The Center for Applied Mathematical Sciences is an organized research unit
based in the Department of Mathematics
The purpose of CAMS is to foster research and graduate education in
Mathematics in a broad sense and in an interdisciplinary mode. One goal
of the center's participants is to facilitate and encourage the development of
applicable mathematics and its utilization in problems in engineering and the
CAMS Prize Winners
Winners of the CAMS Graduate Student Prize for Excellence in Research with a Substantial Mathematical Component.
Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or even larger. In such settings, there is a common remedy for both statistical problems: nonlinear shrinkage of the eigenvalues of the sample covariance matrix. The optimal nonlinear shrinkage formula...
We develop a scattering theory for a class of eternal solutions of the Boltzmann equation posed over all space. In three spatial dimensions each of these solutions has thirteen conserved quantities. The Boltzmann entropy has a unique minimizer with the same thirteen conserved values. This minimizer is a local Maxwellian that is also a global solution of the Boltzmann equation --- a so-called global Maxwellian. We show that each...