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Mathematical Physics Seminar

A Gaussian Gibbs variational principle and geometric inequalities

Location:  Hill 705
Date & time: Thursday, 22 September 2016 at 12:00PM - 12:11PM

Ramon van Handel , Princeton University: The Gibbs variational principle has been a cornerstone of statistical mechanics since at least J. W. Gibbs' seminal 1902 treatise. It has also proved to be remarkably useful in other areas of mathematics, such as in the study of geometric inequalities of Brunn-Minkowski and Brascamp-Lieb type. This fundamental connection, pioneered by C. Borell, is however not sufficiently powerful to obtain the sharp isoperimetric and Brunn-Minkowski inequalities for Gaussian measures. In this talk, I will describe an unexpected Gaussian refinement of the Gibbs variational principle that makes it possible to recover these sharp inequalities. I will aim to explain how this gives rise to new Gaussian inequalities---in particular, a Gaussian improvement of Barthe's reverse Brascamp-Lieb inequality---and why the apparent duality between the Prekopa-Leindler and Holder inequalities is manifestly absent in the Gaussian setting.

BROWN BAG LUNCH.....1-2:00pm

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Department of Mathematics

Department of Mathematics
Rutgers University
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