Gerard Ben Arous
New York University
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Primary Section: 32, Applied Mathematical Sciences Membership Type:
Member
(elected 2020)
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Biosketch
Gérard Ben Arous is a mathematician, interested in randomness and disorder. He works on probability theory and its connections with statistical physics, statistics and data science, industrial applications as well as other domains of mathematics, mainly analysis and differential geometry. Gérard Ben Arous grew up in Paris. He graduated from Ecole Normale Supérieure, and received his masters and doctorate degrees from the University of Paris. After a junior position at Ecole Normale Superieure, he joined the faculty at Orsay in 1988 where he chaired the Mathematics department, and came back to Ecole Normale Superieure as the director of the department of Mathematics and Computer Science, before moving to EPFL in Lausanne, Switzerland in 1997, where he held the Chair of Stochastic Modeling and founded the Bernoulli Institute. He joined the Courant Institute at NYU in 2002, and has been its director from 2011 to 2016.
Research Interests
Gérard Ben Arous’s work began with the study of the geometry of hypo-elliptic operators and their heat kernels, using the tools of stochastic analysis and of large deviations theory. These tools were then used to understand a rather different field i.e. dynamical phase transitions and aging phenomena in statistical physics, and in particular for the dynamics of Spin Glasses, or for the questions of anomalously slow diffusion in random media, which both exhibit a common feature of gradual exploration of complex random trapping landscapes. Some of these questions asked for a better understanding of questions of Random Matrix Theory, as large deviations, or the phase transition for the top eigenvalue of a random matrix submitted to a finite rank perturbation.
More recently the nature of the spin glass phase at low temperature has been approached using a better understanding of the topological and geometric complexity of high dimensional random functions. This approach relies again on the tools of Random Matrix Theory. The hypothesis that the loss landscapes of Data Science and Machine learning might show the same type of complexity has been explored recently, as well as the potential role of this complexity vs the strength of the signal on the optimization dynamics of high dimensional inference.
