|Date: Friday, November 03, 2017
Location: 3096 East Hall (3:10 PM to 4:00 PM)
Title: Groebner Bases: A Computational Tool for Algebraic Geometry
Abstract: Given an ideal in a polynomial ring, it may have a very complicated set of generators involving polynomials with several terms. On the other hand, monomial ideals are well-studied and they exhibit remarkable combinatorial properties. The theory of Groebner bases allows us to associate to any ideal an appropriate monomial ideal which retains part of the structure of the original ideal. Geometrically speaking, this operation allows to move from a complicated space to the intersection of coordinate subspaces. We will talk about the background needed for the theory of Groebner bases, point out some computations that can be made using this tool, and recover some information about our original ideal from the study of its initial monomial ideal.
Speaker: Francesca Gandini