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SUMMARY:Dirichlet spaces with distribution-valued Ricci bounds.
DTSTART:20240528T133000Z
DTEND:20240528T143000Z
DTSTAMP:20240529T125100Z
UID:indico-event-11930@indico.math.cnrs.fr
DESCRIPTION:Speakers: Chiara Rigoni (UniversitĂ© de Vienne (Autriche))\n\n
After recalling the two main approaches to the theory of synthetic Ricci b
ounds\, I will present the theory of "tamed spacesâ€ť\, which are Dirichle
t spaces with distribution-valued lower bounds on the Ricci curvature seen
from an Eulerian point of view. In particular\, the approach is based on
the analysis of singular perturbations of Dirichlet forms by a broad class
of distributions. The distributional Ricci bound is then formulated in te
rms of an integrated version of the Bochner inequality generalizing the we
ll-known Bakry-Emery curvature-dimension condition. Among other things\, w
e show the equivalence of distributional Ricci bounds to gradient estimate
s for the heat semigroup as well as consequences in terms of functional in
equalities. Examples of tamed spaces include in particular Riemannian mani
folds with either interior singularities or singular boundary behavior.Thi
s is a joint work with Matthias Erbar\, Theo Sturm\, and Luca Tamanini.\n\
nhttps://indico.math.cnrs.fr/event/11930/
LOCATION:Fokko (ICJ)
URL:https://indico.math.cnrs.fr/event/11930/
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