This volume presents the extended abstracts from the 2024 Summer School organized by the Ghent Analysis and PDE Center. The school focused on equipping participants with a broad spectrum of mathematical tools for addressing both direct and inverse problems across various fields. Through a combination of lectures, problem-solving sessions, and collaborative discussions, the program fostered the development of innovative methods and techniques. The lectures also include broader related topics in mathematical analysis and partial differential equations, offering a comprehensive perspective on current research directions in the field.
Fourier algebras and homomorphisms.- Dispersion phenomena and
applications to evolution equations.- Subriemannian geometry and analysis of
hypoelliptic PDE.- Stability results for Sobolev, logarithmic Sobolev, and
related inequalities.- Semiconcavity, viscosity solutions and the square
distance in Carnot groups.- Direct and inverse nonstationary scattering
problems for Dirac-type system.- Quantitative homogenisation for differential
equations with highly anisotropic partially degenerating coefficients.-
Rigidity results for evolution PDEs on homogeneuos Lie groups.- An overview
of dualities in non-commutative harmonic analysis.- Colombeau type
extensions, assymptotic scales.- Analytical solutions to the Laplace equation
on a hemispherical domain.- Uniform spectral asymptotics for high-contrast
periodic media.- Asymptotic mean value formulas for the 𝑝-Laplacian
in the Euclidean space and in the Heisenberg Group.- Global solutions for a
class of nonlinear evolution equations in supercritical spaces.- An index
transform method for solutions of the boundary value problems in a wedge.
Mariana Chatzakou is a postdoctoral researcher at Ghent University, Belgium.
Michael Ruzhansky is a senior full professor of Mathematics at Ghent University in Belgium, and a professor of Mathematics at Queen Mary University of London in the United Kingdom.
Karel Van Bockstal is a postdoctoral researcher at Ghent University, Belgium.
