Spring 2019

Hyperbolicity cones and spectrahedra *starts at 10:30 a.m. sharp*

Wednesday, Feb. 20, 2019 10:30 am12:00 pm PST

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Parent Program: 

Mario Kummer, TU Berlin


Room 116

The generalized Lax conjecture states that the hyperbolicity cone $C_h$ of every hyperbolic polynomial h is a spectrahedron. An equivalent formulation is that there is a hyperbolic polynomial q such that qh is the determinant of a symmetric matrix pencil, definite at some point, where $C_q$ contains $C_h$. We first sketch the proof for the existence of such a q when we restrict to strictly hyperbolic h and omit the second condition. Then we discuss this construction in the case of plane hyperbolic curves in more detail. The latter is part of a joint work with S. Naldi and D. Plaumann.