Determinantal representations of hyperbolic curves

Algebra Seminar
Friday, September 19, 2014 - 3:05pm
1 hour (actually 50 minutes)
Skiles 005
Universit├Ąt Konstanz
We study symmetric determinantal representations of real hyperbolic curves in the projective plane. Such representations always exist by the Helton-Vinnikov theorem but are hard to compute in practice. In this talk, we will discuss some of the underlying algebraic geometry and show how to use polynomial homotopy continuation to find numerical solutions. (Joint work with Anton Leykin).