Welcome to CAMS
The Center for Applied Mathematical Sciences is an organized research unit
based in the Department of Mathematics
at USC.
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
sciences.
The mission of the Center is threefold.
 To maintain USC's position as an internationallyrecognized center in
several important and well defined areas of mathematics and its applications
 To be a muchneeded interface between the Department of Mathematics and
other USC departments and institutions outside USC.
 To serve as a catalyst in the development of stateoftheart
activities in applicable mathematics at USC.
CAMS Prize Winners
Winners of the CAMS Graduate Student Prize for Excellence in Research with a Substantial Mathematical Component.
Anand Kumar Narayanan 
Ibrahim Ekren 
Sushmita Allam 
WanJung Kuo 
Yang Huang 





Computer Science 
Mathematics 
Biomedical Engineering 
Physics 
Mathematics 





Upcoming Colloquium
3:30 PMKAP 414

Nets Katz
Caltech
Monday, October 13

On the three dimensional Kakeya problem
We discuss new ideas for obtaining lower bounds on the Hausdorff dimension of Kakeya sets. We discuss joint work in progress with Josh Zahl. Sometimes less is more.


Upcoming Colloquium
3:30 PMKAP 414

Charles Doering
University of Michigan
Monday, October 20

Wall to wall optimal transport
How much stuff can be transported by an incompressible flow containing a specified amount of kinetic energy or enstrophy? We study this problem for steady 2D flows focusing on passive tracer transport between two parallel impermeablewalls, employing the calculus of variations to find divergencefree velocity field with a given intensity budget that maximize transport between the walls. The maximizing velocity fields, i.e. the optimal...


Upcoming Colloquium
3:30 PMKAP 414

Tristan Buckmaster
Courant Institute
Monday, October 27

Onsager's Conjecture
In 1949, Lars Onsager in his famous note on statistical hydrodynamics conjectured that weak solutions to the Euler equation belonging to Hölder spaces with Hölder exponent greater than 1/3 conserve energy; conversely, he conjectured the existence of solutions belonging to any Hölder space with exponent less than 1/3 which dissipate energy. The first part of this conjecture has since been confirmed (cf. Eyink 1994, Constantin, E and...


Upcoming Colloquium
3:30 PMKAP 414

Michael Wolf
University of Zurich
Monday, November 03

Spectrum Estimation: A Unified Framework for Covariance Matrix Estimation and PCA in Large Dimensions
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...



