Ricci Curvature and Differential Harnack Inequalities on Path Space

Mercredi 27 mai 16:00-18:00 - Aaron Charles Naber - Northwestern

Résumé : There has been an observation of late that many analytic estimates on manifolds M with lower Ricci curvature bounds have counterparts on the path space PM of the manifold when there are two sided bounds on Ricci curvature. We will begin reviewing some of these, in particular the estimates of [Nab],[Has-Nab] which generalize the Bakry-Emery-Ledoux estimates to path space. We will then discuss new results, which are joint with Haslhofer and Knofer, which generalize the Li-Yau differential harnack inequalities to the path space, under the assumption of two sided Ricci curvature bounds.
To accomplish this, we will introduce a family of Laplace operators on PM, built from finite dimensional traces of the Markovian hessian. The differential harnacks will take the form of differential inequalities for these operators, and will recover the classical Li-Yau when applied the simplest functions on path space, namely the cylinder functions of one variable.

Lieu : Demander le lien Zoom à jean-michel.bismut@u-psud.fr

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