|Date: Thursday, October 19, 2017
Location: 4088 East Hall (3:00 PM to 4:00 PM)
Title: Stillman's Conjecture and its Applications
Abstract: The talk will discuss the proof, in complete generality and in all characteristics, of Stillman's conjecture, which assets that there is a bound on the projective dimension of an ideal of a polynomial ring which is generated by a specified number n of forms of degree at most d that depends on n and d but not on the number of variables. The method is to show that the forms are in a polynomial subalgebra generated by B(n,d) forms such that the original polynomial ring is a free extension of the "small" subalgebra. This leads to many other bounds, e.g. everything about the primary decomposition of n forms of degree at most d is bounded. Many questions about the best specific bounds remain. This is joint work of Tigran Ananyan and the speaker. These results have been used to give other bounds: for example, given a homogenous prime ideal of a polynomial ring over an algebraically closed field, there is a bound on the number and degrees of the generators of the ideal that depends only on the codimension and multiplicity of the ideal.
Speaker: Mel Hochster
Institution: University of Michigan