Presidential Professor

Alexander Gamburd

Presidential Professor of Mathematics

Department of Mathematics

CUNY Graduate Center

Room 4214.05/ 212-817-8539

agamburd at


Alexander Gamburd specializes in spectral problems in number theory, probability, and combinatorics. His recent work concerns expander graphs, which are highly connected sparse graphs with wide-ranging applications in computer science and mathematics, and his research has resolved major conjectures in proving expansion for Cayley graphs by using recently developed tools from arithmetic combinatorics. This work has a number of applications, in particular in quantum computation theory of quasi-crystals and distribution of prime numbers in non-abelian groups.


Presidential Early Career Award
Sloan Research Foundation Fellowship
Von Neumann Early Career Fellowship 


Fall 2012: MATH 87800: Analysis and Number Theory

Fall 2011: Math 87800 Arithmetic Combinatorics


J.  Bourgain, A. Gamburd: A Spectral Gap Theorem in SU(d). Journal of the European Mathematical Society 14 (2012), no. 5, 1455–1511.

J. Bourgain, A.  Gamburd,  P. Sarnak: Generalization of Selberg's 3/16 theorem and affine sieve. Acta Mathematica 207 (2011), no. 2, 255–290.

E. Breuillard and A. Gamburd: Strong uniform expansion in SL(2,p), GAFA 20 (2010), no. 5, 1201-1209.

J. Bourgain, A. Gamburd, P. Sarnak: Affine linear sieve, expanders and sum-product, Inventiones Mathematicae 179 (2010), n0. 3 559-644.

J. Bourgain and A. Gamburd: On the spectral gap for finitely-generated subgroups of SU(2), Inventiones Mathematicae, 171 (2008), 83-121.

J. Bourgain and A. Gamburd: Uniform expansion bounds for Cayley graphs of SL_2(F_p), Annals of Mathematics, 167 (2008), 625-642.

J. Bourgain, A. Gamburd, P. Sarnak: Sieving and expanders, Comptes Rendus Acad. Sci. Paris, Ser. I, 343 (2006), 155-159.

J. Bourgain and A. Gamburd: New results on expanders, Comptes Rendus Acad. Sci. Paris, Ser. I, 342 ( 2006), 717-721.

D. Bump and A. Gamburd: On the averages of characteristic polynomials from classical groups, Communications in Mathematical Physics, 265 (2006), 227-274.

B. Conrey and A. Gamburd: Pseudomoments of the Riemann zeta-function and pseudomagic squares, Journal of Number Theory 117 (2006), 263-278.

P. Diaconis and A. Gamburd: Random matrices, magic squares and matching polynomials, Electronic Journal of Combinatorics 11, (2004), #2.

A. Gamburd and M. Shahshahani: Uniform diameter bounds for some families of Cayley graphs, International Mathematical Research Notices 71 (2004), 3813-3824.

A. Gamburd: Expander Graphs, Random Matrices, and Quantum Chaos, Random Walks and Geometry, edited by V. A. Kaimanovich, de Gruyter (2004), 109-140.

A. Gamburd: Spectral gap for infinite index "congruence'' subgroups of SL(2, Z), Israel Journal of Mathematics 127 (2002), 157-200.

A. Gamburd, D. Jakobson, and P. Sarnak: Spectra of elements in the group ring of SU(2), Journal of the European Mathematical Society 1 (1999) 51-85.