## Emmy Murphy ŽiMITjƒZƒ~ƒi[ —“yƒZƒ~(ENCOUNTERwithMATHEMATICS”ÔŠO•Ò)

# Rigidity and flexibility in conformal symplectic geometry

- “úŽžF2016”N3ŒŽ26“ú(“y)17F00|19F00
- êŠF“Œ‹žH‹Æ‘åŠwi‘å‰ªŽRj—Šw•”–{ŠÙ 201†Žº

### Abstract:

Conformal symplectic geometry is a generalization of symplectic geometry, so that small neighborhoods in a conformal symplectic manifold look like standard symnplectic C^n, but only defined up to multiplication by a constant. Conformal symplectic manifolds share much of the geometry of symplectic manifolds, such as Hamiltonian dynamics, Moser's theorem, and Lagrangian submanifolds. We'll discuss the basic facets of this geometric structure, and following this we will discuss two recent theorems in the subject. On the flexibility side (joint with Y. Eliashberg) we discuss an existence result for all manifolds with nonzero first betti number. On the rigidity side (joint with B. Chantraine), we discuss a Lagrangian intersection theorem for C^2 small Hamiltonians.

˜A—æFŽO¼@‰À•F

TEL:03-3817-1749

E-MAIL:yoshiATmath.chuo-u.ac.jp