Pseudodifferential operators were first explicitly defined by Kohn-Nirenberg and Hörmander to connect singular integrals and differential operators. The theory of pseudodifferential operators serves as a unifying framework in modern harmonic analysis, which has substantial impact on linear and non-linear PDEs and differential geometry. In this talk, we report our recent work on the spectral asymptotics of pseudodifferential operators, and explain how the spectral asymptotics serve as a key ingredient in quantum calculus in the setting of noncommutative geometry introduced by Alain Connes. We will also mention an application to the semiclassical Weyl law.

报告人简介：熊枭，哈尔滨工业大学数学研究院教授，常务副院长。研究领域为调和分析、非交换分析及其应用等。研究兴趣主要集中在非交换分析，这是泛函分析的分支，主要涉及到调和分析及算子代数，是近年来数学学科最活跃和富有成果的前沿交叉研究领域之一。研究工作主要集中在在算子值调和分析、非交换几何以及群上的调和分析。主要结果发表在 Mem. Amer. Math. Soc., Comm. Math. Phys., Adv. Math., J. Math. Pures Appl., J. Funct. Anal.等国际权威期刊。获2024国际基础科学大会“前沿科学奖”。