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Upcoming Programs

  1. New Challenges in PDE: Deterministic Dynamics and Randomness in High and Infinite Dimensional Systems

    Organizers: Kay Kirkpatrick (University of Illinois at Urbana-Champaign), Yvan Martel (École Polytechnique), Jonathan Mattingly (Duke University), Andrea Nahmod (University of Massachusetts, Amherst), Pierre Raphael (Universite de Nice Sophia-Antipolis), Luc Rey-Bellet (University of Massachusetts, Amherst), LEAD Gigliola Staffilani (Massachusetts Institute of Technology), Daniel Tataru (University of California, Berkeley)

    The fundamental aim of this program is to bring together a core group of mathematicians from the general communities of nonlinear dispersive and stochastic partial differential equations whose research contains an underlying and unifying problem: quantitatively analyzing the dynamics of solutions arising from the flows generated by deterministic and non-deterministic evolution differential equations, or dynamical evolution of large physical systems, and in various regimes. 

    In recent years there has been spectacular progress within both communities in the understanding of this common problem. The main efforts exercised, so far mostly in parallel, have generated an incredible number of deep results, that are not just beautiful mathematically, but are  also important to understand the complex natural phenomena around us.  Yet, many open questions and challenges remain ahead of us. Hosting the proposed program at MSRI would be the most effective venue to explore the specific questions at the core of the unifying theme and to have a focused and open exchange of ideas, connections and mathematical tools leading to potential new paradigms.  This special program will undoubtedly produce new and fundamental results in both areas, and possibly be the start of a new generation of researchers comfortable on both languages.

    Updated on Dec 23, 2013 08:59 AM PST
  2. Differential Geometry

    Organizers: Tobias Colding (Massachusetts Institute of Technology), Simon Donaldson (Imperial College, London), John Lott (University of California, Berkeley), Natasa Sesum (Rutgers University), Gang Tian (Princeton University), LEAD Jeff Viaclovsky (University of Wisconsin)

    Differential geometry is a subject with both deep roots and recent advances. Many old problems in the field have recently been solved, such as the Poincaré and geometrization conjectures by Perelman, the quarter pinching conjecture by Brendle-Schoen, the Lawson Conjecture by Brendle, and the Willmore Conjecture by Marques-Neves. The solutions of these problems have introduced a wealth of new techniques into the field. This semester-long program will focus on the following main themes:
    (1) Einstein metrics and generalizations,
    (2) Complex differential geometry,
    (3) Spaces with curvature bounded from below,
    (4) Geometric flows,
    and particularly on the deep connections between these areas.

    Updated on Dec 19, 2014 03:19 PM PST
  3. Geometric Group Theory

    Organizers: Ian Agol (University of California, Berkeley), Mladen Bestvina (University of Utah), Cornelia Drutu (University of Oxford), Mark Feighn (Rutgers University), Michah Sageev (Technion---Israel Institute of Technology), LEAD Karen Vogtmann (Cornell University)

    The field of geometric group theory emerged from Gromov’s insight that even mathematical objects such as groups, which are defined completely in algebraic terms, can be profitably viewed as geometric objects and studied with geometric techniques Contemporary geometric group theory has broadened its scope considerably, but retains this basic philosophy of reformulating in geometric terms problems from diverse areas of mathematics and then solving them with a variety of tools. The growing list of areas where this general approach has been successful includes
    low-dimensional topology, the theory of manifolds, algebraic topology, complex dynamics, combinatorial group theory, algebra, logic, the study of various classical families of groups, Riemannian geometry and representation theory.

    The goals of this MSRI program are to bring together people from the various branches of the field in order to consolidate recent progress, chart new directions, and train the next generation of geometric group theorists.

    Updated on Oct 11, 2013 02:11 PM PDT