Mini-workshop: A geometric fairytale full of spectral gaps and random fruit. Abstracts from the mini-workshop held November 27 – December 3, 2022. (English) Zbl 1521.00020
Summary: In many situations, most prominently in quantum mechanics, it is important to understand well the eigenvalues and associated eigenfunctions of certain self-adjoint differential operators. The goal of this workshop was to study the strong link between spectral properties of such operators and the underlying geometry which might be randomly generated. By combining ideas and methods from spectral geometry and probability theory, we hope to stimulate new research including important topics such as Bose-Einstein condensation in random environments.
MSC:
| 00B05 | Collections of abstracts of lectures |
| 00B25 | Proceedings of conferences of miscellaneous specific interest |
| 47-06 | Proceedings, conferences, collections, etc. pertaining to operator theory |
| 81-06 | Proceedings, conferences, collections, etc. pertaining to quantum theory |
| 47A75 | Eigenvalue problems for linear operators |
| 58J50 | Spectral problems; spectral geometry; scattering theory on manifolds |
| 60K37 | Processes in random environments |
| 60K40 | Other physical applications of random processes |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 82D03 | Statistical mechanics in condensed matter (general) |
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