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SUMMARY:Aaron Naber (Northwestern University)
DTSTART:20200716T140000Z
DTEND:20200716T145000Z
DTSTAMP:20260423T052459Z
UID:IMS/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IMS/41/">Ric
 ci Curvature and Differential Harnack Inequalities on Path Space.</a>\nby 
 Aaron Naber (Northwestern University) as part of PDE seminar via Zoom\n\n\
 nAbstract\nThere has been an observation of late that many analytic estima
 tes 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 est
 imates of [Nab]\,[Has-Nab] which generalize the Bakry-Emery-Ledoux estimat
 es to path space.  We will then discuss new results\, which are joint with
  Haslhofer and Knofer\, which generalize the Li-Yau differential harnack i
 nequalities to the path space\, under the assumption of two sided Ricci cu
 rvature bounds.  \n\nTo accomplish this\, we will introduce a family of La
 place operators on path space PM\,  built from finite dimensional traces o
 f the Markovian hessian\, which we will review.  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.\n
LOCATION:https://researchseminars.org/talk/IMS/41/
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