Hiraku Nakajima

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

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

Nakajima studied the moduli spaces of instantons on ALE spaces and found connections with the representation theory of affine Kac -Moody algebras and quantum groups. Through the implementation of his quiver varieties, he constructed representation spaces for Kac -Moody algebras. In addition, he constructed representations of the Heisenberg algebra in the direct sum of the homology groups of Hilbert schemes of points on surfaces quasiprojektiven.

In 1997 he received the Award of the Japanese geometry Mathematical Society and in 2000 its prestigious Spring Price. In 2003 he received the Cole prize in algebra. In 2005 he received the JSPS Prize from the Japan Society for the Promotion of Science. In 2002 he was invited speaker ( plenary lecture ) on the ICM in Beijing (Geometric constructions of representations of affine algebras ).

Writings

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