Thursday, April 27, 2023 - 15:00 in V2-210/216
Characterising gradient flows
A talk in the Mathematisches Kolloquium & Mathematisches Kolloquium (SFB 1283) series by
Jan Maas from IST Austria
| Abstract: |
This talk deals with the following general question: consider a vector field $v$ and a functional $F$ on a smooth manifold $M$. Does there exist a Riemannian metric on $M$ that turns the ODE $\dot x = v(x)$ into a gradient flow for $F$? The existence of such a gradient flow structure is often very helpful in the analysis of the equation.
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).
Within the CRC this talk is associated to the project(s): A8 |
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