Deformations of Calabi-Yau varieties in mixed characteristic

A smooth projective variety X is said to be Calabi-Yau if its canonical bundle is trivial. I will discuss joint work with Lukas Brantner, in which we use derived algebraic geometry to study deformations of Calabi-Yau varieties in characteristic p. We prove a positive characteristic analogue of the Bogomolov-Tian-Todorov theorem (which states that deformations of Calabi-Yau varieties in characteristic 0 are unobstructed), and show that 'ordinary' Calabi-Yau varieties admit canonical lifts to characteristic zero (generalising earlier results of Serre-Tate for abelian varieties, and Deligne and Nygaard for K3 surfaces). In this talk, no prior knowledge of derived algebraic geometry will be assumed.