katsuda Atsushi

かつだあつし | katsuda Atsushi

Affiliation and department：
Job title：教授
Research theme for competitive and other funds (33)：

2018 - 2022 Density Theorems of Closed Geodesics for Nilpotent Extensions and Asymptotics of Heat Kernels
2010 - 2012 Structures of manifolds and asymptoticproperties
2008 - 2010 Development of various problems related to integrable geodesic flows
2007 - 2009 Geometric Structures and Topology
2006 - 2008 Asymptotic Analysis in Spectral and Scattering Theory

2006 - 2008 Development of numerical computation brought by spectral theory and geometry

2006 - 2007 Problems related to integrable geodesic flows

2005 - 2007 Metric invariants and space structures

2004 - 2007 studies on the relationship of the structure of manifolds and p-harmonic functions

2004 - 2006 Wellposedness of the Cauchy problems for hyperbolic systems with large data

2004 - 2006 Relations of geometric structure of manifolds and graphs, spectre, asymptotic analysis and their applications

2004 - 2005 Integrable geodesic flows and related problems

2004 - 2005 モジュライ空間の算術幾何に対する種種のグラフ複合体の関与の研究

2003 - 2005 Scattering of Dirac particles by mabnetic fields and spectral theory

2002 - 2005 Galois groups and fundamental groups in anabelian geometry

2002 - 2003 Well-posedness and approximation of Cauchy problems for hyperbolic systems

2002 - 2003 Spectra and Geometric structure of manifolds and graph

2000 - 2003 Relations between space-structures and curvatures

2001 - 2002 Scattering by magnetic fields and Aharonov-Bohm effect

2000 - 2001 Geometric Structures on Manifolds and Graphs

1999 - 2001 The properties of P-harmonic maps and the application to Geometry

1999 - 2000 Spectral Theory for Schrodinger Operators with Magnetic Fields and its Application

1998 - 1999 Geometric structure and topology of manifolds and graphs

1997 - 1998 Spectral and Scattering Theory and its Application

1997 - 1998 SPECTRAL GEOMETRY

1997 - 1998 CURVATURE AND STRUCURE OF SPACES

1996 - 1996 多様体の幾何構造と位相

1996 - 1996 計量構造と多様体構造

1994 - 1994 同変ホモトピー論とその応用

1993 - 1993 双曲力学系及び非線型偏微分方程式

1990 - 1990 計量構造と位相構造

1988 - 1988 一般コホモロジー論

1988 - 1988 曲面論と多様体論の微分幾何学的研究

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Papers (16)：

A. Katsuda and T. Nakamura. A rigidity theorem for Killing vector fields on compact manifolds with almost nonpositive Ricci curvature. Proc. Amer. Math. Soc. 2021. 149. 3. 1215-1224
A. Katsuda and T. Kobayashi. The isometry groups of compact manifolds with almost negative Ricci curvature. Tohoku Math. J. 2018. 70. 391-400
A. Katsuda, Y.V. Kurylev, M. Lassas. Stability of boundary distance representation and reconstruction of Riemannian manifolds. Inverse Probl. Imaging. 2007. 1. 1
M. Anderson, A. Katsuda, Y. Kurylev, M. Lassas, M. Taylor. Boundary regularity for the Ricci equation, geometric convergence, and Gel'fand's inverse boundary problem. Invent. Math. 2004. 158. 2
Atsushi Katsuda. Asymptotics of heat kernels on nilpotent coverings and related topics. Contemporary Mathematics. Amer. Math. Soc. 2004. 348. 155-167

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MISC (9)：

勝田篤. 閉測地線の密度定理. 2020
勝田篤. 書評:浦川肇 (新井仁之・小林俊行・斎藤毅・吉田朋広編):スペクトル幾何 (共立講座数学の輝き,3). 2020
勝田篤. Ricci曲率がほぼ負の多様体の等長変換群. 2014
勝田篤. Closed geodesics and heat kernels on nilpotent coverings. 2011
Atsushi katsuda Polly Wee Sy. An overview of Sunada's work up to age 60. Spectral analysis in geometry and number theory. 2009

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Books (2)：

New analytic and geometric methods in inverse problems
Springer 2004
線形代数学〈1〉正比例からの線形代数
培風館 1998

Lectures and oral presentations (15)：

Bloch-Floquet理論のHeisenberg群へ拡張と熱核の長時間漸近挙動
(2020 RIMS共同研究(公開型) 量子場の数理とその周辺 2021)
Heisenberg extension for heat kernels and geometric Chebotarev density theorems for closed geodesics
(研究集会「測地線及び関連する諸問題」 2021)
閉測地線、熱核、ハイゼンベルグ群
(研究集会「測地線及び関連する諸問題」 2020)
Closed geodesics and heat kernels for Heisenberg extensions
(研究集会「多様体上の微分方程式」 2019)
べき零群,熱核,Dirichletの算術級数定理
(研究集会:岡山-広島解析・確率論セミナー 2017)

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Committee career (16)：

2019/04 - 2022/03 九州大学教職課程専門委員会
2019/04 - 2022/03 九州大学教務委員
2020/04 - 2021/03 日本数学会評議員
2018/05 - 2020/04 九州大学入試実施委員会委員
2019/04 - 2020/03 日本数学会評議員

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Association Membership(s) (1)：

日本数学会

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