The Microlocal Day is an event offering a brief and intensive series of lectures on various aspects of microlocal analysis and related topics. The program includes both research talks and survey lectures, tailored for researchers and PhD students with an interest in the field. Everyone is welcome to attend.

The next “Ghent Methusalem Microlocal Day #11” will take place on

Tuesday, 14 January 2025

Venue: Leslokaal 3.1, Campus Sterre, S8, Ghent University, Belgium

Program

Opening 14:00-14:05

14:05-14:45.  McDonald, Edward Andrew (Eberly College of Science, Pennsylvania, USA) 

Title: Recent work and unsolved problems in Quantum Harmonic Analysis

Abstract: I will give a brief introduction to Quantum Harmonic Analysis, also called the analysis of noncommutative Euclidean spaces. Some recent work has included the study of nonlinear PDE on these spaces. I will give some conjectures about a bilateral theory of pseudodifferential operators that should exist for this setting, but which has yet to be developed.

14:50-15:30.  Shiqi Liu (UNSW, Sydney, Australia)

Title: Weyl asymptotic for hypoelliptic operators on graded Lie group

Abstract: Weyl-type asymptotics have a long history, originating with the pioneering work of H. Weyl. In our recent work, we establish a spectral asymptotic formula for the negative powers of hypoelliptic operators on graded Lie groups. Along the way, we derive elliptic estimates for hypoelliptic operators on graded Lie groups without relying on pseudodifferential calculus, which is a common tool in this area.

This is a joint work with Edward McDonald, Fedor Sukochev, and Dmitriy Zanin.

15:35-16:15. Kai ZENG (Ghent University, Belgium): 

Title: Schatten properties of commutators on twisted crossed products

Abstract: In this talk, we study Fourier multiplier commutators on a twisted crossed product M⋊Rd. We will characterise their Schatten p-class membership by that of their symbols in the associated Besov space. In addition, we show a formula on the Dixmier trace, which also gives us a characterization of the weak Schatten p-class membership of these commutators by a Sobolev space. As an example, our results applied to noncommutative Euclidean Space.
16:20 – Closing.

This Microlocal Day continues the tradition of Microlocal Days that we have been organising at Imperial College London, then continued at Ghent University. So, this Microlocal Day can be viewed as Microlocal Day #11.

Organisers: Kanat Tulenov, Michael Ruzhansky (Ghent Analysis and PDE Center).

Previous Microlocal Days: #1 #2 #3 #4 #5 #6 #7 #8 #9 #10