- 2018 - 2023 Volume minimization principle and obstructions to geometric problems
- 2013 - 2018 Self-similar solutions of geometric flows and GIT stability
- 2012 - 2018 Geometric and Global Analysis of Scalar Curvature and Einstein Metrics
- 2014 - 2017 Gromov-Hausdorff limits and complex analytic geometry
- 2013 - 2017 The study of ideal limits of sequences of test configurations
- 2012 - 2017 Canonical Kahler metrics, algebro-geometric stability and Sasakian geometry
- 2012 - 2016 The latest frontier study on geometry and theory of eigenvalues
- 2011 - 2016 Complex geometry of relative pluricanonical bundles and deformation spaces
- 2011 - 2015 Development of Integrable Geometry
- 2009 - 2014 AdS/CFT correspondence and GIT stablity
- 2011 - 2013 Destabilizing objects and multiplier ideal sheaves
- 2008 - 2010 接触構造と横断するケーラー幾何とAdS/CFT対応
- 2007 - 2010 Fusion of geometry and the theory of integrable systems
- 2006 - 2009 Stability, Global Galois Representations and Non-Abelian Zeta Functions
- 2006 - 2009 Development from Poisson Geometry to Noncommutative Differential Geometry via Integrating of Geometry and Physics
- 2006 - 2008 GIT stability and canonical Kahler metrics
- 2005 - 2008 The finite group action and the equivariant determinant of elliptic operators
- 2005 - 2008 WZW model and 3-manifolds
- 2005 - 2008 Statistical Laws in Geometry
- 2005 - 2007 脱安定化部分概型と標準ケーラー計量
- 2003 - 2006 Study of moduli spaces of projective varieties of general type
- 2004 - 2005 幾何学的不変式論と極小ラグランジュ部分多様体,安定ケーラー多様体
- 2002 - 2005 Geometric Non-linear problems and stability in invariant theory
- 2003 - 2004 Conformal Field Theory and Witten Invariant
- 2002 - 2004 Kahler metrics of constant curvature on complex manifolds and topological invariants
- 2001 - 2004 A synthetic study of positive solutions to elliptic and parabolic partial differential equations
- 2001 - 2002 Gauge Theory and 3-Dimensional Manifolds
- 2000 - 2002 Quasiprojectivity of moduli spaces of algebraic varieties
- 2000 - 2001 The structure of polarized varieties
- 1999 - 2000 Gauge Theory and 3-Dimensional Manifolds
- 1997 - 2000 Einstein metric on complex manifolds and the lifted Futaki invariant
- 1997 - 1998 Geometry related to harmonic maps
- 1997 - 1998 Uniformization for smooth manifolds
- 1996 - 1996 Uniformization Theorems on Manifolds
- 1995 - 1995 多様体上の諸構造と不変量
- 1993 - 1993 多様体論における一意化定理の一般化
- 1990 - 1990 低次元多様体上の諸構造の研究
- 1990 - 1990 リ-マン多様体の曲率と位相構造の研究
- 1988 - 1988 多様体上の代数的構造と解析的構造
- 1986 - 1986 安定理論とその応用
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