P A U L    B O U R G A D E 

Benjamin Peirce Fellow in the Department of Mathematics, Harvard University.
Research interests: random matrices, stochastic processes, analytic number theory.

Email: bourgade@math.harvard.edu
Office: 341, Science Center, One Oxford Street, Cambridge MA 02138 USA
Tel: (617) 495-8477

Teaching

• Spring 2012	Probability
  Fall 2011	Dynamical systems
  Spring 2011	Algebraic Combinatorics
  Fall 2010	Stochastic Analysis

Research

• Strong Szegő asymptotics and zeros of L-functions, with J. Kuan pdf.


• Bulk universality of general β-ensembles with non-convex potential, with L. Erdős and H.-T. Yau pdf.


• Universality of general β-ensembles, with L. Erdős and H.-T. Yau pdf.


• Extreme gaps in the eigenvalues of random matrices, with G. Ben Arous, to appear in Annals of Probability pdf.


• A unitary extension of virtual permutations, with J. Najnudel and A. Nikeghbali pdf.


• Quantum chaos, random matrix theory, and the Riemann &zeta-function, with J. Keating, to appear at the proceeding of the Seminaire Poincare, Birkhauser pdf.


• Mesoscopic fluctuations of the ζ zeros, Probability Theory and Related Fields, Volume 148, Numbers 3-4, 479-500, 2010 pdf.


• Circular Jacobi ensembles and deformed Verblunsky coefficients, with A. Nikeghbali and A. Rouault, International Mathematical Research Notes, Vol. 2009, no. 23, pp. 4357-4394 pdf.


• Conditional Haar measures on classical compact groups, Annals of Probability vol 37, no. 4, 1566-1586, 2009 pdf.


• Ewens measures on compact groups and hypergeometric kernels, with A. Nikeghbali and A. Rouault, Séminaire de Probabilités XLIII, Springer, 2011 pdf.


• The characteristic polynomial of a random unitary matrix: a probabilistic approach, with C.P. Hughes, A. Nikeghbali and M. Yor, Duke Mathematical Journal vol 145, no. 1, 45-69, 2008 pdf.


• The characteristic polynomial on compact groups with Haar measure: some equalities in law, with A. Nikeghbali and A. Rouault, Comptes Rendus de l'Académie des Sciences, Série I 345, 4, 229-232, 2007 pdf.


• 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 pdf.

Various texts

• Stochastic Analysis, lecture notes pdf.


• On random matrices and L-functions, my PhD thesis pdf.


• Tea time in Princeton, a note for the Harvard College Undergraduate Review pdf.


• Lois de Poisson-Dirichlet,, my senior thesis pdf.


• Annales des Olympiades internationnales de mathématiques, available here.

Conferences, seminars

• 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.