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News in 2008 for Mathematics   Current...  ViewAll  Archive  RSS

  • November 01, 2008 - Virginia Tech Math Contest
    Victoria L. Hain, for ugrad, 2009/02/16 18:53:30

    Saturday, November 1, 9-11:30  

  • August 27, 2008 - Organizational DUMU meeting and Math 149S information session
    Victoria L. Hain, for ugrad, 2009/02/16 18:51:39

    August 27, 2008 at 7:30pm in Physics 128  

  • May 05-07, 2008 - Gergen lectures
    Yunliang Yu, 2008/04/24 08:40:13

    Optimal Transport and Riemannian Geometry

    1 - The Monge-Kantorovich problem: The Monge-Kantorovich problem asks about the most economic way to transport matter from one prescribed distribution to another one. Born in France around the time of the Revolution, this problem has become a classic one in probability and economics. At the end of the eighties, the independent works of Brenier, Cullen and Mather announced a sharp turn of the theory, with renewed interest by the analysts. The speaker will present a summary of the modern theory of this problem.
    Monday, May 5, 2008 at 4:00 p.m. in Physics 128

    2 - Monge, Boltzmann and Ricci: Starting from works of Otto and Villani, it was understood that Ricci curvature bounds are intimately linked with the behavior of Boltzmann's entropy functional along geodesics (in the space of probability measures on the manifold of interest) induced by the optimal transport problem. This observation can be exploited to give a new point of view of Ricci curvature, with probabilistic and geometric applications (one is the weak stability of Ricci curvature bounds, which was proven independently by Lott and Villani, and by Sturm).
    Tuesday, May 6, 2008 at 4:00 p.m. in Physics 119

    3 - Regularity, curvature and the cut locus: The regularity of optimal transport in curved geometry is a singularly difficult problem because of the sharp interaction between geometry and analysis. In connection with this problem a new curvature tensor has been introduced by Ma, Trudinger and Wang; it plays a key role in the analysis of the smoothness of optimal transport. As shown in a work with Loeper, this tensor also has striking implications about the shape of the cut locus.
    Wednesday, May 7, 2008 at 4:00 p.m. in Physics 119

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