P=W conjecture for LG models

11.07.2018 16:00 - 15:00

Andrew Harder (Univ. of Miami)

Abstract: Classical mirror symmetry predicts that if X and Y are mirror compact Calabi-Yau varieties, then the Hodge numbers of X and Y are “flipped”. In this talk, I’ll discuss how this expectation can be extended to mirror log Calabi-Yau pairs. Furthermore, since log Calabi-Yau varieties are noncompact, their cohomology also admits a weight filtration. I’ll discuss some results which suggest that this weight filtration might be related to a certain perverse Leray filtration on the mirror log Calabi-Yau variety, and how this interacts with conjectures of Katzarkov, Kontsevich, and Pantev.


SR 09, 2. OG, OMP 1