J-GLOBAL         Last updated: Mar 21, 2019 at 11:37
The University of Tokyo
Kavli Institute for the Physics and Mathematics of the Universe
Doctor of Science(The University of Tokyo), Master of Science(The University of Tokyo)
Other affiliation
Kyoto University
Research funding number
Twitter ID

Research Areas


Academic & Professional Experience

Apr 1987
Mar 1992
Assistant Professor, Department of Sciences, The University of Tokyo
Apr 1992
Mar 1995
Associate Professor, Department of Sciences, Tohoku University
Apr 1995
Mar 1997
Associate Professor, Graduate School of Mathematical Sciences, The University of Tokyo
Apr 1997
Sep 2000
Associate Professor, Graduate School of Sciences, Kyoto University
Dec 2000
Sep 2008
Professor, Graduate School of Sciences, Kyoto University
Oct 2008
Mar 2018
Professor, Research Institute for Mathematical Sciences, Kyoto University
Apr 2018
Professor, Kavli Insitute for the Physics and Mathematics of the Universe, The University of Tokyo

Awards & Honors

The geometry Prize of the Mathematical Society of Japan
The spring Prize of the Mathematical Society of Japan
American Mathematical Society, Cole Prize in Algebra
Revolutionary Development of Geometric Representation Theory, JSPS Prize, Japan Society for the Promotion of Science
Geometric Representation Theory and Theoretical Physics, the Japan Academy Prize, The Japan Academy

Published Papers

Geometric Satake correspondence for affine Kac-Moody Lie algebras of type A
Hiraku Nakajima
Kinosaki Algebraic Geometry Symposium 2018   18-29   2018
Hiraku Nakajima
Modern Geometry: A Celebration of the Work of Simon Donaldson, Proceedings of Symposia in Pure Mathematics   99 193-211   2018
Nicolas Guay, Hiraku Nakajima and Curtis Wendlandt
Adv. Math.   338 865-911   2018
Ryosuke Kodera and Hiraku Nakajima
String-Math 2016, Proceedings of Symposia in Pure Mathematics   98 49-78   2018
Introduction to a provisional mathematical definition of Coulomb branches of 3-dimensional N=4 gauge theories
Hiraku Nakajima
第61回代数学シンポジウム報告集   22-33   2017
Hiraku Nakajima and Yuuya Takayama
Selecta Mathematica   23 2553-2633   2017
Hiraku Nakajima
Geometry of Moduli Spaces and Representation Theory, IAS/Park City Mathematics Series   24 381-436   2017
Introduction to quiver varieties - for ring and representation theorists
Hiraku Nakajima
Proceedings of the 49th Symposium on Ring Theory and Representation Theory   96-114   2017
More lectures on Hilbert schemes of points on surfaces
Hiraku Nakajima
Adv. Stud. Pure Math.   69 173-205   2016   [Refereed]
Instanton moduli spaces and W-algebras
A. Braverman, M. Finkelberg and H. Nakajima
Astérisque   385 vii+128 pages   2016   [Refereed]
Hiraku Nakajima
Advances in Theoretical and Mathematical Physics   20(3) 595-669   2016   [Refereed]
Hiraku Nakajima
Journal of Algebra   441 601-608   2015   [Refereed]
Cluster algebras and singular supports of perverse sheaves.
Hiraku Nakajima
EMS Series of Congress Reports   211-230   2014   [Refereed]
Refined Chern-Simons theory and Hilbert schemes of points on the plane.
Hiraku Nakajima
Contemporary Math.   610 305-331   2014   [Refereed][Invited]
Hiraku Nakajima
Springer Proceedings in Mathematics & Statics   40 403-428   2013   [Refereed]
Handsaw quiver varieties and finite W-algebras
H. Nakajima
Moscow Mathematical Journal   12(3) 633-666   2012   [Refereed]
L. Göttsche; H. Nakajima; K. Yoshioka
Publications of the Research Institute for Mathematical Sciences   47(1) 307-359   Mar 2011   [Refereed]
H. Nakajima; K. Yoshioka
Journal of Algebraic Geometry   20(1) 47-100   Jan 2011   [Refereed]
H. Nakajima
Kyoto Journal of Mathematics   51(1) 71-126   2011   [Refereed]
H. Nakajima; K. Yoshioka
Kyoto Journal of Mathematics   51(2) 263-335   2011   [Refereed]
Preface to the special issue "The Golden Jubilee of Algebraic Analysis"
M. Jimbo; M. Kashiwara; T. Kawai; T. Miwa; H. Nakajima; T. Oshima
Publications of the Research Institute for Mathematical Sciences   47(1) 1-9   2011   [Refereed]
Perverse coherent sheaves on brow-up. I. A quiver description
H. Nakajima and K. Yoshioka
Adv. Stud. Pure Math., vol. 61, Math. Soc. Japan, Tokyo, 2011, pp. 349-386   349-386   2011   [Refereed]
t-analogs of q-characters of quantum affine algebras of type E6, E7, E8
Hiraku Nakajima
Progr. Math.,vol. 284, Birkhauser / Springer, New York, 2010, pp. 257-272.   284 257-272   2010   [Refereed]
K-theoretic Donaldson invariants via instanton counting
L. Göttsche; H. Nakajima; K. Yoshioka
Pure and Applied Mathematics Quarterly   5(3) 1029-1111   2009   [Refereed]
Hiraku Nakajima
SIGMA Symmetry Integrability Geom. Methods Appl. 5 (2009), Paper 003, 37.      2009   [Refereed]
Instanton counting and Donaldson invariants
L. Göttsche; H. Nakajima; K. Yoshioka
Journal of Differential Geometry   80(3) 343-390   Nov 2008   [Refereed]
Nakajima Hiraku, Yoshioka Kota
Tokyo Sugaku Kaisya Zasshi   59(2) 131-153   Apr 2007
Sheaves on ALE spaces and quiver varieties
Nakajima, Hiraku
Moscow Math. Journal   7(4) 699-722   2007   [Refereed]
Crystal, canonical and PBW bases of quantum affine aloebras
H. Nakajima
Algebraic groups and homogeneous spaces, Tata Inst. Fund. Res. Stud. Math.,Tata Inst. Fund. Res., Mumbai, 2007, pp. 389-421.   389-421   2007   [Refereed]
Level 0 monomial crystals
D. Hernandez; H. Nakajima
Nagoya Mathematical Journal   184 85-153   2006   [Refereed]
H. Nakajima; K. Yoshioka
Inventiones Mathematicae   162(2) 313-355   Nov 2005   [Refereed]
H. Nakajima; K. Yoshioka
Transformation Groups   10(3月4日) 489-519   2005   [Refereed]
Quiver varieties and t-analogs of q-characters of quantum affine algebras
H. Nakajima
Annals of Mathematics   160(3) 1057-1097   Nov 2004   [Refereed]
Crystal bases and two-sided cells of quantum affine algebras
J. Beck; H. Nakajima
Duke Mathematical Journal   123(2) 335-402   Jun 2004   [Refereed]
Lectures of instanton counting, Algebraic structares and moduli spaces
H. Nakajima, K. Yoshioka
CRM Proc. Lecture Notes, vol.38, Amer. Math. Soc., Providence, RI, 2004, pp.31-101      2004   [Refereed]
Cells in Quantum Affine Algebras
H. Nakajima
Algebra Colloquium   11(1) 141-154   2004   [Refereed]
H. Nakajima
Representation Theory   7 259-274   2003   [Refereed]
H. Nakajima
Mathematische Annalen   327(4) 671-721   2003   [Refereed]
H. Nakajima
Inventiones Mathematicae   146(2) 399-449   Nov 2001   [Refereed]
H. Nakajima
Journal of the American Mathematical Society   14(1) 145-238   2001   [Refereed]
I. Yukari; H. Nakajima
Topology   39(6) 1155-1191   2000   [Refereed]
H. Nakajima
Annals of Mathematics   145(2) 379-388   Mar 1997   [Refereed]
H. Nakajima
Nuclear Physics B - Proceedings Supplements   46(1月3日) 154-161   1996   [Refereed]
Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras
Hiraku Nakajima
Duke Mathematical Journal   76 365-416   1994   [Refereed]
Homology of moduli spaces of instantons on ALE spaces.I
Hiraku Nakajima
J. of Differential Geometry   40 105-127   1994   [Refereed]
Resolutions of moduli spaces of ideal instantons on R^4
Hiraku Nakajima
Topology, Geometry and Field Theory, World Scientific   129-136   1994   [Refereed]
Gauge theory on resolution of simple singularities and simple Lie algebras
Hiraku Nakajima
Inter. Math. Res. Notices   2 61-74   1994   [Refereed]
Monopoles and Nahm's equations
Hiraku Nakajima
Einstein metrics and Yang-Mills connection   193-211   1993   [Refereed]

Books etc

Lecfures on Hilbert schemes of points on surfaces
Hiraku Nakajima
American Mathematical Society,   1999   

Conference Activities & Talks

Towards geometric Satake correspondences for Kac-Moody algebras
中島 啓
MSJ Spring Meeting   17 Mar 2019   
Coulomb branches of symmetrizable quiver gauge theories
Hiraku Nakajima
GTM seminar   7 Mar 2019   
Coulomb branches of quiver gauge theories and Kac-Moody Lie algebras [Invited]
Hiraku Nakajima
Geometry and Everything, Fukaya 60   17 Feb 2019   
Vertex algebras in 4 dimensional theories [Invited]
Hiraku Nakajima
SCGP Weekly Talk   18 Dec 2018   
Wild Hitchin moduli spaces [Invited]
Hiraku Nakajima
D-modules, Quantum geometry and related topics   3 Dec 2018   
Introduction to Coulomb branches of 3d N=4 SUSY gauge theories without affine Grassmannian [Invited]
Hiraku Nakajima
Infinite dimensional algebras, geometry and integrable systems   1 Nov 2018   
Towards geometric Satake correspondence for Kac-Moody algebras [Invited]
Hiraku Nakajima
GRT: Geometric Satake and Beyond   29 Oct 2018   
Coulomb branches of 3d SUSY gauge theories [Invited]
Hiraku Nakajima
Kinosaki Algebraic Geometry Symposium 2018   22 Oct 2018   
Moore-Tachikawa 2d TQFTs whose values are holomorphic symplectic varieties [Invited]
Hiraku Nakajima
RIMS Workshop "Vertex Operator Algebras and Symmetries"   9 Jul 2018   
3d N=4 QFT and ring objects on the affine Grassmannian [Invited]
Hiraku Nakajima
String-Math 2018   18 Jun 2018   

Association Memberships


Research Grants & Projects

Quiver varieties, quautized envelopiug algebras and Hecke algebras
Heisenberg Algebra and Hibert Schemes of Points on Projective Surfaces
Instanton counting
Project Year: 2003