Speaker: Fuxiang Yang
University of Notre Dame
Will give a Algebraic Geometry and Commutative Algebra Seminar entitled:
Recent progress on the Eisenbud-Huneke-Ulrich conjecture
Abstract: Over a polynomial ring, an ideal I is said to be linearly presented if its first syzygy module is generated by linear relations. More generally, the resolution of I is linear for p steps if this linearity continues through the first p steps. In this talk, we explore some fundamental properties of ideals with partially linear minimal free resolution, such as asymptotic behavior of powers, Castelnuovo-Mumford regularity, and lower bounds on the number of minimal generators. In particular, we prove the Eisenbud-Ulrich conjecture on powers of linearly presented ideals and establish a linear effective bound toward the more general Eisenbud-Huneke-Ulrich conjecture.
Date: 09-03-2026
Time: 3:30 pm
Location: 258 Hurley Hall