u-regeneration: solving systems of polynomials equation-by-equation

Algebra Seminar
Tuesday, November 2, 2021 - 10:00am for 1 hour (actually 50 minutes)
Skiles 006
Jose Rodriguez – University of Wisconsin, Madison – jrodriguez43@wisc.edu
Ashley K. Wheeler

Solving systems of polynomial equations is at the heart of algebraic geometry. In this talk I will discuss a new method that improves the efficiency of equation-by-equation algorithms for solving polynomial systems. Our approach uses fewer homotopy continuation paths than the current leading method based on regeneration.  Moreover it is applicable in both projective and multiprojective settings. To motivate the approach I will also give some examples coming from applied algebraic geometry.
This is joint work with Tim Duff and Anton Leykin.