CMSA Algebraic Geometry in String Theory Seminar: Deformations of Landau-Ginzburg models and their fibers


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November 6, 2023 10:30 am - 11:30 am
CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138

Andrew Harder - Lehigh

In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties, focusing on the case of threefolds. I'll discuss how this characterization relates to the deformation and Hodge theory of (Y,w), and in particular, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.