Technion - Israel Institute of Technology
          Department of Mathematics
Please note the special date, time, and place!!!
DATE:  Wednesday, March 28, 2012
SPEAKER: Alexander Kolesnikov (Moscow)
TITLE: Hessian metrics, $C(N,K)$-spaces, and optimal transportation
PLACE: Room 719, Amado Mathematics Building, Technion
TIME:  13:30 
ABSTRACT: Hessian manifolds are Riemannian manifolds with metrics
which can be locally written as the Hessian
of a potential function $\Phi$: $g=\mathrm{Hess}\, \Phi$. We consider
a special case when $\nabla \Phi$ is the optimal transportation
pushing forward a  (log-concave) probability measure $\mu$  onto
another (log-concave) probability measure.
We discuss analytic and geometric properties of the  metric-measure
space $M=(\mathbb{R}^d, g, \mu)$, and prove, in particular,
sufficient conditions for $M$ to belong to the family of
$C(N,K)$-spaces. Applications  of these results include some
dimension-free bounds on the operator norm $\| D^2 \Phi\|$.
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