Perspectives in Analysis

The Conference "Perspectives in Analysis" was held during May 26-28, 2003 at the Royal Institute of Technology in Stockholm, Sweden. The purpose of the conference was to consider the future of analysis along with its relations to other areas of mathematics and physics, and to celebrate the seventy-?fth birthday of Lennart Carleson. The scienti?c theme was one with which the name of Lennart Carleson has been associated for over ?fty years. His modus operandi has long been to carry out a twofold approach to the selection of research problems. First one should look for promising new areas of ana- sis, especially those having close contact with physically oriented problems of geometric character. The second step is to select a core set of problems that require new techniques for their resolutions. After making a central contri- tion, Lennart would usually move on to a new area, though he might return to the topic of his previous work if new techniques were developed that could break old mathematical log jams. Lennart's operating approach is based on fundamental realities of modern mathematics as well as his own inner c- victions. Here we ?rst refer to an empirical fact of mathematical research: All topics have a ?nite half-life, with ?fteen years being an upper bound for most areas. After that time it is usually a good idea to move on to so- thing new.

InhaltsangabeThe Rosetta Stone of L-functions.- New Encounters in Combinatorial Number Theory: From the Kakeya Problem to Cryptography.- Perspectives and Challenges to Harmonic Analysis and Geometry in High Dimensions: Geometric Diffusions as a Tool for Harmonic Analysis and Structure Definition of Data.- Open Questions on the Mumford-Shah Functional.- Multi-scale Modeling.- Mass in Quantum Yang-Mills Theory (Comment on a Clay Millennium Problem).- On Scaling Properties of Harmonic Measure.- The Heritage of Fourier.- The Quantum-Mechanical Many-Body Problem: The Bose Gas.- Meromorphic Inner Functions, Toeplitz Kernels and the Uncertainty Principle.- Heat Measures and Unitarizing Measures for Berezinian Representations on the Space of Univalent Functions in the Unit Disk.- On Local and Global Existence and Uniqueness of Solutions of the 3D Navier-Stokes System on ?3.- Analysis on Lie Groups: An Overview of Some Recent Developments and Future Prospects.- Encounters with Science: Dialogues in Five Parts.