P A U L    B O U R G A D E 


I spend the 2013-2014 year in Princeton, at the Institute for advanced study.
My research interests lie in probability, in particular random matrices, statistical physics, their links with analytic number theory, and stochastic processes.

Teaching
Spring 2013Analytic Number Theory
Fall 2012Random Matrices and Number Theory
Spring 2012Probability
Fall 2011Dynamical Systems
Spring 2011Algebraic Combinatorics
Fall 2010Stochastic Analysis
Research
The eigenvector moment flow and local quantum unique ergodicity, with H.-T. Yau, preprint.
Edge Universality of β-ensembles, with L. Erdős and H.-T. Yau, preprint.
Bulk universality for one-dimensional log-gases, a note to appear in the XVIIth International Congress On Mathematical Physics, World Scientific Publishing.
The local circular law II: the edge case, with H.-T. Yau and J. Yin, to appear in Probability Theory and Related Fields.
The local circular law for random matrices, with H.-T. Yau and J. Yin, to appear in Probability Theory and Related Fields.
Strong Szegő asymptotics and zeros of the ζ  function, with J. Kuan, to appear in Communications on Pure and Applied Mathematics.
Bulk universality of general β-ensembles with non-convex potential, with L. Erdős and H.T. Yau, to appear in J. of Math. Phys., special issue in honor of E. Lieb's 80th birthday.
Universality of general β-ensembles , with L. Erdős and H.T. Yau, to appear in Duke Math. Journal.
Extreme gaps in the eigenvalues of random matrices , with G. Ben Arous, Annals of Probability vol 41 n 4, 2648-2681 (2013).
A unitary extension of virtual permutations, with J. Najnudel and A. Nikeghbali, to appear in International Mathematical Research Notices.
Quantum chaos, random matrix theory, and the Riemann ζ  function , with J. Keating, to appear in the proceedings of the Séminaire Poincaré, Birkhauser.
Mesoscopic fluctuations of the ζ zeros, Probability Theory and Related Fields, Volume 148, Numbers 3-4, 479-500, 2010.
Circular Jacobi ensembles and deformed Verblunsky coefficients, with A. Nikeghbali and A. Rouault, International Mathematical Research Notices, Vol. 2009, no. 23, 4357-4394.
Conditional Haar measures on classical compact groups, Annals of Probability vol 37, no. 4, 1566-1586, 2009.
Ewens measures on compact groups and hypergeometric kernels, with A. Nikeghbali and A. Rouault, Séminaire de Probabilités XLIII, 351-377, Springer, 2011.
The characteristic polynomial on compact groups with Haar measure: some equalities in law, with A. Nikeghbali and A. Rouault, Comptes Rendus de l'Ac. des Sc., 345, 4, 2007.
Euler's formula for ζ(2n) and products of Cauchy variables, with T. Fujita and M. Yor, Electronic Communications in Probability 12, 73-80, 2007.
The characteristic polynomial of a random unitary matrix: a probabilistic approach, with C.P. Hughes, A. Nikeghbali and M. Yor, Duke Math. Journal vol 145, no. 1, 45-69, 2008.
Various texts
Stochastic Analysis, lecture notes from my graduate course given in Fall 2010 (this version: 2012, 120p.).
Tea time in Princeton, an expository article about the analogies between the statistics of random eigenvalues and zeros of L-functions, Harvard College Math. Review (2012).
On random matrices and L-functions, my Ph.D. thesis, under supervision of M. Yor (this version: 2010).
Lois de Poisson-Dirichlet, my senior thesis, about the occurrences of this measure for excursions and the distribution of large prime factors (in French, 2007).
Annales des Olympiades internationnales de mathématiques, published by the éditions Cassini (in French, 2005).
Conferences
Seminars
The Harvard Probability Seminar.
Random Matrices, Random Geometry, a joint Harvard-MIT probability afternoon.
Mathematics seminars in Harvard, Probability seminars in Paris.
The conference in honor of A.S. Üstünel for his 60th birthday.
The Random Matrices conference, at Institut Henri Poincaré.
The Stochastic Analysis seminar, at Institut Henri Poincaré.

Contact

email
bourREMOVETHISTEXTgade@math.harvard.edu
address
1 Oxford Street
Cambridge, MA 02138, USA

Here is my curriculum vitae.