- 2023 - 2027 Theory for convergence of discrete surfaces with conformal structures
- 2018 - 2023 Geometric analysis for unitary transition operators
- 2017 - 2022 Discrete surface theory for optimal mass transportation in porous materials
- 2015 - 2019 The development of discrete geometric analysis
- 2013 - 2019 Quantum walks from a view point of discrete geometric analysis
- 2012 - 2017 Discrete Geometric Analysis for Quantum Spin System
- 2013 - 2016 Development of the index theorem on foliated manifolds
- 2012 - 2016 Development of Discrete Geometric Analysis
- 2009 - 2014 Spectral and scattering theory of Schroedinger equations
- 2009 - 2012 Problems on geometric asymptotic analysis over convex polytopes
- 2008 - 2012 Universality of Random Matrices and Semiclassical Quantum Theory
- 2009 - 2011 Development and applications of discrete geometric analysis
- 2008 - 2011 Study of Geometry of a discrete space through randomness
- 2007 - 2010 Integrated study of probability and representation theory towards harmonic analysis on huge groups
- 2006 - 2009 Development from Poisson Geometry to Noncommutative Differential Geometry via Integrating of Geometry and Physics
- 2006 - 2008 Problems in geometric asymptotic analysis from a viewpoint of quantum statistics
- 2005 - 2008 Statistical Laws in Geometry
- 2003 - 2005 非可換解析を基礎とする非可換微分幾何学の構築と超弦理論への展開
- 2003 - 2005 楕円型作用素、並びに群作用に対する固有関数とその値分布の漸近挙動の研究
- 2002 - 2004 Study of Non-Commutative Geometry focusing on the Index theorem, and low-dimensional maniflod theory,
- 2000 - 2002 Study of Poisson geometry and its application
- 2001 - 2001 ポアンカレ円板上のワイル型擬微分作用素とウィグナー変換
- 2000 - 2001 Non-Commutative Geometry and the Spectral Flow Index Theorem
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