Mathematical Physics and Harmonic Analysis Seminar

Date: December 3, 2021

Time: 1:50PM - 2:50PM

Location: Zoom

Speaker: Patricia Alonso Ruiz, TAMU

Title: Minimal eigenvalue spacing in the Sierpinski gasket

Abstract: In the 80s, the physicists Rammal and Tolouse observed that suitable series of eigenvalues in the finite graph approximations of the Sierpinski gasket produced an orbit of a particular dynamical system. That observation lead to a complete description of the spectrum of the standard Laplace operator by Fukushima and Shima. The study of this spectrum has since then revealed structures with many interesting features not seen in other more classical settings. For instance, it presents large exponential gaps (or spacings), whose existence and properties have extensively been studied. What happens with the small gaps? This fairly challenging question had eluded previous investigations and is the main subject of the present talk, where we discuss yet another remarkable fact: Any two consequent eigenvalues in the Dirichlet or in the Neumann spectrum of the Laplacian on the Sierpinski gasket are separated at least by the spectral gap.