Takahashi Junya

タカハシジュンヤ | Takahashi Junya

Affiliation and department：
Job title： Assistant Professor
Homepage URL (2)： https://www.math.is.tohoku.ac.jp/~junya/ , https://www.math.is.tohoku.ac.jp/~junya/index.html

Research field (1)： Geometry

Research keywords (7)： harmonic forms , L^2 Stokes theorem , elliptic boundary value problem , collapsing of Riemannian manifolds , differential forms , eigenvalues , Hodge-Laplacian

Research theme for competitive and other funds (7)：

2017 - 2022 Analysis of elliptic operators and its applications to Geometric Function Theory
2016 - 2021 特異点の幾何とホッジ・ラプラシアンの固有値の研究
2012 - 2016 多様体の崩壊に対するホッジ・ラプラシアンの固有値の極限の研究
2007 - 2009 Convergence theory of metric measure spaces and its development
2007 - 2008 微分形式における小さい固有値の位相的性質の研究

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Papers (13)：

Colette Anné, Junya Takahashi. Small eigenvalues of the rough and Hodge Laplacians under fixed volume. to appear in Ann. Fac. Sci Toulouse. 2022
Junya Takahashi. L2-harmonic forms on incomplete riemannian manifolds with positive Ricci curvature. Mathematics. 2018. 6. 5. 1-11
Colette Anné, Junya Takahashi. Partial collapsing and the spectrum of the Hodge-de Rham operator. Analysis & PDE. 2015. 8. 5. 1025-1050
Colette Anné, Junya Takahashi. p-spectrum and collapsing of connected sums. Transactions of the American Mathematical Society. 2012. 364. 4. 1711-1735
Junya Takahashi. Collapsing to Riemannian manifolds with boundary and the convergence of the eigenvalues of the Laplacian. Manuscripta Mathematica. 2006. 121. 2. 191-200

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Lectures and oral presentations (47)：

Small eigenvalues of the Hodge-Laplacian with sectional curvature bouded below
(2024)
Small eigenvalues of the Hodge-Laplacian with sectional curvature bouded below
(Global Analysis and Geometry 2023 at Osaka, Osaka Metropolitan Univ. 2023)
Small eigenvalues of the Hodge-Laplacian with sectional curvature bouded below
(2023)
Small eigenvalues of the rough and Hodge Laplacians under fixed volume
(Geometry and Analysis Seminar -- Mini Workshop 2023, Tohoku Univ. 2023)
Small eigenvalues of the rough and Hodge Laplacians under fixed volume
(2022)

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Professional career (1)：

博士(数理科学) (The University of Tokyo)

Association Membership(s) (1)：

Mathematical Society of Japan

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