Kenneth Chan
Noncommutative rational singularities
We introduce the notion of Brauer log pairs and explain their connection with noncommutative algebraic geometry. There is a theory, analogous to the log MMP, which provides terminal models for Brauer log pairs over surfaces. We define the notion of "numerical rationality" for Brauer log pairs, and discuss some of their properties. This provides us with a notion of noncommutative rational singularities.

Kai Behrend (UBC)
Derived moduli of non-commutative projective schemes
TBA

Kevin Tucker (Princeton)
F-signature and minimal log discrepancy
In positive characteristic, Frobenius splitting methods have long been used to measure singularities. Although these techniques originally found applications in commutative algebra and representation theory, in recent years they have increased in importance following the discovery of surprising connections to the singularities of the minimal model program. Nevertheless, many parts of this link remain mysterious. In this talk, I will introduce a local numerical invariant (introduced by C. Huneke and G. Leuschke) governing the asymptotic behavior of F-splittings called the F-signature and describe the (somewhat loose) relationship to the minimal log discrepancy (partially joint work with M. Blickle and K. Schwede).