| Speaker: | Yu Tung Yau (Kavli IPMU) |
|---|---|
| Title: | Quantization via transverse PBW theorem and asymptotic locality of Toeplitz operators |
| Date (JST): | Thu, Jan 22, 2026, 15:30 - 17:00 |
| Place: | Seminar Room B |
| Abstract: |
On a prequantizable Kähler manifold X, Konstant-Souriau and Toeplitz operators provide two complementary links between quantum observables and quantum states. Kostant–Souriau operators give an exact Poisson algebra representation on H0(X,Lk), but only for polarization-preserving observables, whereas Toeplitz operators apply to all smooth functions but satisfy the star product relations only asymptotically. Recent work of Chan–Leung–Li and Andersen introduced constructions of genuine star product actions for certain subalgebras of functions in the Kähler setting, extending the classical notion of quantizable (polarization-preserving) observables. In this talk, I explain how these ideas extend to quantization with arbitrary non-singular polarization via a transverse Poincaré–Birkhoff–Witt theorem (joint work with D. Wang). I also describe how, in the Kähler case, this framework yields a new asymptotic expansion of Toeplitz operators in terms of holomorphic differential operators (joint work with K. Chan, N. C. Leung, and Q. Li). |
