Davide Pradovera: Connecting the dots: Graph algorithms for parametric eigenvalues

Abstract: Eigenvalue problems are fundamental to modeling complex systems, from understanding structural vibrations to preventing catastrophic resonant failures in engineering. However, when system parameters vary, tracking how multiple eigenvalues evolve becomes a non-trivial combinatorial challenge. In this talk, I show how tracking dynamic spectrum trajectories can be framed using familiar tools from computer science and discrete math. By reformulating eigenvalue continuity through optimal bipartite matching and detecting topological branch points using maximum clique search, I present an accessible, data-driven framework for tracking and resolving complex parametric eigenvalue problems.