UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 19, 2013

939 Evans Hall

3:45PM: The cone of Betti tables over a rational normal curve

Steven Sam

Recent work of Eisenbud and Schreyer describes all of the linear inequalities that are satisfied by the Betti tables of graded modules over polynomial rings. There has been interest in giving analogous descriptions for other graded rings. In recent work with Kummini, we consider the homogeneous coordinate ring of a rational normal curve and relate its cone of Betti tables to the corresponding cone for a polynomial ring in 2 variables. As in the case of polynomial rings, the extremal rays are given by "pure resolutions". I will explain the idea behind this work and give conjectures for other rings of finite Cohen-Macaulay representation type.

5:00PM: Robust Toric Ideals

Elina Robeva

An ideal of $k[x_1,..,x_n]$ is robust if it is minimally generated by a universal Gröbner basis. This rare property is shared by monomial ideals, ideals of maximal minors of generic matrices, and Lawrence ideals. In this talk we'll discuss recent attempts to classify robust toric ideals, including a complete description for ideals generated in degree two. Along the way there will be many examples, some conjectures, and plenty of counterexamples. This is joint work with Adam Boocher.

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