- 2015 - 2020 Uniformity of Zeta Functions
- 2011 - 2016 Geometric moduli theory and its theoretical applications
- 2011 - 2015 Stability and Arithmetic Gormetry
- 2010 - 2012 On families of rational curves and Fano varieties.
- 2008 - 2010 A global study of the moduli spaces of abelian varieties over the ring of integers
- 2006 - 2009 Stability, Global Galois Representations and Non-Abelian Zeta Functions
- 2006 - 2008 GIT stability and canonical Kahler metrics
- 2005 - 2008 Statistical Laws in Geometry
- 2004 - 2007 The global geometry of moduli spaoes
- 2002 - 2005 From Stability, Riemann-Roch to Non-Abelian Zeta Functions
- 2002 - 2005 Geometric Non-linear problems and stability in invariant theory
- 2001 - 2003 The Hitchin-Kobayashi correspondence for Manifolds
- 2000 - 2001 符号付きリーマン面のモジュライ空間の数論的分解の研究
- 1998 - 2000 Symplectic Structures and Geometry of Canonical Bundle
- 1997 - 2000 Radon transformation in Nevanlinina theory and Diophantire approximation
- 1998 - 1999 Geometry of twistor space
- 1997 - 1999 正則写像のモジュライ空間の数理物理学的研究
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