New Directions Lecture Series

The New Directions Lecture Series are a series of lectures or mini-courses offered by mathematics faculty.

The talks are designed to introduce students to a current area of research.

November 14:

Speaker: An Huang

Title: A numerical approach to computational commutative algebra

Abstract: Given a finite list of polynomials, a basic problem in computational commutative algebra is to compute the polynomial relations among the given polynomials. The problem becomes computationally hard when the given list of polynomials are complicated. We shall explore a statistical numerical approach to this problem, by using regression and more general neural networks. We test the approach on the toy model of the Veronese embedding of P^1 into P^2, i.e. we use regression/machine learning to find polynomial relations among x^2, xy, y^2. The next objective is to use this approach to (hopefully) find polynomial relations among invariants of plane quartic curves, where one has a complicated list of 13 polynomials in 15 variables. This is an ongoing project.

Previous semesters: Spring 2022