Michal Kapustka

Title: Mukai roofs and equivalences of Calabi-Yau manifolds

Abstract: 
A simple Mukai pair is a pair of a prime Fano manifold F together with an ample 
vector bundle E satisfying c_1(E)=c_1(F). We will call Mukai roofs Fano manifolds 
of Picard number 2 that have two presentations as projectivizations of vector bundles 
coming from Mukai pairs. The classification of Mukai roofs is an interesting open 
problem, with partial results obtained by Kanemitsu. In this talk I will discuss how 
Mukai roofs can be used to generate pairs of derived equivalent non-birational 
Calabi-Yau manifolds. We will focus on the case of K3 surfaces aiming to understand 
the general picture. This is joint work with Marco Rampazzo.