Euler-Poincare equation was introduced by Holm, Marsden and Ratiu. It can be viewed as a natural multi-dimensional generalization of the popular Camassa-Holm equations. I will discuss some recent results on this model.
Ergodic Theory & Statistical Mechanics
This weekly seminar welcomes many visiting speakers and also provides a forum for results by Princeton/IAS faculty and graduate students. While most talks focus on one of the two namesake topics, there tends to be overlap with other fields. Most recently, talks have included material on celestial mechanics, number theory, probability theory, the Schrodinger equation, spectral theory and Teichmueller theory.
University of British Columbia
We consider an asymptotic setting for ergodic operators generalizing that for the Szego theorem on the asymptotics of determinants of finite-dimensional restrictions of the Toeplitz operators.
Institute for Low Temperature Physics, Kharkiv, Ukraine
The restricted isometry property (RIP) is a compressed sensing matrix specification which leads to performance guarantees for a wide variety of sparse signal reconstruction algorithms.
I will discuss recent CLT type results for linear eigenvalue statistics and related objects in various ensembles of Random Matrices. Joint works with Lingyun Li (UC Davis) and Sean O'Rourke (Yale).