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Explore the intricacies of cohomology rings of character varieties in this comprehensive lecture by Anton Mellit from the University of Vienna. Delve into recent advancements in understanding these complex mathematical structures, including the proof of the P=W conjecture and the computation of the zero-dimensional COHA. Examine the case of punctured spheres, where an explicit description relating cohomology rings to the Hilbert scheme of C^2 is presented, refining conjectures by Hausel-Letellier-Rodriguez-Villegas and Chuang-Diaconescu-Donagi-Pantev. Gain valuable insights into the cohomology rings of character varieties of Riemann surfaces during this hour-long presentation, suitable for advanced mathematics students and researchers.
