Noncommutative Geometry and Semiclassical Analysis on Quantum Tori

Explore advanced mathematical concepts in this seminar lecture from the BIMSA-Tsinghua Quantum Symmetry Seminar series. Delve into the semiclassical Weyl's law, a fundamental result in semiclassical analysis, and discover how it extends to quantum spaces. Learn about the solution to a conjecture regarding semiclassical Weyl's laws for curved quantum tori - quantum tori equipped with arbitrary Riemannian metrics. Examine spectral asymptotics for negative order pseudodifferential operators on noncommutative tori, which provides a quantum analogue of the classical Birman-Solomyak result from the 1970s. Understand connections to recent developments in spectral asymptotics for quantized differentials on quantum tori. The presentation covers key topics in noncommutative geometry, global analysis, pseudodifferential operators, and semiclassical analysis, delivered by Professor Raphaël Ponge from Sichuan University, a distinguished researcher whose work has been published in leading mathematical journals including Advances in Mathematics and Communications in Mathematical Physics.