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  1. Program New Geometric Methods in Number Theory and Automorphic Forms

    Organizers: Pierre Colmez (L'Institut de Mathématiques de Jussieu), LEAD Wee Teck Gan (National University of Singapore), Michael Harris (L'Institut de Mathématiques de Jussieu), Elena Mantovan (California Institute of Technology), Ariane Mézard (L'Institut de Mathématiques de Jussieu), Akshay Venkatesh (Stanford University)

    The branches of number theory most directly related to the arithmetic of automorphic forms have seen much recent progress, with the resolution of many longstanding conjectures. These breakthroughs have largely been achieved by the discovery of new geometric techniques and insights. The goal of this program is to highlight new geometric structures and new questions of a geometric nature which seem most crucial for further development. In particular, the program will emphasize geometric questions arising in the study of Shimura varieties, the p-adic Langlands program, and periods of automorphic forms.

    Updated on Oct 11, 2013 02:02 PM PDT
  2. Program Geometric Representation Theory

    Organizers: LEAD David Ben-Zvi (University of Texas), Ngô Bảo Châu (University of Chicago), Thomas Haines (University of Maryland), Florian Herzig (University of Toronto), Kevin McGerty (University of Oxford), David Nadler (University of California, Berkeley), Catharina Stroppel (Hausdorff Research Institute for Mathematics, University of Bonn), Eva Viehmann (TU München)

    The fundamental aims of geometric representation theory are to uncover the deeper geometric and categorical structures underlying the familiar objects of representation theory and harmonic analysis, and to apply the resulting insights to the resolution of classical problems. One of the main sources of inspiration for the field is the Langlands philosophy, a vast nonabelian generalization of the Fourier transform of classical harmonic analysis, which serves as a visionary roadmap for the subject and places it at the heart of number theory. A primary goal of the proposed MSRI program is to explore the potential impact of geometric methods and ideas in the Langlands program by bringing together researchers working in the diverse areas impacted by the Langlands philosophy, with a particular emphasis on representation theory over local fields.

    Another focus comes from theoretical physics, where new perspectives on the central objects of geometric representation theory arise in the study supersymmetric gauge theory, integrable systems and topological string theory. The impact of these ideas is only beginning to be absorbed and the program will provide a forum for their dissemination and development.

    Updated on Aug 13, 2014 09:08 AM PDT
  3. Workshop Breaking the Neural Code

    Organizers: Larry Abbott (Columbia University), Ingrid Daubechies (Duke University), Michael Jordan (University of California), LEAD Liam Paninski (Columbia University)

    For decades, neuroscientists have dreamed about the possibility of recording from all the neurons in a brain, or of having access to a complete large brain wiring diagram, or ideally to obtain both of these datasets simultaneously, in the same brain.  Recent technical advances have brought this dream close to reality in some cases.  Now the challenge will be to understand these massive datasets.  A few domains will be particularly relevant:

    • Inferring network structure from noisy and incomplete data
    • Inferring computational input-output function from structure
    • Optimal experimental design (incl. compressive sensing methods) for observation of networks
    • Modeling structured stochastic network dynamics
    • Optimal control of network dynamics
    • Inferring low-dimensional dynamics from high-dimensional observations

    There’s a strong need in neuroscience for deep new ideas from mathematics and statistics, and our hope is that this small, focused workshop without many formal talks will spark collaborations that will lead to breakthroughs in the areas described above.

    This workshop is by invitation only.

    This workshop is supported by a generous donation from Sanford Grossman.

    Updated on Oct 29, 2014 12:22 PM PDT