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.
Homotopical and higher-categorical methods are becoming increasingly important in areas such as geometry, topology, algebra, mathematical physics, and lately also logic and computer science. The insight can be summarized in realizing that many deep problems in these areas and elsewhere are homotopical in nature, and that native homotopical tools are necessary for a natural treatment of them as well as for obtaining viable solutions that can serve as a basis for further developments.
The present program aims at gathering experts from these areas in order to foster new lines of research and stimulate young researchers. Among the big challenges which will be addressed are: development of higher-categorical tools for theory and computations in algebraic K-theory and related theories, including topological cyclic homology and topological Hochschild homology; factorization homology and graph homology; higher Segal spaces; presentability and accessibility; explicit descriptions of fully extended topological field theories; applications of Goodwillie calculus; deformation theory; derived geometry.