Representation theory

Berlin algebraist who created the character theory of finite groups and left his name on results across linear algebra, differential equations and number theory.

group theory, representation theory, linear algebra

Berlin algebraist who founded much of the representation theory of finite groups and of GL(n), and whose name is attached to results across algebra, combinatorics and analysis.

representation theory, group theory, linear algebra

Algebraist who introduced the Brauer group, founded modular representation theory and set the strategy that led to the classification of finite simple groups.

representation theory, finite group theory, algebra

Founder of the theory of Banach and C*-algebras and of the representation theory of non-compact groups, whose Moscow seminar shaped generations of mathematicians.

functional analysis, representation theory, operator algebras

Physicist turned mathematician who created the harmonic analysis of semisimple Lie groups, from the Harish-Chandra isomorphism to the discrete series and the Plancherel formula.

representation theory, harmonic analysis, lie groups

Founder of the Langlands programme, which conjectures deep correspondences between Galois representations and automorphic forms through the principle of functoriality.

number theory, automorphic forms, representation theory

Belgian mathematician who proved the Riemann hypothesis over finite fields and created the theory of weights, mixed Hodge structures and Deligne–Mumford stacks.

algebraic geometry, number theory, hodge theory

Proved the Langlands correspondence for GL(2) over function fields with Drinfeld modules and shtukas, and created quantum groups, associators and, with Beilinson, the geometric Langlands framework of opers and chiral algebras.

number theory, algebraic geometry, representation theory