UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

November 14, 2017

939 Evans Hall

3:45PM: An introduction to a conjecture of Lech

Craig Huneke

Lech wrote a series of three papers in the early 1960s which studied the multiplicity of rings. He paid special attention to the behavior of multiplicity under flat extensions and formulated a simple conjecture which remains unsolved. In some sense, what his conjecture shows is that we do not understand flatness. I will talk about his conjecture and some recent work by Linquan Ma which resolves the conjecture in dimension 3.

5:00PM: Stillman's Question, Solved! (Part 3)

Justin Chen

We continue the proof of Stillman's question due to Ananyan-Hochster. Using the tools described in Part 2, we show how to obtain "small" bounds for invariants related to free resolutions in commutative algebra, including a strong form of Stillman's question. As time permits, we will also discuss recent work of Erman-Sam-Snowden which extends Ananyan-Hochster's result to obtain Stillman-type bounds for a very general class of invariants.

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