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Differential calculus on RCD spaces - part 1

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Speaker: 
Nicola Gigli
Affiliation: 
SISSA
Date: 
Mon, 2017-09-25 11:00 - 11:40
Location: 
MPIM Lecture Hall

In the lecture I will survey recent advances on calculus on RCD spaces. I shall start recalling how the concept of `L2-normed L1 module' allows to give a reasonable de finition of
(co)tangent space and to build a first-order theory on abstract metric measure spaces. The Bochner inequality, which properly interpreted de fines RCD spaces, will then allow
to build a second order calculus in such setting: we shall review it and, if time permits, see some applications to the study of geometry of RCD spaces.

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