Symmetry and Determinantal Polynomials - SIAM SAGA Seminar

Explore the fascinating world of symmetry and determinantal polynomials in this one-hour seminar presented by Cynthia Vinzant from the University of Washington. Delve into the intricate connections between matrix spaces, determinantal representations, and symmetry, spanning from 19th-century algebraic geometry to modern applications in matrix theory and polynomial geometry. Discover how individual symmetric polynomials possess representations that certify their symmetry, and learn about the invariance of determinantal polynomials under large group actions. Examine specific examples of symmetry in determinantal polynomials, including representations of plane curves invariant under cyclic and dihedral group actions, and explore the relationship between determinantal representations of multiaffine polynomials and the principal minor map. Gain insights from joint works with Abeer Al Ahmadieh, Daniel Plaumann, and Faye Pasley Simon in this comprehensive exploration of applied geometry and algebra.