3:45PM: An introduction to a conjecture of LechCraig HunekeLech 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 ChenWe continue the proof of Stillman's question due to AnanyanHochster. 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 ErmanSamSnowden which extends AnanyanHochster's result to obtain Stillmantype bounds for a very general class of invariants.
