Algebra & Number Theory

Georgia Benkart Lie theory, representation theory, quantum groups, combinatorics	Dave Benson Cohomology of finite and compact Lie groups, modular representation theory, algebraic topology, invariant theory for finite groups
Richard E. Borcherds Automorphic forms, Lie groups and Lie algebras	John H. Coates Iwasawa theory, arithmetic geometry, L-functions
Jean-Louis Colliot-Thélène Rational points, algebraic cycles, Galois cohomology, linear algebraic groups, rationally connected varieties	Brian D. Conrad Group schemes, rigid geometry, abelian varieties, deformation theory
David Eisenbud Classical Algebraic Geometry, especially the theory of curves and their moduli and deformations; Commutative Algebra, especially free resolutions and Castelnuovo-Mumford regularity; Singularity theory; Computational methods applied to all these fields	Hélène Esnault Cohomology theories (motivic, Hodge theory, l-adic), rational points (finite fields), connections (characteristic classes, Tannaka groups)
Hubert Flenner Affine algebraic geometry, connections between commutative algebra and algebraic geometry, deformation theory	Edward Frenkel Representation theory and Mathematical Physics
Andrew Granville Analytic and multiplicative number theory, elementary and algorithmic number theory, additive combinatorics, the abc-conjecture and consequences	Joseph Gubeladze Homological and K-theoretic aspects of algebraic combinatorics, toric varieties lattice polytopes and related discrete structures
Ehud Hrushovski Connections of geometry with model theory	Craig Huneke Characteristic p methods in commutative algebra and algebraic geometry, local cohomology, homological methods, liaison, syzygies, and computational commutative algebra
Mikhail Kapranov	Yujiro Kawamata Birational geometry (Kodaira dimension, minimal models and derived categories)
János Kollár Algebraic geometry, especially higher dimensional questions	Hendrik W. Lenstra Number theory, algorithms, algebra
Yuri Manin	Barry Mazur
Susan Montgomery Non-commutative algebras, Hopf algebras	Shigefumi Mori
Andrei Okounkov	Raman Parimala Quadratic forms, Brauer groups, Linear algebraic groups and homogeneous spaces
Bjorn Poonen Rational points on varieties, explicit methods, connections between arithmetic geometry and logic	Victor Reiner Algebraic, topological, geometric combinatorics (e.g. combinatorial commutative algebra and representation theory)
Karl Rubin Elliptic curves, Iwasawa theory, special values of L-functions	Peter Sarnak
Michael Singer Algebraic theory of differential and difference equations and connections with logic, symbolic computation	Ronald Solomon
Vasudevan Srinivas Algebraic cycles, geometric commutative algebra, algebraic K-theory, homological algebra, characteristic p methods	J. Toby Stafford Noncommutative algebra, noncommutative algebraic geometry
Bernd Sturmfels Applied and computational aspects of commutative algebra, combinatorics and algebraic geometry.	Richard Taylor Galois representations, arithmetic theory of automorphic forms, applications to number theory
Ravi Vakil Algebraic geometry (including moduli spaces and related topics)	Michel van den Bergh
Marie-France Vignéras Modular representations of reductive p-adic groups, local Langlands correspondence, automorphic representations	Kei-Ichi Watanabe Commutative ring theory, related to singularity theory and algebraic geometry; characteristic p method to analyze singularities; invariant theory of finite groups
Andrei Zelevinsky Algebraic and combinatorial methods in representation theory and algebraic geometry	Efim Zelmanov