09-24【李 勤】管研楼1418 Holomorphic differential operators via Fedosov quantization

发布者:万宏艳发布时间:2021-09-18浏览次数:293

报告题目: Holomorphic differential operators via Fedosov quantization


报告人:李勤(南方科技大学)


时间:2021年9月24日(周五)上午10:00-11:00


教室:管研楼1418


摘要:  Although Toeplitz operators on K\ahler manifolds associate smooth function to operators on Hilbert spaces $\mathcal{H}_k=H^0(X,L^{\otimes k})$, their composition only gives a formal deformation quantization by considering the asymptotic $k\rightarrow \infty$ and turning $1/k$ to $\hbar$. In this talk, I  apply the method of Fedosov to quantize a subclass of smooth functions $\A\subset C^\infty(X)$ to holomorphic differential operators on $\mathcal{H}_k$. This gives a strong version of quantization since $\A$ acts on Hilbert spaces as differential operators which gives a non-formal deformation of the classical multiplication.