Math @ Duke

 November 01, 2008  Virginia Tech Math Contest
Victoria L. Hain, for ugrad, 2009/02/16 18:53:30
Saturday, November 1, 911:30
 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 0507, 2008  Gergen lectures
Yunliang Yu, 2008/04/24 08:40:13
Optimal Transport and Riemannian Geometry
1  The MongeKantorovich problem: The MongeKantorovich 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 [more]


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