Introduction to P=W and Mirror Symmetry

Explore the intricacies of topological mirror symmetry and its applications in a comprehensive lecture. Delve into the arithmetic of character varieties and their role in understanding the weight filtration on cohomology. Examine the P=W conjecture, which establishes a connection between the weight filtration on character variety cohomology and the perverse filtration of the Hitchin system on Higgs moduli space cohomology. Gain insights into the motivations behind studying Langlands dual Higgs bundle moduli spaces and their implications for mirror symmetry. This 1 hour and 40 minute talk by Tamas Hausel, presented by ICTP Mathematics, offers a deep dive into advanced mathematical concepts at the intersection of algebraic geometry, topology, and arithmetic.