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Kuznetsov’s Homological projective duality (HPD) in algebraic geometry is a powerful theorem that allows to extract information about semiorthogonal decompositions of derived categories of certain varieties. I will give a GLSMs perspective based on categories of B-branes. I will focus mostly on the case of Fano (hypersurfaces) manifolds. In general, for such cases the HPD can be interpreted as a non-commutative (nc) resolution of a compact variety. I will give a physical interpretation of this fact and present some conjectures.

For information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/algebraic-geometry-in-string-theory/

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In this talk, we will discuss bordered aspects of the Heegaard Floer surgery formulas of  Ozsvath–Szabo and Manolescu–Ozsvath. In particular, we will explain how their theories naturally define bordered invariants for manifolds with toroidal boundary components. Time permitting, we will discuss applications of the theory. One application is a proof of the equivalence of lattice homology and Heegaard Floer homology. Another application is a description of the link Floer complexes of algebraic links, which is parallel to Ozsvath and Szabo’s description of the knot Floer complex of an L-space link. The latter application is joint with M. Borodzik and B. Liu.