The Two-or-Infinity Conjecture for Reeb Orbits
김수현
129동 406호
0
2131
07.27 09:30
| 구분 | 동역학 |
|---|---|
| 일정 | 2026-08-05(수) 13:30~14:30 |
| 세미나실 | 129동 406호 |
| 강연자 | 이동해 (하버드대학교) |
| 담당교수 | 임선희 |
| 기타 |
The two-or-infinity conjecture in Reeb dynamics states that a Reeb flow has either exactly two or infinitely many simple periodic orbits. In this talk, I will first introduce embedded contact homology and state the Weyl law for ECH spectral invariants, and explain how they imply the existence of at least two simple Reeb orbits. Next, assuming that the first Chern class of the contact structure is torsion, I will discuss the proof of the conjecture for nondegenerate contact forms using a Birkhoff section and considering its Poincaré return map. Finally, I will briefly introduce the recent proof without the nondegeneracy assumption, focusing on the main technical difficulty and how it is overcome.
