ALEXANDER GAMBURD Professor of Mathematics Ph.D., Princeton University

Phone: 831-459-4550 Office: Baskin 361C Office Hours: By Appt. Email: agamburd@ucsc.edu

RESEARCH INTERESTS

Gamburd's research concerns spectral problems in number theory, probability and combinatorics, particularly problems related to random matrices and expander graphs.

SELECTED PUBLICATIONS

J. Bourgain, A. Gamburd, P. Sarnak: Affine linear sieve, expanders and sum-product, Inventiones Mathematicae, to appear

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.