[Turkmath:4716] Seminar on December 18 2020 via Google Meet

[Mehmet Akif Erdal]

Dear list members,

You are most cordially invited to the first E-seminar of this semester,
organized by the Department of Mathematics, Yeditepe University.

Title: On the Existence of a Self-Adjoint Hamiltonian for a Singular
Interaction on Manifolds

Speaker: Fatih Erman (İzmir Institute of Technology)

Abstract: According to the postulates of Quantum Mechanics, the dynamics of
quantum systems are generated by a self-adjoint operator, namely
Hamiltonian operator associated with the energy of the system. Dirac delta
potentials are known as one class of singular interactions, which have many
applications in various areas of physics. There are different
mathematically rigorous approaches for the description of such systems by
some self-adjoint Hamiltonian operator in $L^2(\mathbb{R}^n)$. In this
talk, I would like to introduce the subject in a rather elementary way and
briefly discuss such interactions in one dimension heuristically and from
the Von Neumann's self-adjoint extension point of view. Then, I shall
extend the same model onto the two and three dimensional Cartan-Hadamard
manifolds with Ricci curvature bounded below by describing the system in
terms of "limit" of resolvent of the regularized version of the initial
singular Hamiltonian. This will be accomplished by the heat kernel defined
on manifolds and its Li-Yau type of estimates.


Date: Friday, December 18, 2020
Time: 13:00
Google Meet: Please contact the organizer for the seminar link.
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