Ian Grojnowski | |
|---|---|
 | |
| Nationality | Australian |
| Alma mater | University of Sydney Massachusetts Institute of Technology (PhD) [1] |
| Awards | Fröhlich Prize (2004) |
| Scientific career | |
| Institutions | University of Cambridge |
| Thesis | Character Sheaves on Symmetric Spaces (1992) |
| Doctoral advisor | George Lusztig [1] |
| Doctoral students | Kevin Costello [2] [1] |
Ian Grojnowski is a mathematician working at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. [3]
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.
Pierre René, Viscount Deligne is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal.
In mathematics, the Iwahori–Hecke algebra, or Hecke algebra, named for Erich Hecke and Nagayoshi Iwahori, is a deformation of the group algebra of a Coxeter group.
George Lusztig is a Romanian-born American mathematician and Abdun Nur Professor at the Massachusetts Institute of Technology (MIT). He was a Norbert Wiener Professor in the Department of Mathematics from 1999 to 2009.
Ian Grant Macdonald was a British mathematician known for his contributions to symmetric functions, special functions, Lie algebra theory and other aspects of algebra, algebraic combinatorics, and combinatorics.
In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of linear partial differential equations. Since around 1970, D-module theory has been built up, mainly as a response to the ideas of Mikio Sato on algebraic analysis, and expanding on the work of Sato and Joseph Bernstein on the Bernstein–Sato polynomial.
In mathematics, the Hall algebra is an associative algebra with a basis corresponding to isomorphism classes of finite abelian p-groups. It was first discussed by Steinitz (1901) but forgotten until it was rediscovered by Philip Hall (1959), both of whom published no more than brief summaries of their work. The Hall polynomials are the structure constants of the Hall algebra. The Hall algebra plays an important role in the theory of Masaki Kashiwara and George Lusztig regarding canonical bases in quantum groups. Ringel (1990) generalized Hall algebras to more general categories, such as the category of representations of a quiver.
In the mathematical field of representation theory, a Kazhdan–Lusztig polynomial is a member of a family of integral polynomials introduced by David Kazhdan and George Lusztig (1979). They are indexed by pairs of elements y, w of a Coxeter group W, which can in particular be the Weyl group of a Lie group.
Alexander A. Beilinson is the David and Mary Winton Green University professor at the University of Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1999, Beilinson was awarded the Ostrowski Prize with Helmut Hofer. In 2017, he was elected to the National Academy of Sciences. In 2018, he received the Wolf Prize in Mathematics and in 2020 the Shaw Prize in Mathematics.
In mathematics, Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ-adic cohomology with compact support, introduced by Pierre Deligne and George Lusztig (1976).
James Alexander "Sandy" Green FRS was a mathematician and Professor at the Mathematics Institute at the University of Warwick, who worked in the field of representation theory.
In mathematics, the Springer representations are certain representations of the Weyl group W associated to unipotent conjugacy classes of a semisimple algebraic group G. There is another parameter involved, a representation of a certain finite group A(u) canonically determined by the unipotent conjugacy class. To each pair (u, φ) consisting of a unipotent element u of G and an irreducible representation φ of A(u), one can associate either an irreducible representation of the Weyl group, or 0. The association
James Harold Davenport is a British computer scientist who works in computer algebra. Having done his PhD and early research at the Computer Laboratory, University of Cambridge, he is the Hebron and Medlock Professor of Information Technology at the University of Bath in Bath, England.
Shahn Majid is an English pure mathematician and theoretical physicist, trained at Cambridge University and Harvard University and, since 2001, a professor of mathematics at the School of Mathematical Sciences, Queen Mary, University of London.
Izak (Ieke) Moerdijk is a Dutch mathematician, currently working at Utrecht University, who in 2012 won the Spinoza prize.
Thomas Andrew Bridgeland is a Professor of Mathematics at the University of Sheffield. He was a senior research fellow in 2011–2013 at All Souls College, Oxford and, since 2013, remains as a Quondam Fellow. He is most well-known for defining Bridgeland stability conditions on triangulated categories.
Richard Paul Winsley Thomas is a British mathematician working in several areas of geometry. He is a professor at Imperial College London. He studies moduli problems in algebraic geometry, and ‘mirror symmetry’—a phenomenon in pure mathematics predicted by string theory in theoretical physics.
Kevin Joseph Costello FRS is an Irish mathematician, since 2014 the Krembil Foundation's William Rowan Hamilton chair of theoretical physics at the Perimeter Institute in Waterloo, Ontario, Canada.
Valeria Correa Vaz de Paiva is a Brazilian mathematician, logician, and computer scientist. Her work includes research on logical approaches to computation, especially using category theory, knowledge representation and natural language semantics, and functional programming with a focus on foundations and type theories.
Mark William Gross is an American mathematician, specializing in differential geometry, algebraic geometry, and mirror symmetry.
Geordie Williamson is an Australian mathematician at the University of Sydney. He became the youngest living Fellow of the Royal Society when he was elected in 2018 at the age of 36.
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