Ultraproducts, Hilbert’s Syzygy Theorem, and Stillman’s Conjecture

When and where:

3-3:50pm, December 7, in Keller 403

Abstract:

Hilbert’s Syzygy Theorem is a classic finiteness result about
a construction in algebra known as a free resolution.

Stillman once proposed an analogue of Hilbert’s result, which involved potentially considering polynomials in infinitely many variables.

Stillman’s Conjecture was recently solved, and perhaps the simplest proof is based upon a novel use of an ultraproduct.

I’ll give an expository overview of the history of Stillman’s Conjecture (very little algebraic background will be assumed), and then explain how and why ultra products came to play such a key role.