This book offers an overview of the research results presented by group members and guests of the Ghent Analysis & PDE Center during the weekly seminar that took place from 2021 to 2022. It is an informal event of the Analysis & PDE Center and associated researchers, where everyone can present their work or relevant literature for about 20-30 minutes. The seminar aims to exchange ideas and foster effective learning and collaboration. In this book, group members and guests summarise their results presented during the seminar and provide outlooks for future work. In this way, the book also provides an overview of the recent developments in the Ghent Analysis & PDE Center. The main topics are functional analysis, Fourier analysis, noncommutative analysis, geometric analysis, partial differential equations of different types, harmonic analysis, functional inequalities, pseudo-differential operators, fractional derivatives, special functions, microlocal analysis, inverse problems and imaging. The target audience of this book is any researcher working in the above fields.

Autorentext

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. His research interests mainly lie in Partial Differential Equations, Microlocal and Harmonic Analysis, and Pseudo-Differential Operators on Lie Groups and Manifolds. Previously, he had appointments at Utrecht University, Johns Hopkins University, University of Edinburgh, and Imperial College London. He is the recipient of various awards and fellowships, notably, the Ferran Sunyer i Balaguer Prize in 2014 and 2018, Daiwa Adrian Prize in 2010, and the ISAAC award in 2007. He is serving as the head of the Ghent Analysis & PDE Center of Ghent University.Dr Karel Van Bockstal obtained his PhD (in mathematical engineering) in 2015 at Ghent University, Belgium, and is currently a postdoctoral researcher (Ghent Analysis & PDE Center) at the Department of Mathematics: Analysis, Logicand Discrete Mathematics, Ghent University. His area of specialisation is related to mathematical analysis, evolutionary partial differential equations and the development of numerical algorithms and their implementation. This research focus concerns direct and inverse problems with applications in heat transfer, elasticity, electromagnetism and thermo-elasticity. He authors 37 publications included in ISI Web of Science. In addition, he was awarded the EAIP Young Scientist Award of the 8th International Conference "Inverse Problems: Modelling and Simulation", May 2016.