Symplectic

Event Information Adiabatic limits, Theta functions, and geometric quantization
14:10 on Monday October 22, 2018
15:00 on Monday October 22, 2018
BA6183, Bahen Center, 40 St. George St.
Takahiko Yoshida
http://www.isc.meiji.ac.jp/~takahiko/
Meiji University
http://www.isc.meiji.ac.jp/

In the geometric quantization of Lagrangian fibrations, the index of the Spin^c Dirac operator is often observed to be equal to the number of Bohr-Sommerfeld fibers in the several examples, such as, the nonsingular Lagrangian fibrations case, projective toric varieties, Gelfand-Cetlin integrable system on the complex flag variety, the Goldman's integrable system on the moduli space of flat connections on a surface. In this talk, for the prequantizable nonsingular Lagrangian fibrations with a certain class of compatible complex structures let us formally" construct a basis of the space of holomorphic sections of the prequantum line bundle such that the basis is indexed by the Bohr-Sommerfeld points and the support of each section in the basis converges to the corresponding Bohr-Sommerfeld fiber by the adiabatic limit. We will discuss the general case if time is permitted.