Real stable polynomials define real hypersurfaces with special topological structure. These polynomials bound the feasible regions of semidefinite programs and appear in many areas of mathematics, including optimization, combinatorics and differential equations. Recently, tight connections have been developed between these polynomials and combinatorial objects called matroids. This led to a counterexample to the generalized Lax conjecture, which concerned high-dimensional feasible regions of semidefinite programs. I will give an introduction to some of these objects and the fascinating connections between them.

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Location: SH202 Cynthia Vinzant, North Carolina State University