Alex Lubotzky has made fundamental contributions in group theory and its applications to geometry and number theory. His wide-ranging interests include topics such as the congruence subgroup problem, lattices in Lie groups and hyperbolic geometry, Kazhdan Property T, subgroup growth, pro-finite groups, generation of finite simple groups. His work with Sarnak and Phillips on the explicit construction of Ramanujan graphs via modular forms and the problem of distributing points on the sphere attracted a great deal of attention in computer science and engineering. Recently he solved (jointly with M. Belolipetsky) the very old problem of realizing every finite group as the isometry group of some n-dimensional compact hyperbolic manifold.
Lubotzky has been a Professor of Mathematics at Hebrew University of Jerusalem since 1985 and has held visiting positions at Columbia, Yale, Stanford, and the University of Chicago. He has published more than 80 papers and is the recipient of the Erdos prize and the Rothschild prize. He twice received the Ferran Sunyer L. Baloger prize for his research monographs "Discrete Groups, Expanding Graphs, and Invariant Measures" and "Subgroup Growth" (written with D. Segal). He was an invited speaker in the Zurich ICM in 1994, and has given numerous distinguished lecture series at various universities (Yale, Columbia, UCLA, Rice, and others) as well as many invited lectures at international conferences.