The CRM opens an annual call for CRM Intensive Research Programmes (IRP) approximately two years in advance. The CRM started organising IRPs in 2003 and has held two to three per year since then. Each programme consists of a number of resident researchers, from junior to senior, and at least two scientific events (workshops, advanced courses, and conferences). Each research programme also runs an informal weekly seminar that serves as a get-together meeting for the research visitors and local mathematicians.
IRP participants benefit from the CRM well established experience staff and the comfortable premises, with the commodities of a campus environment and the nearby entertainment of the lively city of Barcelona.
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.
The mini courses should be October 26-30 and the workshop November 2-6.
Advanced courses in free boundary problems
The first week of the program will consist of three mini-courses delivered by Professors Max Engelstein (UMN), Bozhidar Velichkov (Università di Pisa), and Zihui Zhao (JHU). While the details of the courses are still to be determined, a large emphasis will be placed on techniques for the regularity theory for free boundary problems, and regularity of harmonic/elliptic measure. Each course will consist of 7 hours of lectures. During this week, additional time will be allotted for discussions regarding the lectures, and further connections to active areas in research.
Connections in free boundaries, harmonic measure, and unique continuation
The second week of the program aims to bring together experts in various fields in Analysis and PDE, especially those working on topics in elliptic and parabolic free boundaries, and geometric measure theory and harmonic analysis in rough domains. In particular, this week will consist of roughly 15-17 hour long research talks, along with shorter blocks planned for students to have a chance to present their work. A strong emphasis will be placed on uniting techniques from those in adjacent research areas in elliptic and parabolic PDE.