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Caltech

Algebraic Geometry Seminar

Monday, March 16, 2015
4:00pm to 5:00pm
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Determinantal representations of hyperbolic polynomials and hyperbolic varieties
Cynthia Vinzant, Assistant Profrssor, Mathematics, UC Berkeley,

If a real symmetric matrix of linear forms is positive definite at some
point, then its determinant is a hyperbolic hypersurface. In 2007, Helton
and Vinnikov proved a converse in three variables, namely that every
hyperbolic plane curve has such a definite determinantal representation.
Recently, some of this work has also been extended to varieties of higher
codimension. I will talk about constructing definite determinantal
representations of plane curves and a family of hyperbolic varieties whose
Chow forms have determinantal representations.

For more information, please contact Pablo Solis by email at pablos@caltech.edu or visit http://www.its.caltech.edu/~pablos/agsem.html.