Ashkan Nikeghbali

Nikeghbali just received his Ph.D. from the University of Paris under the direction of Marc Yor. His thesis consists of 10 papers, mostly on the topic of random times with respect to different filtrations. In probability theory, filtrations represent the information available at the current time. Stopping times are those times which can be determined without being able to forsee the future. Stopping times are very important in practice, and their properties are well studied. Nikeghbali has identified a class of random times which enjoy many of the properties of stopping times. Not much was previously known about random times which are not stopping times. This work has already had applications to mathematical finance. In collaboration with Chris Hughes of the American Institute of Mathematics, Nikeghbali has recently solved some long-standing problems about the zeros of random polynomials.

Nikeghbali is being supported by Steve Gonek's focused research grant in number theory. One of the most amazing mathematical discoveries in recent years involves a deep connection between probability and number theory. The primes are thought to have many of the properties of a random sequence. In particular, the zeros of the Riemann zeta function, which give crucial information about primes, have much in common with the eigenvalues of random matrices. Nikeghbali plans to use his expertise in probability to study this connection.