Asymptotics, Operators, and Functionals

Speaking in 2025:

10 February (Start time: 16:15) Luis Silva (IIMAS-UNAM) Title: Spectral analysis of infinite Marchenko-Slavin matrices. Abstract: In this talk we deal with the problem of spectral characterization of a class of infinite matrices arising from the modeling of small oscillations in a system of interacting particles. The class of matrices under discussion corresponds to the infinite Marchenko-Slavin class. The spectral functions of these matrices are completely characterized and an algorithm is provided for the reconstruction of the matrix from its spectral function. The techniques used in this work are based on recent results for the spectral characterization of infinite band symmetric matrices with so-called degenerations.

24 March (Start time: 16:15) Uzy Smilansky (Weizmann) Title: Graph theory and scrambling of quantum information. Abstract: The introduction of quantum computing brought with it the need to adopt classical and well-founded concepts from information theory to the quantum-mechanical world. In particular, concepts like information scrambling, chaos and its measure in terms of Lyapunov exponents had to be reformulated to coexist with tenets of quantum theory such as Heisenberg's uncertainty principle, while complying with Bohr's correspondence principle. I will try to show how a new approach based on many results and concepts from graph theory is able to offer a solution to the above-mentioned difficulties. This is a joint project with Sven Gnutzmann (Nottingham).

31 March Elena Cherkaev (Utah)

6 October Ludmila Prikazchikova (Keele) Title: Asymptotic analysis of 3D boundary-value problems for three-layered high-contrast plates. Abstract: 3D equations in linear elasticity governing a thin, three-layered plate are considered. The stiffness of the inner (core) layer is assumed to be much smaller than that of the outer (skin) ones. Leading order 2D equilibrium equations extending the classical theory for plate bending are derived for various parametric setups. In general case they are of the sixth order, requiring three boundary conditions at the plate edge. The latter follows from three decay conditions, extending the canonical Saint-Venant's principle applied to a high-contrast three-layered semi-infinite elastic strip. They express the absence of the overall transverse stress resultant, and longitudinal stress resultant and couple for each of the outer layers. The obtained equations are tested by comparison with the exact solution for a sinusoidal surface loading.