Research Areas

Differential Geometry

Educational Background

1973 April - 1977 March : University of Tokyo (Bachelor degree).

1977 April - 1979 March : University of Tokyo (Master degree).

1979 April - 1981 March : University of Tokyo (retired before taking Ph.D because of the employment as Lecturer at Chiba University).

1987 March : Ph.D at the University of Tokyo.

Work Experience

1981 April - 1987 March, Lecturer at Chiba University.

1987 April - 1989 May, Assistant Professor at Chiba University.

1989 June - 1996 June, Assistant Professor at Tokyo Institute of Technology.

1996 July - 2012 September, Professor at Tokyo Institute of Technology.

2012 October - 2018 March, Professor at University of Tokyo.

2018 April - present, Professor at Tsinghua University.

Emeritus Professor :

University of Tokyo

Tokyo Institute of Technology

Visiting positions:

1984, August - 1986, July : University of California at Berkeley, Research Associate supported by Japan Society for the Promotion of Science.

1991, October - 1992, September : Max-Planck Insitut f\"ur Mathematik, visiting member.

1994, August - 1995, May : Mathematical Sciences Research Institute at Berkeley, California supported by Japanese Ministry of Education.

2001, September - 2002, February : Institut des Hautes \'Etudes Scientifiques, visiting member.

2011, September - 2011, October : Tsinghua University, Mathematical Sciences Center, visiting member.

2016, January - 2016, March : Mathematical Sciences Research Institute at Berkeley, California (Simons Visiting Professor).

Honors and Awards

1990 Geometry Prize, Mathematical Society of Japan

2011 Autumn Prize, Mathematical Society of Japan

Publications

Irregular Eguchi-Hanson type metrics and their soliton analogues. Pure and Applied Mathematics Quarterly, 17(2021), 27--53.

(with L. La Fuente-Gravy) Quantum moment map and obstructions to the existence of closed Fedosov star products. J. Geom. Phys. 163 (2021), 104118.

(with Y.Y. Zhang) Residue formula for an obstruction to Coupled Kähler-Einstein metrics. J. Math. Soc. Japan. 73(2021), 389-401.

(with Y.Y. Zhang) Coupled Sasaki-Ricci solitons. Science China Math., 64(2021), 1447-1462.

(with L. La Fuente-Gravy) Deformation quantization and Kähler geometry with moment map. ICCM 2018 Proc. pp 31--66, (2020) International Press of Boston. arXiv:1904.11749.

(with H.Ono) Geometric nonlinear problems and GIT stability through moment maps, In: The Role of Metrics in the Theory of Partial Differential Equations. Advanced Studies in Pure Mathematics 85 (2020), pp 105–114. Math. Soc. Japan.

(with H.Ono) On the existence problem of Einstein-Maxwell Kähler metrics, In: Chen J., Lu P., Lu Z., Zhang Z. (eds) Geometric Analysis. Progress in Mathematics, vol 333 (2020), 93-111. Birkhäuser, Cham.

(with H.Ono) Cahen-Gutt moment map, closed Fedosov star product and structure of the automorphism group, J. Symplectic. Geom. 18(2020), 123-145.

(with H.Ono) Conformally Einstin-Maxwell Kähler metrics and structure of the automorphism group, Math. Zeit. 292(2019), 571-589.

(with H.Ono) Volume minimization and obstructions to solving some problems in Kähler geometry, ICCM Notices, 6(2018), 51-60.

(with H.Ono) Volume minimization and Conformally Kähler, Einstein-Maxwell geometry. J. Math. Soc. Japan. 70(2018), 1493-1521.

(with S.Honda and S.Saito) Fano-Ricci limit spaces and spectral convergence. Asian J. Math., 21(2017), 1015-1062.

Einstein metrics and GIT stability. II. Sugaku Expositions 28 (2015), no. 2, 231–249.

The weighted Laplacians on real and complex metric measure spaces, in Geometry and Analysis on Manifolds, In Memory of Professor Shoshichi Kobayashi, (eds. T.Ochiai et al), Progress in Mathematics, vol.308(2015), 343-351, Birkhauser.

(with K.Hattori and H.Yamamoto) Self-similar solutions to the mean curvature flows on Riemannian cone manifolds and special Lagrangians on toric Calabi-Yau cones, Osaka J. Math., 51(2014), 1053-1079.

(with H.Z.Li and X.D.Li) On the first eigenvalue of the Witten-Laplacian and the diameter of compact shrinking solitons, Ann. Global Anal. Geom. 44 (2013), no. 2, 105--114.

(with Y.Sano) Lower diameter bounds for compact shrinking Ricci solitons, Asian J. Math., 17(2013), No.1, 17-31.

(with K.Hattori and L.Ornea) An integral invariant from the view point of locally conformally Kähler geometry. Manuscripta Math. 140 (2013), no. 1-2, 1--12.

Asymptotic Chow polystability in Kähler geometry, in Fifth International Congress of Chinese Mathematicians Part 1, AMS/IP Studies in Advanced Mathematics, vol. 51, Amer. Math. Soc., Providence, RI, 2012, pp. 139-153.

(with Y.Sano) Multiplier ideal sheaves and geometric problems. Variational problems in differential geometry, 68--93, London Math. Soc. Lecture Note Ser., 394, Cambridge Univ. Press, Cambridge, 2012.

(with H. Ono) Einstein metrics and GIT stability, Sugaku Expositions, 24(2011), 93-122. Translated from Sugaku, 60(2008), 175--202 in Japanese.

(with Y.Sano) Multiplier ideal sheaves and integral invariants on toric Fano manifolds, Mathematische Annalen, 350(2011), 245-267.

(with M.T.Wang) Constructing Kähler-Ricci solitons from Sasaki-Einstein manifolds, Asian Journal of Mathematics, 15(2011), 33--52.

Momentum construction on Ricci-flat Kähler cones, Tohoku Math. J. 63(2011), pp.21-40.

(with H.Ono and Y.Sano) Hilbert series and obstructions to asymptotic semistability, Advances in Math., 226 (2011), 254--284.