Olivetti Club

Dylan PeiferCornell University
Signature Gröbner Bases

Tuesday, November 13, 2018 - 4:30pm
Malott 406

Gröbner bases are sets of polynomials with properties that make them especially useful for computation.
Many questions about sets of polynomials or the ideals they generate can be computed easily from a Gröbner basis, so one of the key problems in computational algebra is how to efficiently compute a Gröbner basis of an ideal from an arbitrary set of polynomial generators.

In 2002, Faugère introduced the $F_5$ algorithm, a new algorithm for computing Gröbner bases that used the new idea of signatures.
$F_5$'s impressive performance resulted in a great deal of interest in signature Gröbner bases and the algorithms that can be used to compute them.

In this talk we will introduce signatures and signature Gröbner bases, using many explicit examples and comparisons to standard techniques.
Basic Gröbner bases will be reviewed, but a previous understanding at the level of MATH 4370, MATH 6340, or Chapter 2 of Ideals, Varieties, and Algorithms by Cox, Little, and O'Shea would be helpful.

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