Delve into an advanced mathematics lecture on the mirror P=W conjecture, delivered by Andrew Harder from Lehigh University. Explore the conjecture's prediction of how the weight filtration on the cohomology of a log Calabi-Yau pair behaves under mirror symmetry. Review the conjecture's statement and examine evidence in low dimensions, including proofs for complements of smooth elliptic curves in del Pezzo surfaces and their mirrors, as well as complements of smooth K3 surfaces in Fano threefolds and weak Fano toric threefolds. Discover how weight and perverse Leray filtrations can be interpreted through Lagrangian torus fibrations, and learn about potential applications for verifying the mirror P=W conjecture more broadly. Gain insights into ongoing research conducted in collaboration with Katzarkov-Przyjalkowski and Katzarkov-Pantev in this hour-long exploration of cutting-edge mathematical concepts.
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