Hiraku Nakajima

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Hiraku Nakajima ( Japanese 中 島 啓 , Nakajima Hiraku ; born November 30, 1962 in Tokyo ) is a Japanese mathematician who deals with representation theory, mathematical physics, algebraic geometry and differential geometry.

Nakajima studied at the University of Tokyo , where he received his bachelor's degree in 1985 and his master's degree in 1987. In 1991 he received his doctorate there with Takushiro Ochiai. In 1992 he was assistant professor at Tōhoku University , in 1995 at Tokyo University and in 1997 at Kyoto University , where he was given a full professorship in 2000. In 1998/99 and 2007/08 he was at the Institute for Advanced Study and in 2002 at the Center for Advanced Study in Oslo .

Nakajima studied the modular spaces of instantons on ALE spaces and found connections with the representation theory of affine Kac-Moody algebras and quantum groups. With the quiver varieties he introduced, he constructed representation spaces for Kac-Moody algebras. He also constructed representations of the Heisenberg algebra in the direct sum of the homology groups of Hilbert schemes of points on quasi-projective surfaces.

In 1997 he received the Geometry Prize of the Japanese Mathematical Society and in 2000 its prestigious Spring Prize. In 2003 he received the Cole Prize in Algebra. In 2005 he received the JSPS Award from the Japanese Society for the Advancement of Science. In 2002 he was invited speaker (plenary lecture) at the ICM in Beijing (Geometric constructions of representations of affine algebras). In 2016 he received the Asahi Prize .

Fonts

  • Lectures on Hilbert Schemes and Points on Surfaces. AMS.
  • Quiver varieties and Kac-Moody algebras. Duke Mathematical Journal, Vol. 91, 1998, pp. 515-560.
  • Quiver varieties and finite dimensional representations of quantum affine algebras. Journal of the AMS, Vol. 14, 2001, pp. 145-238.
  • Heisenberg algebra and Hilbert schemes of points on projective surfaces. Annals of Mathematics, Vol. 145, 1997, pp. 379-388.

Web links

Remarks

  1. ↑ ALE stands for Asymptotically local Euclidean. These are special four-dimensional hyperkähler manifolds that are examined in physics as gravitational instanton solutions. Hyperkähler manifolds are holomorphic symplectic algebraic varieties. Nakajima's Quiver varieties provide examples of non-compact hyperkähler varieties.
personal data
SURNAME Nakajima, Hiraku
BRIEF DESCRIPTION Japanese mathematician
DATE OF BIRTH November 30, 1962
PLACE OF BIRTH Tokyo