Geometric Analysis and Topology Seminar

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Notions of Differential Calculus on Metric Measure Spaces

Speaker: Nicola Gigli, SISSA

Location: Warren Weaver Hall 517

Date: Friday, April 22, 2016, 11 a.m.

Synopsis:

I shall discuss in which sense generic metric measure spaces possess a weak first-order differential structure. Building on this, I will then turn to spaces with Ricci curvature bounded from below and illustrate how a second-order calculus can be built on them. In particular, concepts like Hessian, covariant derivative and Ricci curvature will all be well defined.