Ian Grojnowski

Grojnowski was the first recipient of the Fröhlich Prize of the London Mathematical Society in 2004 for his work in representation theory and algebraic geometry. The citation reads[4]

Grojnowski's insights into geometric contexts for representation theory go back to his thesis with George Lusztig on character sheaves over homogeneous spaces.[5] He has exploited these ideas to make breakthroughs in several completely unexpected areas, including representations of the affine Hecke algebras at roots of 1 (generalising results of Kazhdan and Lusztig), the representation theory of the symmetric groups Sn in characteristic p, the introduction (simultaneously with Nakajima) of vertex operators on the cohomology of the Hilbert schemes of finite subschemes of a complex algebraic surface, and (in joint work with Fishel and Teleman) the proof of the strong Macdonald conjecture of Hanlon and Feigin for reductive Lie algebras.