3:00 p.m., Wednesday (January 16, 2008)
WMAX 110 (PIMS)
University of Toronto
Curvature and continuity of optimal transport
Abstract: In optimal transport theory, one wants to understand optimizing
phenomena occurring when transporting mass distributions in
Economics, Physics, Probability, Analysis, Geometry, and Biology. In
this talk, we will discuss continuity of optimal transport maps, in
view of a pseudo-Riemannian structure which we have formulated
recently. Curvature of this geometry plays an essential role for
continuity of optimal transportation. This natural geometric
framework provides new methods, elementary proofs and extensions of
some key ingredients in the regularity theory of Ma, Trudinger, Wang,
and Loeper. It also provides new examples, perspectives and research
This is joint work with Robert McCann (University of Toronto).
Refreshments will be served at 2:45 p.m. (PIMS Lounge).