## CYMS Seminar - Andrew Harder (Lehigh University)

### Thursday, March 12th, 2020

**Time:** 2:40-4:00 p.m ** Place:** Jeffery Hall 319

**Speaker:** Andrew Harder (Lehigh University)

**Title:** Calabi--Yau threefolds fibered K3 surfaces and their mirrors.

**Abstract:** Mirror symmetry predicts that, given a family of Calabi--Yau varieties, there is a mirror dual family of Calabi--Yau varieties, so that the algebraic aspects of the first are reflected by the symplectic aspects of the other, and vice versa. However, given a family of Calabi--Yau threefolds, it is not usually clear how its mirror family can be constructed. We address this problem for smooth Calabi--Yau threefolds that are built by smoothing degenerate Calabi--Yau threefolds made up of unions of pairs of quasi-Fano manifolds. This leads to a classification of a certain class of Calabi--Yau threefolds, and a surprising relationship to Ishkovskih's famous classification of smooth Fano threefolds of Picard rank 1. This is based on joint work with C. Doran, A. Novoseltsev, and A. Thompson.