[math-ias] Analysis seminar on Tuesday, November 13 at 3:15pm

[Aynur Bulut]

Dear All,

This is a reminder that Eric Carlen (of Rutgers University) will give  
a talk at the Analysis seminar tomorrow.

Please find enclosed below the details.

Best, Aynur


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Analysis Seminar

Day: Tuesday, November 13, 2012
Time: 3:15pm - 4:15pm
Room: S-101
Speaker: Eric Carlen
Title: A Non-Commutative Analog of the 2-Wasserstein Metric for which  
the Fermionic Fokker-Planck Equation is Gradient Flow for the Entropy

Abstract:

The Fermionic Fokker-Planck equation is a quantum-mechanical analog of  
the classical Fokker-Planck equation with which it has much in common,  
such as the same optimal hypercontractivity properties. In this paper  
we construct a Riemannian metric on the space of density matrices that  
we show to be a natural analog of the classical $2$-Wasserstein  
metric, and we show that, in analogy with the classical case, the  
Fermionic Fokker-Planck equation is gradient flow in this metric for  
the relative entropy with respect to the ground state. We derive a  
number of consequences of this, such as a sharp Talagrand inequality  
for this metric, and we prove a number of results pertaining to this  
metric. Several open problems are raised. This is joint work with Jann  
Maas.