Hodge-Theoretic Aspects of Mirror Symmetry

Explore a 55-minute lecture on Hodge-theoretic aspects of mirror symmetry delivered by Victor Przyjalkowski from Steklov Institute. Delve into the fascinating world of mirror symmetry for Fano varieties from a Hodge theory perspective. Begin with a review of the Hodge diamond rotation phenomena for Calabi-Yau varieties. Progress to an examination of Fano varieties, focusing on the Katzarkov-Kontsevich-Pantev conjectures and their proofs in low dimensions. Conclude with an in-depth discussion of the mirror P=W conjecture, which establishes mirror correspondence in terms of mixed Hodge structures, and investigate its relationships with other Hodge mirror symmetry conjectures. Gain valuable insights into this advanced topic in algebraic geometry and mathematical physics.