The Microlocal Day is an event featuring a brief and intensive series of lectures on various aspects of microlocal analysis and related topics. The program consists of both research presentations and survey lectures intended for researchers and PhD students interested in the field. Everyone is welcome to attend.

The next “Ghent Methusalem Microlocal Day #12” will take place on Tuesday, 8 April 2025

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

Zoom link to join: https://us02web.zoom.us/j/83095584409?pwd=c3huaUhZcWFrZ2NNMU05Ujg4aUlWQT09

Meeting ID: 830 9558 4409

Passcode: 135803

Schedule: all times CEST

Opening 11:00-11:05

11:05-11:50.  Sergo Yepiskoposyan  (National Polytechnic University of Armenia, Armenia) 

Title: Orthonormal Systems and Greedy Algorithms

Abstract: The lecture will present classical orthonormal systems such as Rademacher, Walsh, Haar, Christenson-Levy systems and their properties. As well as greedy algorithms for these systems. Convergence results of the greedy algorithm for the Walsh system in the spaces $L^1[0,1)$ and $L_{\mu}^1[0,1)$ will be presented.

14:00-14:45.  Sergo Yepiskoposyan (continuation)

15:00-15:30.  Bolys Sabitbek (Queen Mary University of London, UK)

Title: Critically degenerate/singular hyperbolic equations

Abstract: We will discuss the wave equations that becomes weakly hyperbolic and singular at time t = 0. We provide precise quantifications for the asymptotics of solutions as t approaches 0, the scattering problem and the loss of regularity caused by the degeneracies at t = 0.

15:40-16:00. Aidyn Kassymov (Institute of Mathematics and Mathematical Modelling, Kazakhstan): 

Title: On fractional inequalities on metric measure spaces with polar decomposition

Abstract: In this paper, we prove the fractional Hardy inequality on polarisable metric measure spaces. The integral Hardy inequality for 1<p≤q<∞ is playing a key role in the proof. Moreover, we also prove the fractional Hardy-Sobolev type inequality on metric measure spaces. In addition, logarithmic Hardy-Sobolev and fractional Nash type inequalities on metric measure spaces are presented. In addition, we present applications on homogeneous groups and on the Heisenberg group. (joint paper with M. Ruzhansky and G. Zaur).

16:00 – 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 #12.

Organisers: Zhirayr Avetisyan, Michael Ruzhansky (Ghent Analysis and PDE Center).

Previous Microlocal Days: #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11