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 interests are in analysis, number theory, probability and combinatorics. His recent work concerns interactions between sum-product phenomena in arithmetic combinatorics, expansion and spectral gap bounds, and primes in orbits of linear groups.

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.