Ian Grojnowski
Encyclopedia
Ian Grojnowski is a mathematician working at the Department of Pure Mathematics and Mathematical Statistics of the University of Cambridge
. 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
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
. Grojnowski was the first recipient of the Fröhlich Prize
Fröhlich Prize
The Fröhlich Prize of the London Mathematical Society is awarded in even numbered years in memory of Albrecht Fröhlich. The prize is awarded for original and extremely innovative work in any branch of mathematics...
of the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
in 2004 for his work in representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
and algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
. The citation reads
- Grojnowski's insights into geometric contexts for representation theory go back to his thesis with George Lusztig on character sheaves over homogeneous spaces. He has exploited these ideas to make breakthroughs in several completely unexpected areas, including representations of the affine Hecke algebraAffine Hecke algebraIn mathematics, an affine Hecke algebra is the Hecke algebra of an affine Weyl group, and can be used to prove Macdonald's constant term conjecture for Macdonald polynomials.-Definition:...
s at roots of 1 (generalising results of KazhdanDavid KazhdanDavid Kazhdan or Každan, Kazhdan, formerly named Dmitry Aleksandrovich Kazhdan , is a Soviet and Israeli mathematician known for work in representation theory.-Life:...
and Lusztig), the representation theoryRepresentation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
of the symmetric groupSymmetric groupIn mathematics, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself...
s Sn in characteristic pCharacteristic (algebra)In mathematics, the characteristic of a ring R, often denoted char, is defined to be the smallest number of times one must use the ring's multiplicative identity element in a sum to get the additive identity element ; the ring is said to have characteristic zero if this repeated sum never reaches...
, 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.