Olivetti Club

Dylan PeiferCornell University
The Grobner walk

Tuesday, October 18, 2016 - 4:30pm
Malott 406

Grobner bases are the foundation of computational algebra, where computing a Grobner basis of an ideal is often the first step in determining properties of ideals and algebraic varieties. Unfortunately, the Grobner basis and the work required to compute it depend greatly on the chosen monomial order, with some desired monomial orders leading to difficult or impossible computations. The Grobner walk is an algorithm that sidesteps this problem by first computing the Grobner basis of an ideal $I$ with respect to an easy monomial order and then moving in small steps towards the hard monomial order while making small adjustments to the Grobner basis for $I$. The end result is a Grobner basis for $I$ with respect to the hard monomial order that has been computed using dramatically less time and memory. In this talk we will review the concept of a Grobner basis and present the steps involved in the basic Grobner walk.

Refreshments will be served in the lounge at 4:00 PM.