UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

January 30, 2018

939 Evans Hall

3:45PM: On the Lex-plus-powers conjecture

Alessio Sammartano

Let I be a homogeneous polynomial ideal containing a regular sequence of forms of prescribed degrees. The Lex-plus-powers conjecture predicts upper bounds for the Betti table of I, in terms of the Betti table of a monomial ideal with the same Hilbert function as I and containing the appropriate monomial regular sequence. I will give a brief overview of the conjecture and discuss some cases. The This is a joint work with Giulio Caviglia.

5:00PM: Introduction to Chow rings

Chrie Eur

We give a gentle introduction to intersection theory. We start with the definition of Chow rings and few tools for working with them along with their functorial properties. We then look to projective spaces and curves on surfaces as the first applications of these concepts. We conclude with a glimpse of liaison theory and a toy enumeration problem on a moduli space.

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