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Optimal Transportation and Applications

Characterisation of gradient flows

speaker: Jan Maas (IST Austria)

abstract: Consider a vector field $v$ and a functional $F$ on a manifold $M$. Does there exist a Riemannian metric on $M$ that turns the ODE $\dot x = v(x)$ into a gradient flow for $F$? In this talk we present conditions on $v$ and $F$ that are necessary and sufficient. As an application we characterise the class of quantum Markov semigroups that arise as gradient flow of the von Neumann entropy. This answers a question that arose in joint work with E. Carlen. Joint work with Morris Brooks (IST Austria).

timetable:
Wed 26 Oct, 11:45 - 12:30, Aula Magna Bruno Pontecorvo
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