Special Year 2016-17: Homological Mirror Symmetry - Seminar

I will discuss Lipshitz and Sarkar's space level refinement of Khovanov homology. Their approach is combinatorial in nature and is inspired by Cohen-Segal-Jones' construction for Floer homology.

I will describe the non-homological (i.e. enumerative) aspect of mirror symmetry for a particular toric Calabi-Yau 3-fold, the total space of the canonical bundle over $\mathbb P^2$. In this case, there is a simpler B-model on its mirror curve which...

The wrapped Fukaya category of an algebraic hypersurface $H$ in $(C*)^n$ is conjecturally related via homological mirror symmetry to the derived category of singularities of a toric Calabi-Yau manifold $X$, whose moment polytope is determined by the...

Homological mirror symmetry postulates a derived equivalence between the wrapped Fukaya category of an exact symplectic manifold and a category of coherent sheaves or matrix factorizations on a mirror space. This talk will provide an introduction to...

Consider $T^*P^1$ as the B-model of a mirror equivalence. It turns out that the A-model mirror depends on choices and I will describe two of these mirrors: one with underlying symplectic manifold the complement of a conic in $T^*S^2$, and the other...