

Principle Seminar of the Department of Probability Theory, Moscow State University
October 9, 2019 16:45–17:45, Moscow, MSU, auditorium 1224






Differential Operators and Dynamics of Localized Quantum States on Singular Spaces of Variable Dimension. Relation to the Behaviour of Geodesics and to Certain Problems of Analytic Number Theory
A. I. Shafarevich^{} ^{} Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract:
We study properties of evolution equations (for example, Schroedinger or
wave equations) on singular spaces. These spaces can be obtained from graphs
via replacing vertices by lowdimensional Riemannian manifolds. In particular,
the behaviour of localized solutions appears to be connected with global properties
of geodesic flows on these manifolds as well as with popular problems of
analytic number theory.

