# Capital Fund Management sponsors postdocs in random matrix theory

The Department of Mathematics announces the sponsorship of postdoctoral research by Capital Fund Management (CFM). CFM is an investment management firm whose investment strategy is based on a quantitative and scientific approach to financial markets. The sponsor provides support for postdoctoral fellows at UCLA working in Random Matrix Theory and its application to data science. The research sponsored by CFM may also be related to statistical physics, computational biology, high dimensional inference, machine learning and related fields.

The first CFM postdoctoral fellow is Nick Cook (pictured on the left, next to CFM's co-CEO and head of research, Marc Potters) who also has support from the US National Science Foundation. Cook completed his PhD at UCLA in 2016 under the direction of Terence Tao and spent his first postdoctoral year at Stanford as an NSF Postdoctoral Fellow, working with Amir Dembo. His mentor at UCLA is Prof. Jun Yin, new to UCLA in the past year.

**About Cook’s research**

The study of eigenvalues of large random matrices goes back to influential work of Wigner (1955), who sought a model for the energy levels of heavy nuclei. Since then random matrices have been used to elucidate a diverse range of phenomena, from the stability of ecological and neurological systems, to liquid crystal growth, to quantum gravity. There are also tantalizing similarities between statistics of the eigenvalues of large random unitary matrices and the zeros of the Riemann zeta function.

The appearance of a few characteristic properties of random matrix eigenvalues in such a diverse range of systems is an instance of the *universality phenomenon*. Our present understanding of universality is largely confined to matrices whose entries are independent and identically distributed (iid) random variables. Cook’s work has focused on extending some of these universal laws to sparse random matrices with non-iid entries, which are of interest in neuroscience and ecology. With the CFM sponsorship, Cook will turn to the study of random matrix eigenvectors, which are less understood than eigenvalues, and which have important applications to graph theory and finance.