprehensive foundation in contemporary quantum geometric methods and their applications.
