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\textsc{Joint SIAM Student Chapter and Dixieland Analysis Seminar}
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\textit{Extremal doubly stochastic measures and optimal transportation}
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Prof. Robert J. McCann\par
Mathematics Department, University of Toronto
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\textbf{Abstract:} Square N by N matrices with non-negative entries whose columns and rows all sum to one form a convex set with N! vertices. Each vertex corresponds to a permutation on N letters, according to a theorem of Birkhoff and von Neumann.
In 1948 Birkhoff asked what the infinite dimensional analog of this theorem should be. We resolve this problem, by giving a condition on the support of a measure on the square which characterizes extremality among non-negative measures with the same x- and y-marginal projections. Our condition is used to derive a new sufficient condition for uniqueness of minimizer in Kantorovich's optimal transportation problem, in terms of the topology of the transportation cost.\vspace{\fill}
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Monday, November 12, 2007, 4:30 pm\par
Mathematics and Science Center: W301
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Refreshments will be served at 4:00pm in the Department Lounge.
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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