Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Stillman's Question, Solved! (Part 1)
Seminar | October 31 | 5-6 p.m. | 939 Evans Hall
Madeline Brandt, UC Berkeley
In this talk, we will give an introduction to the resolution of Stillman's conjecture by Ananyan and Hochster. Stillman's question asks whether or not there exists a bound on the projective dimension of a homogeneous ideal in a polynomial ring which only depends on the number of generators of the ideal and their degrees. We will start by giving all relevant background material and providing a brief history of the problem, including special cases in which it was previously solved. We will then state Ananyan and Hochster's result, and give examples of families of ideals with interesting projective dimension. We conclude by defining the notions of collapse and strength.