## Graduate Algebraic Geometry Seminar

Wes Townsend

UIC

Second Coefficient Problems in Commutative Algebra

**Abstract:**The Hilbert-Kunz Function and F-Signature are two key invariants of rings with positive characteristic. In a 2008 paper, Craig Huneke, Paul Monsky, and Moira A. McDermott established a tighter estimate on the asymptotic behavior of the Hilbert-Kunz Function for suitably geometric rings. There are strong connections between the F-Signature and the Hilbert-Kunz Function, but it remains an open question whether it is possible to obtain the same estimates for F-Signature of excellent local normal rings in positive characteristic. We will discuss Huneke, Monsky, and McDermott's result and attempts to extend it to the F-Signature.

Wednesday March 1, 2017 at 3:00 PM in SEO 712