# Algebraic Geometry Seminar

#### Calabi-Yau Compactifications and Landau-Ginzburg Hodge Numbers

**Speaker:**
Victor Przyjalkowski, Higher School of Economics

**Location:**
Warren Weaver Hall 201

**Date:**
Tuesday, February 14, 2017, 3:30 p.m.

**Synopsis:**

The Landau-Ginzburg model for a Fano variety is often constructed as a Laurent polynomial satisfying certain conditions. We discuss fiberwise compactification of a family of fibers of the map given by the Laurent polynomial such that the total space of the compactification is an (open) Calabi-Yau variety. The compactification principle states that the Calabi-Yau compactification is a Landau-Ginzburg model from the point of view of Homological Mirror Symmetry. We use this to compute invariants of the original Fano variety. More precisely, we compute Landau-Ginzburg Hodge numbers for del Pezzo surfaces to check that they satisfy the mirror symmetry rotation. We also discuss Calabi-Yau compactifications in a threefold case.