Robert Friedman (Columbia): Deformations of singular Fano and Calabi-Yau varieties

We will survey recent results concerning deformations of Fano and Calabi-Yau varieties with isolated singularities related to the notions of higher Du Bois and higher rational singularities. First we show that the deformations of such varieties are unobstructed under various natural hypotheses. Second, we describe joint results with Radu Laza as well as more recent work of Tenie concerning when such varieties can be smoothed, or at least can be deformed to varieties with milder singularities.