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).