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Explore the intricacies of resonance varieties and Koszul modules in this comprehensive lecture by Gavril Farkas. Delve into the cohomological invariants studied across topological, combinatorial, and geometric contexts. Examine the structure of resonance varieties in a general algebraic setting and discover a sharp formula for the Hilbert series of the associated Koszul module. Gain insights into applications spanning vector bundles on curves, moduli and Koehler groups, and hyperplane arrangements. The lecture, based on joint work with Aprodu, Raicu, and Suciu, offers a deep dive into advanced mathematical concepts for those interested in algebraic geometry and related fields.
