. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
| |
Program Search
|
 |
| |
Upcoming Programs: |
| |
| Symplectic and Contact Geometry and Topology |
| August 17, 2009 to May 21, 2010 |
| Organized By: Yakov Eliashberg *(Stanford University), John Etnyre (Georgia Institute of Technology), Eleny-Nicoleta Ionel (Stanford University), Dusa McDuff (Barnard College), and Paul Seidel (Massachusetts Institute of Technology) |
| In the slightly more than two decades that have elapsed since the fields of Symplectic and Contact Topology were created, the field has grown enormously and unforeseen new connections within Mathematics and Physics have been found. The goals of the 2009-10 program at MSRI are to:
I. Promote the cross-pollination of ideas between different areas of symplectic and contact geometry;
II. Help assess and formulate the main outstanding fundamental problems and directions in the field;
III. Lead to new breakthroughs and solutions of some of the main problems in the area;
IV. Discover new applications of symplectic and contact geometry in mathematics and physics;
V. Educate a new generation of young mathematicians, giving them a broader view of the subject and the capability to employ techniques from different areas in their research. |
| |
| Tropical Geometry |
| August 17, 2009 to December 18, 2009 |
| Organized By: Eva-Maria Feichtner *(University of Bremen), Ilia Itenberg (Institut de Recherche Mathématique Avancée de Strasbourg), Grigory Mikhalkin (Université de Genève), and Bernd Sturmfels (UCB - University of California, Berkeley) |
| Tropical Geometry is the algebraic geometry over the min-plus algebra. It is a young subject that in recent years has both established itself as an area of its own right and unveiled its deep connections to numerous branches of pure and applied mathematics. From an algebraic geometric point of view, algebraic varieties over a field with non-archimedean valuation are replaced by polyhedral complexes, thereby retaining much of the information about the original varieties. From the point of view of complex geometry, the geometric combinatorial structure of tropical varieties is a maximal degeneration of a complex structure on a manifold.
The tropical transition from objects of algebraic geometry to the polyhedral realm is an extension of the classical theory of toric varieties. It opens problems on algebraic varieties to a completely new set of techniques, and has already led to remarkable results in Enumerative Algebraic Geometry, Dynamical Systems and Computational Algebra, among other fields, and to applications in Algebraic Statistics and Statistical Physics. |
| |
| Homology Theories of Knots and Links |
| January 11, 2010 to May 21, 2010 |
| Organized By: Mikhail Khovanov (Columbia University), Dusa McDuff (Barnard College), Peter Ozsváth* (Columbia University), Lev Rozansky (University of North Carolina), Peter Teichner (University of California, Berkeley), Dylan Thurston (Barnard College), and Zoltan Szabó (Princeton University) |
The aims of this program will be to achieve the following goals:
- Promote communication with related disciplines, including the symplectic geometry program in 2009-2010.
- Lead to new breakthroughs in the subject and find new applications to low dimensional topology (knot theory, three-manifold topology, and smooth four manifold topology).
- Educate a new generation of graduate students and PhD students in this exciting and rapidly-changing subject.
The program will focus on algebraic link homology and Heegaard Floer homology. |
| |
| Random Matrix Theory, Interacting Particle Systems and Integrable Systems |
| August 16, 2010 to December 17, 2010 |
| Organized By: Jinho Baik (University of Michigan), Alexei Borodin (California Institute of Technology), Percy A. Deift* (New York University, Courant Institute), Alice Guionnet (École Normale Supérieure de Lyon), Craig A. Tracy (University of California, Davis), and Pierre van Moerbeke, (Université Catholique de Louvain) |
| The goal of this program is to showcase the many remarkable developments that have taken place in the past decade in Random Matrix Theory (RMT) and to spur on further developments on RMT and the related areas Interacting Particle Systems (IPS) and Integrable Systems (IS): IPS provides an arena in which RMT behavior is frequently observed, and IS provides tools which are often useful in analyzing RMT and IPS/RMT behavior. |
| |
| Inverse Problems and Applications |
| August 16, 2010 to December 17, 2010 |
| Organized By: Liliana Borcea (Rice University), Maarten V. de Hoop (Purdue University), Carlos E. Kenig (University of Chicago), Peter Kuchment (Texas A&M University), Lassi Päivärinta (University of Helsinki), Gunther Uhlmann* (University of Washington), and Maciej Zworski (University of California, Berkeley) |
| 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. During the last 10 yeas or so there has been
significant developments both in the mathematical theory and applications
of inverse problems. The purpose of the program would be to bring together
people working on different aspects of the field, to appraise the current
status of development and to encourage interaction between mathematicians
and scientists and engineers working directly with the applications. |
| |
| Free Boundary Problems, Theory and Applcations |
| January 10, 2011 to May 20, 2011 |
| Organized By: Luis Caffarelli (University of Texas), Henri Berestycki (Centre d’Analyse et de Math´ematique Sociales), Laurence C. Evans (University of California), Mikhail Feldman (University of Wisconsin, Madison), John Ockendon (University of Oxford), Arshak Petrosyan (Purdue University), Henrik Shahgholian* (The Royal Institute of Technology), Tatiana Toro (University of Washington), and Nina Uraltseva (Steklov Mathematical Institute (POMI) |
| This program aims at the study of various topics within the area of Free Boundaries Problems, from the viewpoints of theory and applications.
Many problems in physics, industry, finance, biology, and other areas can be
described by partial differential equations that exhibit apriori unknown sets, such
as interfaces, moving boundaries, shocks, etc. The study of such sets, also known
as free boundaries, often occupies a central position in such problems. The aim of
this program is to gather experts in the field with knowledge of various applied and
theoretical aspects of free boundary problems. |
| |
| Arithmetic Statistics |
| January 10, 2011 to May 20, 2011 |
| Organized By: Brian Conrey (American Institute of Mathematics), John Cremona (University of Warwick), Barry Mazur (Harvard University), Michael Rubinstein* (University of Waterloo), Peter Sarnak (Princeton University), Nina Snaith (University of Bristol), and William Stein (University of Washington) |
| L -functions attached to modular forms and/or to algebraic varieties and algebraic number fields are prominent in quite a wide range of number theoretic issues, and our recent growth of understanding of the analytic properties of L-functions has already lead to profound applications regarding among other things the statistics related to arithmetic problems. This program will emphasize statistical aspects of L-functions, modular forms, and associated arithmetic and algebraic objects from several different perspectives — theoretical, algorithmic, and experimental. |
| |
