Algebra, algebraic geometry and number theory are central areas of mathematics, based on the interplay between algebraic formulas and geometric intuition. Many of the most spectacular recent developments in mathematics rely on unexpected combinations of algebraic and geometric ideas. Examples include Kontsevich's proof of Witten's conjecture on the moduli space of curves, Voevodsky's proof of the Milnor conjecture relating K-theory and Galois cohomology, and Khare-Wintenberger's proof of Serre's conjecture on modularity of Galois representations.

The group at UCLA in algebra, algebraic geometry, number theory, and related fields includes many distinguished researchers. It was ranked #5 nationally in 2014 in US News and World Report's Best Graduate Schools. Its members have a broad range of research interests including algebraic groups, algebraic cycles, representation theory, modular and automorphic forms, Galois representations, analytic number theory, string theory, model theory, combinatorics and cryptography. In addition to the strength of its researchers, the group has a long and successful history of training mathematicians.

The RTG grant (DMS-0838697) from the National Science Foundation has as its main goal to increase the number of US citizens and residents who study algebra, algebraic geometry, number theory, and related fields. The grant funds graduate students and postdoctoral scholars at UCLA, as well as workshops and other activities.

Please use the links at the top of this page to learn about our programs.