Please note: This PhD seminar will take place in DC 2306C and online.
Sriram Gopalakrishnan, PhD candidate
David R. Cheriton School of Computer Science
Supervisor: Professor Éric Schost
The polynomial ideal generated by the minors of a fixed size of a polynomial matrix is called a determinantal ideal. These ideals arise naturally in a variety of scientific contexts, including real algebraic geometry and optimization. When using a signature-based Gröbner basis algorithm such as F5 to compute a grevlex Gröbner basis for such ideals, many reductions to zero are encountered since determinantal ideals cannot, in general, be generated by a regular sequence. In this talk, I will give refined versions of the F5 Gröbner basis algorithm adapted to specific kinds of determinantal varieties, and apply these new algorithms to the problem of computing the critical points of a polynomial restricted to an algebraic set.
This talk is based on joint work with Vincent Neiger and Mohab Safey El Din.
To join this PhD seminar in person, please go to DC 2306C. You can also attend virtually on Zoom.