The study of free boundary problems (FBP) is a classical topic in Analysis and PDE that has seen an enormous development in the last years. On the one hand, these problems are central to modeling a vast array of physical and natural phenomena, including phase transitions, flame propagation, and fluid dynamics. On the other hand, FBP have deep connections to Geometric Measure Theory, Harmonic Analysis, and the Calculus of Variations, and appear for example in the study of the harmonic measure in rough domains.

While the motivation and origin of these two topics of research are quite different, there have been important connections between them, and the development we have seen in the last years would have not been possible without such deep connections. This Intensive Research Program aims to bring together leading experts in both Analysis and PDE, working on topics including: elliptic and parabolic FBP, geometric measure theory, harmonic measure, and unique continuation in rough sets. The first part of the program will consist of two intensive weeks: the first week consists of three intensive mini-courses, while the second week consists of a workshop including research talks given by roughly 17 leading researchers in the field. Following these intensive weeks, the program will continue with 2 weekly seminars, and the opportunity for long-term visitors to collaborate.

CIMPA and CRM jointly offer fellowships to support the participation of young researchers from developing countries. These fellowships are aimed at researchers aged 36 or younger, or who have completed their PhD within the last five years. Fellows will be selected through an open call for applications to be published soon on the CIMPA website. The program includes travel, accommodation during the whole program, full board, and visa fees if required, enabling selected participants to attend the program.

Applications must be submitted via the CIMPA website (https://www.cimpa.info/fr/node/8205). The deadline to apply is July 1.

TBP