## Graduate Algebraic Geometry Seminar

Jay Kopper

UIC

Counterexamples to Hilber's fourteenth problem

**Abstract:**Hilbert's fourteenth problem asks whether certain subrings of polynomial rings over a field $k$ must be finitely generated over $k$. Nagata first found a counterexample in 1958. Since then, considerable progress has been made in producing many new interesting counterexamples. In this two part seminar, I will discuss another counterexample of Nagata that exploits a surprising relationship between algebra and geometry.

Wednesday January 25, 2017 at 3:00 PM in SEO 712