This volume presents contributions of modern developments in analysis, PDEs and geometric analysis by leading experts, as well as distinguished junior and senior researchers.

The book includes contributions from speakers at the Methusalem Colloquium, Methusalem Junior Seminar, and Geometric Analysis Seminar, all of which were held at the Department of Mathematics, Ghent University from 2023 to 2024. Additionally, it features colloquia and mini-courses delivered by visiting and invited guests.

The book has two main directions:

1. Analysis and PDEs: Covers topics in noncommutative analysis and geometry, functional and harmonic analysis, geometry and spectral methods, and applications to mathematical physics.
2. Geometric Analysis: Covers topics in modern analytic techniques applied to elliptic, hypoelliptic, and subelliptic PDEs. A central theme of this book is the role of pseudo-differential operators in spectral analysis of geometric structures, with direct implications for index theory, noncommutative geometry, and quantization.

Presents the latest results and trends from leading global experts in analysis, PDEs, and geometric analysis Features high-quality short research announcements, communications, or summaries Provides a platform for exceptional young researchers in various fields of analysis and PDEs to share their ideas

Autorentext

David Santiago Gómez Cobos is doctoral candidate at Ghent University, Belgium.

Tapendu Rana 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 UK.

Inhalt

Global existence result for a semilinear wave equation on quantum tori.- Bergman Spaces on Homogeneous.- Logarithmic convexity of evolution equations and application to inverse problems.- Existence of Least Energy Nodal Solutions for p-Laplace Equations Involving Singularity.- Existence and Uniqueness Theorems for One Class of Hammerstein-Type Nonlinear Integral Equations.- A spatial dependent inverse source problem for a fractional pseudoparabolic equation.- Lp- Lq multipliers for the Weyl transform.- Schatten properties of commutators on twisted crossed product.