This volume is a collection of short summaries of reports from lectures delivered at Tbilisi Analysis & PDE seminars and workshops in 2024. The contributions present some new developments and ideas in differential equations, mathematical analysis, harmonic analysis, inequalities, integral equations, and applications.  In particular, it contains some applications and several open questions as a source of inspiration for further research. The Tbilisi Analysis & PDE seminars are held bi-weekly since 2019, and the workshop is organized every year since 2023. Researchers in the named fields will find this volume useful.

Georgi Tephnadze is a scientific fellow at the Institute of Mathematics and head of the master’s program “Pure and Applied Mathematics” at the University of Georgia, Georgia.
Roland Duduchava is a professor and director of the  Institute of Mathematics of the University of Georgia.
Eugene Shargorodsky is a professor of mathematics at Kings colledge London.