January 12 -16, 2015
Functional analysis is a well-established field of research for nearly a century. The problems addressed by this theory changed of course significantly over the time. Most of the original problems were qualitative and topological. In modern times however, functional analysis turned towards more quantitative topics, and its interplay with the so-called hard analysis significantly increased. News links were created with non-linear topics such as graph theory and combinatorial properties of discrete metric spaces. The width and depth of today’s functional analysis is such that research runs from logic and set theory to numerical analysis and encompasses combinatorics, harmonic and complex analysis, partial differential equations and theoretical physics.
Geometry of Banach spaces is nowadays one of the main branches of functional analysis. We can single out the following topics as being particularly active in the last decade : non-linear geometry, bases and substitutes for bases, singular integrals, interpolation. These topics are distinct but tightly related.
Nigel Kalton (1946-2010) contributed to functional analysis with more than 250 articles, and most of these articles were actual breakthroughs. He was a major figure in each of the fields covered by this conference. This meeting is therefore dedicated to Nigel Kalton’s memory. However, the CIRM would not be the proper place for a mere commemorative celebration. Our meeting is a scientific event, where active researchers will present their current research to their peers, as usual. But moreover, we thought it was relevant to gather mathematicians who recently contributed to these distinct but related fields. Our hope is to bring together researchers who do not meet so often and to favor exchange of ideas and new collaborations. It would be presumptuous to claim that we can complete the works that Nigel Kalton left, sadly, unfinished. However, it depends on us to convey his ideas to the next generation of researchers, and to underline links and analogies which could be less obvious to us than they were to him. A meeting where these links will be operative seems to be the best way to do so.