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Solving Polynomial Systems via Homotopy Continuation and Monodromy

Jeff Sommars
(University of Illinois at Chicago)
Algebra Seminar
Tuesday, 29 August, 2017, at 16:15-17:15, in Aud. D3 (1531-215)

I will present a probabilistic algorithm for finding the solution set of a generic system in a family of polynomial systems with parametric coefficients. Under the theoretical assumption that monodromy actions are generated uniformly, the expected number of homotopy paths tracked by this algorithm is linear in the number of solutions. Our software implementation of this algorithm is competitive with the existing state-of-the-art methods implemented in other software packages. I will mention preliminary results from a new parallel implementation. This talk is based on joint work with Timothy Duff, Cvetelina Hill, Anders Jensen, Kisun Lee, Anton Leykin, and Nathan Bliss.

Contact person: Anders Nedergaard Jensen