- 2020 - 2025 代数多様体の自己写像に関する多角的研究
- 2018 - 2023 Berkovich 解析空間とトロピカル幾何,代数・数論力学系の展開
- 2015 - 2019 Nonarchimedean geometry, algebraic, arithmetic dynamics and related fields
- 2013 - 2018 Moduli spaces of algebraic varieties and self-morphisms
- 2011 - 2016 Analytic torsion and geometry
- 2012 - 2015 Canonical heights and algebraic/arithmetic dynamics
- 2010 - 2015 Rational manifolds and Calabi-Yau manifolds in the view of complex dymanics
- 2010 - 2015 Constructions and developments of geomerty on moduli spaces and arithmetic varieties
- 2009 - 2011 canonical heights and related topics
- 2007 - 2011 Analytic torsion and geometry of moduli spaces
- 2006 - 2008 canonical heights on varieties defined over a number field and related topics
- 2005 - 2008 Diophantine geometry and moduli problems
- 2002 - 2006 Geometry of integrable systems with infinite degrees of freedom and new development of moduli theory.
- 2003 - 2005 Complex symplectic varieties and derived categories
- 2002 - 2004 Arakelov幾何とQuillen計量
- 1998 - 1998 数論的曲面の研究-特にGreen-Arakelov関数について
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