Student Algebraic Geometry Seminar: Computations in Local Rings using Macaulay2

Seminar | April 24 | 4-5 p.m. | 891 Evans Hall

 Mahrud Sayrafi, UC Berkeley

 Department of Mathematics

Local rings are ubiquitous in algebraic geometry. Not only are they naturally meaningful in a geometric sense, but also they are extremely useful in proving theorems. When studying finitely generated modules over local rings, for instance, projectivity, flatness, and freeness are all equivalent. Above all, many important results depend on Nakayama's lemma, which holds over local rings. In this talk, I attempt to (1) give examples and applications of computations over local rings (e.g. resolution of singularities, testing for Cohen-Macaulayness, computing intersection product, etc.) and (2) present progress on developing computational methods in Macaulay2 for working over local rings.