 Location
 MSRI: Simons Auditorium
 Video


 Abstract
 Given a homogeneous ideal I in a polynomial ring R over a field, one can compute a minimal graded free resolution of I (or R/I). The length of this resolution, called the projective dimension, is finite and at most the number of variables of R by Hilbert's Syzygy Theorem. When I has few generators in low degree, one expects that projdim(R/I) cannot be arbitrarily large, even when R has many variables. Stillman asked precisely for a bound on projdim(R/I) in terms of the degrees of the minimal generators of I. In this talk I will survey the history of this problem and recent developments toward a solution, including the exponential bound of AnanyanHochster in the case of ideals generated by quadrics, specific bounds for threegenerated ideals in low degree by EisenbudHuneke and Engheta, and families of ideals with large projective dimension.
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