Random matrix theory (RMT) was introduced into the theoretical physics community by Eugene Wignerinthe 1950s as a model for the scattering resonances of neutrons off large nuclei. In multivariate statistics, random matrix models were introduced in the late 1920s by John Wishart and subsequently developed by Anderson, James and others. Since these early beginnings RMT has found an extraordinary variety of mathematical, physical and engineering applications that, to name some, include number theory, stochastic growth models, tiling problems and wireless communications.

 

This workshop will provide a forum for researchers on both sides (and the middle!) of hybrid symbolic-numeric computation. We anticipate inviting as primary speakers some of the original contributors in the field, as well as younger researchers making strong contributions on different aspects of the field.


 

Inverse Problems are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth's substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes, and modelling in the life sciences.
The speakers in the workshop will cover a broad range of the most recent developments in the theory and applications of inverse problems.





 

This workshop will focus on the ideas surrounding the recent solution to the Arf-Kervaire invariant problem in stable homotopy theory by Mike Hill, Mike Hopkins and Doug Ravenel. There will be talks on relevant aspects of equivariant stable homotopy theory, including the norm functor and the slice tower. The pertinent parts of chromatic homotopy theory will be covered including formal groups and formal $A$-modules, the Hopkins-Miller theorem, finite subgroups of Morava stabilizer groups and Ravenel's 1978 solution to the analogous problem at primes bigger than 3. There will also be several talks by the organizers giving a detailed account of the proof of the main theorem. Finally there will be a discussion of the questions raised by the unexpected statement of the theorem.




 

Topics covered in this workshop will include fundamental problems in random matrices, including universality questions and connections to physics, free probability, Riemann Hilbert problems and applications to other areas of mathematics such as number theory and numerical analysis.

In the spring of 1999, MSRI hosted a very successful and influential one-semester program on RMT and its applications. At the workshops during the semester, there was a sense of excitement as brand new and very recent results were reported. The goal of the 2010 Program is to showcase the many remarkable developments that have taken place since 1999 and to spur further developments in RMT and Related areas of interacting particle systems (IPS) and integrable systems (IS) as well as to highlight various applications of RMT.

Inverse Problems are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth’s substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modelling in the life sciences.