P A U L    B O U R G A D E 


My research interests lie in probability, in particular random matrices, statistical physics, their links with analytic number theory, and stochastic processes.

Teaching
Fall 2016Stochastic Analysis
Fall 2015Probability
Spring 2015Random Matrix Theory
Fall 2014Probability
Spring 2013Analytic Number Theory
Fall 2012Random Matrices and Number Theory
Spring 2012Probability
Fall 2011Dynamical Systems
Spring 2011Algebraic Combinatorics
Fall 2010Stochastic Analysis
Research
Universality for a class of random band matrices, with L. Erdős, H.-T. Yau and J. Yin, prepublication, 2016.
Maximum of the characteristic polynomial of random unitary matrices, with L.-P. Arguin and D. Belius, to appear in Communications in Mathematical Physics, 2016.
Local density for two-dimensional one-component plasma, with R. Bauerschmidt, M. Nikula and H.-T. Yau, prepublication, 2015.
Fixed energy universality for generalizd Wigner matrices, with L. Erdős, H.-T. Yau and J. Yin, to appear in Communications on Pure and Applied Mathematics, 2016.
The eigenvector moment flow and local quantum unique ergodicity, with H.-T. Yau, to appear in Communications in Mathematical Physics, 2016.
Edge Universality of β-ensembles, with L. Erdős and H.-T. Yau, Communications in Mathematical Physics, vol. 332, no. 1, 261-353, 2014.
Bulk universality for one-dimensional log-gases, proceedings of the XVIIth International Congress On Mathematical Physics, World Scientific Publishing, 2013.
The local circular law II: the edge case, with H.-T. Yau and J. Yin, Probability Theory and Related Fields, vol. 159, no. 3-4, 619-660, 2014.
The local circular law for random matrices, with H.-T. Yau and J. Yin, Probability Theory and Related Fields, vol. 159, no. 3-4, 545-595, 2014.
Strong Szegő asymptotics and zeros of the ζ  function, with J. Kuan, Communications on Pure and Applied Mathematics, vol. 67, mo. 6, 1028–1044, 2014.
Bulk universality of general β-ensembles with non-convex potential, with L. Erdős and H.T. Yau, J. of Math. Phys., special issue in honor of E. Lieb's 80th birthday, vol. 53, 2012.
Universality of general β-ensembles , with L. Erdős and H.T. Yau, Duke Mathematical Journal vol. 163, no. 6, 1127-1190, 2014.
Extreme gaps in the eigenvalues of random matrices , with G. Ben Arous, Annals of Probability, vol. 41, no. 4, 2648-2681, 2013.
A unitary extension of virtual permutations, with J. Najnudel and A. Nikeghbali, Int. Math. Research Notices vol. 2013, no. 18, 4101–4134, 2013.
Quantum chaos, random matrix theory, and the Riemann ζ  function , with J. Keating, proceedings of the Séminaire Poincaré, Birkhauser, Chaos Progress in Mathematical Physics, vol. 66, 2013, 125-168, 2013.
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
Marc Yor et les matrices aléatoires, numéro spécial de la Gazette des mathématiciens (in French, 2015).
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 NYU Probability and Mathematical Physics Seminar.
Columbia/Courant probability seminar series (Fall 2014, Spring 2015, Fall 2015, Spring 2016, Fall 2016 ).
The Northeast probability seminar.
The Harvard Probability Seminar.
Random Matrices, Random Geometry, a joint Harvard-MIT probability afternoon.
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@cims.nyu.edu
address
251 Mercer Street
New York, NY 10012-1185, USA

Here is my curriculum vitae.