## Homological versus Hodge-theoretic mirror symmetry

Timothy Perutz

University of Texas, Austin; von Neumann Fellow, School of Mathematics

January 30, 2017

I'll describe joint work with Sheel Ganatra and Nick Sheridan which rigorously establishes the relationship between different aspects of the mirror symmetry phenomenon for Calabi-Yau manifolds. Homological mirror symmetry---an abstract, categorical statement---implies Hodge theoretic mirror symmetry, a concrete relation between counts of rational curves and variations of Hodge structure.