Applications of Bernstein's Other Theorem in Geometry and Algebra

Explore the applications of Bernstein's Other Theorem in a 47-minute seminar presented by Frank Sottile from Texas A&M University. Delve into the intricacies of sparse polynomial equations and their solutions in the torus, examining when systems deviate from being Bernstein-general. Discover how polynomial systems from real-world applications often achieve Bernstein's bound, despite rarely being general given their supports. Learn about the polyhedral homotopy as an optimal algorithm for computing solutions in such cases. Investigate specific examples of non-general but Bernstein-general polynomial systems from various applications. Cover topics including monomials, bounds, general quadratic programming, critical points, periodic graphs, selfadjoint operators, dispersion relation, real structure, and critical point equations.