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Tuesday Seminar on Topology
Seminar information archive ～09/24｜Next seminar｜Future seminars 09/25～
| Date, time & place | Tuesday 16:00 - 17:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | IKE Yuichi, KONNO Hokuto, SAKASAI Takuya |
Next seminar
2026/10/06
16:00-17:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Kouichi Taira (Kyushu University)
Large eigenvalues and logarithmic Weyl law of the Connes-Moscovici operator (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kouichi Taira (Kyushu University)
Large eigenvalues and logarithmic Weyl law of the Connes-Moscovici operator (JAPANESE)
[ Abstract ]
The Bohr-Sommerfeld quantization condition is a principle that describes the semiclassical eigenvalues of a quantum system in terms of action integrals along closed trajectories of the corresponding classical system. A refined quantization condition incorporating the Maslov index as a correction term was independently discovered by Keller and Maslov, and a mathematically rigorous framework was subsequently developed by Arnold and Hörmander. On the other hand, for one-dimensional Sturm-Liouville systems under suitable boundary conditions, it may give rise to discrete eigenvalues even in situations where the usual Bohr-Sommerfeld picture based on closed classical trajectories does not directly apply. In this talk, we focus on the prolate operator recently introduced by Connes and Moscovici, and explain how eigenvalues arise when the corresponding classical system has no closed trajectories, as well as how these eigenvalues can be related to action integrals and Maslov index. As an application, we present a result concerning a Weyl law with a logarithmic term, conjectured by Connes and Moscovici, which describes the asymptotic behavior of the eigenvalue counting function. This is a joint work with M. Willems(Utrecht University) and M.Wrochna (Utrecht University).
[ Reference URL ]The Bohr-Sommerfeld quantization condition is a principle that describes the semiclassical eigenvalues of a quantum system in terms of action integrals along closed trajectories of the corresponding classical system. A refined quantization condition incorporating the Maslov index as a correction term was independently discovered by Keller and Maslov, and a mathematically rigorous framework was subsequently developed by Arnold and Hörmander. On the other hand, for one-dimensional Sturm-Liouville systems under suitable boundary conditions, it may give rise to discrete eigenvalues even in situations where the usual Bohr-Sommerfeld picture based on closed classical trajectories does not directly apply. In this talk, we focus on the prolate operator recently introduced by Connes and Moscovici, and explain how eigenvalues arise when the corresponding classical system has no closed trajectories, as well as how these eigenvalues can be related to action integrals and Maslov index. As an application, we present a result concerning a Weyl law with a logarithmic term, conjectured by Connes and Moscovici, which describes the asymptotic behavior of the eigenvalue counting function. This is a joint work with M. Willems(Utrecht University) and M.Wrochna (Utrecht University).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
