Speaker: Daniel Erman (University of Wisconsin)
Title: 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.