Algebraic Geometry Seminar

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.