Explore the spectral aspects of symmetric matrix signings in this 30-minute lecture by Alexandra Kolla from the University of Illinois at Urbana-Champaign. Delve into the importance of graph spectra, the concept of signings, and their relationship to 2-lifts and eigenvalues. Examine key questions surrounding the spectra of signings and investigate polynomial identity testing. Learn about randomized bipartite matching algorithms and discover the connection between signings and 2-matchings. Uncover the link to Alon's Combinatorial Nullstellensatz and techniques for finding non-zeros of polynomials. This talk, part of the "Hierarchies, Extended Formulations and Matrix-Analytic Techniques" series at the Simons Institute, offers valuable insights into advanced graph theory and its applications.