Spectral Invariants of Integrable Polygons

Watch a 58-minute mathematics seminar presentation exploring the fascinating world of integrable polygons and their spectral invariants. Delve into the geometric properties of polygons whose interior angles follow the form π/n for positive integers n, and discover how these shapes uniquely tessellate the plane. Learn about groundbreaking research conducted with Gustav Mårby that reveals new spectral invariants for these mathematical structures. Explore the extension of integrable polygon concepts into higher dimensions through collaborative work with M. Blom, H. Nordell, O. Thim, and J. Vahnberg, examining the relationships between strict tessellation, Dirichlet Laplace eigenfunctions, and crystallographic Coxeter groups. Gain insights into the interconnections between geometric, analytic, and algebraic characterizations of these mathematical objects in this advanced mathematical exploration presented by Julie Rowlett from Chalmers University.