**On Monday, 23rd April (2:15 - 3:45 p.m.)**

**Dr. Andrea Petracci (Nottingham)**

**will give a talk on**

**Mirror Symmetry, Fano varieties and deformations of toric varieties**

Abstract: Fano manifolds are the basic building blocks of algebraic varieties. In the context of Mirror Symmetry it is crucial to study their toric degenerations, or conversely to study the smoothings of toric Fano varieties, which are easier to classify via the combinatorial geometry of polytopes. Deformations of affine toric varieties have been extensively studied by Altmann, who noted that Minkowski decompositions of polytopes induce different deformations. In this talk, I will present an approach to construct deformations of Gorenstein affine toric 3-folds in the context of the Gross-Siebert program. This approach can be globalised and gives a combinatorial recipe to construct smoothings of Gorenstein toric Fano 3-folds.

This talk is partly based on work in progress in collaboration with Alessio Corti and Paul Hacking.

**The talk will take place in SR 119, Arnimallee 3.**

**Schedule and Abstracts: summer semester 2017****Forschungsseminar "Algebraische Geometrie" an der HU**