# 吉川 謙一

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(日本語)

(英語)
Analytic torsion, Quillen metrics, and their applications to automorphic forms and moduli spaces

(日本語)
（１）解析的捩率を用いたCalabi-Yau型多様体の不変量の構成 （２）モジュライ空間上の関数としての解析的捩率不変量の構造決定 （３）分岐被覆とQuillen計量 （４）解析的捩率の退化挙動の決定 （５）Borcherds Φ-関数の代数的表示
(英語)
(1) Construction of invariant for varieties of Calabi-Yau type by using analytic torsion (2) Determination of the analytic torsion invariant as an explicit function on the moduli space (3) Branched covering and Quillen metrics (4) Determination of the boundary behavior of analytic torsion (5) An algebraic expression for the Borcherds Phi-function

キーワード(日本語) キーワード(英語)

FANG Hao, LU Zhiqin, 吉川　謙一 FANG Hao, LU Zhiqin, 吉川　謙一 FANG Hao, LU Zhiqin, YOSHIKAWA Ken-Ichi Analytic torsion for Calabi--Yau threefolds Analytic torsion for Calabi--Yau threefolds Analytic torsion for Calabi--Yau threefolds Journal of Differential Geometry, 80, 175-259 Journal of Differential Geometry, 80, 175-259 Journal of Differential Geometry, 80, 175-259 2008 英語 研究論文(学術雑誌)

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タイトル タイトル(日本語) タイトル(英語) 会議名 会議名(日本語) 会議名(英語) 主催者 主催者(日本語) 主催者(英語) 開催年月日 記述言語 会議種別
Enriques 2n-folds and analytic torsion[招待あり] Enriques 2n-folds and analytic torsion [招待あり] Enriques 2n-folds and analytic torsion [招待あり] Intercity Seminar in Arakelov Geometry 2018 Intercity Seminar in Arakelov Geometry 2018 Intercity Seminar in Arakelov Geometry 2018 2018/09/05 英語 口頭発表(招待・特別)
Holomorphic torsion invariants for K3 surfaces with involution and Borcherds products[招待あり] Holomorphic torsion invariants for K3 surfaces with involution and Borcherds products [招待あり] Holomorphic torsion invariants for K3 surfaces with involution and Borcherds products [招待あり] Moduli spaces and Modular forms Moduli spaces and Modular forms Moduli spaces and Modular forms 2016/04/26 英語 口頭発表(招待・特別)
Analytic torsion for K3 surfaces with involution[招待あり] Analytic torsion for K3 surfaces with involution [招待あり] Analytic torsion for K3 surfaces with involution [招待あり] 2015 Taipei Conference on Complex Geometry 2015 Taipei Conference on Complex Geometry 2015 Taipei Conference on Complex Geometry 2015/12/20 英語 口頭発表(招待・特別)
Analytic torsion for K3 surfaces with involution[招待あり] Analytic torsion for K3 surfaces with involution [招待あり] Analytic torsion for K3 surfaces with involution [招待あり] Trends in Modern Geometry & 10th Pacific Rim Complex Geometry Conference Trends in Modern Geometry & 10th Pacific Rim Complex Geometry Conference Trends in Modern Geometry & 10th Pacific Rim Complex Geometry Conference 2015/07/31 英語 口頭発表(招待・特別)
Analytic torsion invariant for K3 surfaces with involution Analytic torsion invariant for K3 surfaces with involution Analytic torsion invariant for K3 surfaces with involution Modular Forms and Geometry of Modular Varieties Modular Forms and Geometry of Modular Varieties Modular Forms and Geometry of Modular Varieties 2015/05/05 英語 口頭発表(招待・特別)
BCOV invariant for Calabi-Yau threefolds[招待あり] BCOV invariant for Calabi-Yau threefolds [招待あり] BCOV invariant for Calabi-Yau threefolds [招待あり] New Developments in Algebraic Geometry, National Taiwan University New Developments in Algebraic Geometry, National Taiwan University New Developments in Algebraic Geometry, National Taiwan University 2014/08 英語 口頭発表(招待・特別)
Equivariant analytic torsion for $K3$ surfaces with involution[招待あり] Equivariant analytic torsion for $K3$ surfaces with involution [招待あり] Equivariant analytic torsion for $K3$ surfaces with involution [招待あり] Moduli spaces of irreducible symplectic varieties, cubics and Enriques surfaces Moduli spaces of irreducible symplectic varieties, cubics and Enriques surfaces Moduli spaces of irreducible symplectic varieties, cubics and Enriques surfaces 2014/03 英語 口頭発表(招待・特別)
Resultants and the Borcherds Phi-function[招待あり] Resultants and the Borcherds Phi-function [招待あり] Resultants and the Borcherds Phi-function [招待あり] Complex Geometry Conference, Korea Institute for Advanced Study Complex Geometry Conference, Korea Institute for Advanced Study Complex Geometry Conference, Korea Institute for Advanced Study 2013/05 英語 口頭発表(招待・特別)
Equivariant analytic torsion for $K3$ surfaces with involution[招待あり] Equivariant analytic torsion for $K3$ surfaces with involution [招待あり] Equivariant analytic torsion for $K3$ surfaces with involution [招待あり] Control, index, traces and determinants, Universit¥'e Paris-Sud Control, index, traces and determinants, Universit¥'e Paris-Sud Control, index, traces and determinants, Universit¥'e Paris-Sud 2013/05 英語 口頭発表(招待・特別)
Analytic torsion of log-Enriques surfaces[招待あり] Analytic torsion of log-Enriques surfaces [招待あり] Analytic torsion of log-Enriques surfaces [招待あり] Algebraic geometry, modular forms and applications to physics, International Centre for Mathematical Sciences Algebraic geometry, modular forms and applications to physics, International Centre for Mathematical Sciences Algebraic geometry, modular forms and applications to physics, International Centre for Mathematical Sciences 2012/12 英語 口頭発表(招待・特別)
Singularities and analytic torsion[招待あり] Singularities and analytic torsion [招待あり] Singularities and analytic torsion [招待あり] Workshop “Spectral Invariants on Non-compact and Singular Spaces”, Centre de Recherches Math¥'ematiques Workshop “Spectral Invariants on Non-compact and Singular Spaces”, Centre de Recherches Math¥'ematiques Workshop “Spectral Invariants on Non-compact and Singular Spaces”, Centre de Recherches Math¥'ematiques 2012/07 英語 口頭発表(招待・特別)
A trinity of Borcherds $¥Phi$ -function[招待あり] A trinity of Borcherds $¥Phi$ -function [招待あり] A trinity of Borcherds $¥Phi$ -function [招待あり] Analytic torsion and its applications, Universit¥'e Paris-Sud Analytic torsion and its applications, Universit¥'e Paris-Sud Analytic torsion and its applications, Universit¥'e Paris-Sud 2012/06 英語 口頭発表(招待・特別)

On the value of Borcherds $¥Phi$ -function[招待あり] On the value of Borcherds $¥Phi$ -function [招待あり] On the value of Borcherds $¥Phi$ -function [招待あり] Automorphisms of algebraic varieties -- Dynamics and Arithmetic, Shirahama Automorphisms of algebraic varieties -- Dynamics and Arithmetic, Shirahama Automorphisms of algebraic varieties -- Dynamics and Arithmetic, Shirahama 2011/12 英語 口頭発表(招待・特別)
Resultants and Borcherds $¥Phi$ -function[招待あり] Resultants and Borcherds $¥Phi$ -function [招待あり] Resultants and Borcherds $¥Phi$ -function [招待あり] Automorphic forms and moduli spaces, Centre International de Rencontres Math¥'ematiques Automorphic forms and moduli spaces, Centre International de Rencontres Math¥'ematiques Automorphic forms and moduli spaces, Centre International de Rencontres Math¥'ematiques 2011/10 英語 口頭発表(招待・特別)
On the value of Borcherds $¥Phi$ -function[招待あり] On the value of Borcherds $¥Phi$ -function [招待あり] On the value of Borcherds $¥Phi$ -function [招待あり] Workshop on Arithmetic and Geometry of \$K3\$ surfaces and Calabi-Yau threefolds, The Fields Institute for research in Mathematical Sciences Workshop on Arithmetic and Geometry of \$K3\$ surfaces and Calabi-Yau threefolds, The Fields Institute for research in Mathematical Sciences Workshop on Arithmetic and Geometry of \$K3\$ surfaces and Calabi-Yau threefolds, The Fields Institute for research in Mathematical Sciences 2011/08 英語 口頭発表(招待・特別)
Singularities and analytic torsion Singularities and analytic torsion Singularities and analytic torsion Kyoto Symposium on Complex Analysis in Several Variables XIV Kyoto Symposium on Complex Analysis in Several Variables XIV Kyoto Symposium on Complex Analysis in Several Variables XIV 2011/07 英語 口頭発表(招待・特別)
Resultants and Borcherds $¥Phi$ -function[招待あり] Resultants and Borcherds $¥Phi$ -function [招待あり] Resultants and Borcherds $¥Phi$ -function [招待あり] Infinite Analysis 11, University of Tokyo Infinite Analysis 11, University of Tokyo Infinite Analysis 11, University of Tokyo 2011/07 英語 口頭発表(招待・特別)
Singularities and analytic torsion[招待あり] Singularities and analytic torsion [招待あり] Singularities and analytic torsion [招待あり] Geometric quantization in noncompact setting, Mathematisches Forschungsinstitut Oberwolfach Geometric quantization in noncompact setting, Mathematisches Forschungsinstitut Oberwolfach Geometric quantization in noncompact setting, Mathematisches Forschungsinstitut Oberwolfach 2011/02 英語 口頭発表(招待・特別)
Elliptic $J$ -function and Borcherds $¥Phi$ -function[招待あり] Elliptic $J$ -function and Borcherds $¥Phi$ -function [招待あり] Elliptic $J$ -function and Borcherds $¥Phi$ -function [招待あり] Lattices, Reflection Groups and Algebraic Geometry, Nagoya Lattices, Reflection Groups and Algebraic Geometry, Nagoya Lattices, Reflection Groups and Algebraic Geometry, Nagoya 2010/11 英語 口頭発表(招待・特別)
Analytic torsion of certain Calabi-Yau threefolds and Borcherds product[招待あり] Analytic torsion of certain Calabi-Yau threefolds and Borcherds product [招待あり] Analytic torsion of certain Calabi-Yau threefolds and Borcherds product [招待あり] Automorphic forms, Kac-Moody algebras and Strings, The Max-Planck Institut f¥"ur Mathematik Automorphic forms, Kac-Moody algebras and Strings, The Max-Planck Institut f¥"ur Mathematik Automorphic forms, Kac-Moody algebras and Strings, The Max-Planck Institut f¥"ur Mathematik 2010/05 英語 口頭発表(招待・特別)
Elliptic $J$ -function and Borcherds $¥Phi$ -function[招待あり] Elliptic $J$ -function and Borcherds $¥Phi$ -function [招待あり] Elliptic $J$ -function and Borcherds $¥Phi$ -function [招待あり] The 5th Franco-Japanese Symposium on Singularities The 5th Franco-Japanese Symposium on Singularities The 5th Franco-Japanese Symposium on Singularities 2009/08 英語 口頭発表(招待・特別)
An Introduction to Borcherds Products (I), (II), (III)[招待あり] An Introduction to Borcherds Products (I), (II), (III) [招待あり] An Introduction to Borcherds Products (I), (II), (III) [招待あり] Holomorphically Symplectic Varieties and Moduli Spaces Holomorphically Symplectic Varieties and Moduli Spaces Holomorphically Symplectic Varieties and Moduli Spaces 2009/06 英語 口頭発表(招待・特別)
Analytic torsion and invariants of $K3$ and Calabi-Yau manifolds (I), (II), (III)[招待あり] Analytic torsion and invariants of $K3$ and Calabi-Yau manifolds (I), (II), (III) [招待あり] Analytic torsion and invariants of $K3$ and Calabi-Yau manifolds (I), (II), (III) [招待あり] ICTS Program on `Differential Geometric Methods in Algebraic Geometry', Tata Institute of Fundamental Research ICTS Program on `Differential Geometric Methods in Algebraic Geometry', Tata Institute of Fundamental Research ICTS Program on `Differential Geometric Methods in Algebraic Geometry', Tata Institute of Fundamental Research 2009/04 英語 口頭発表(招待・特別)
Analytic Torsion and Automorphic Forms[招待あり] Analytic Torsion and Automorphic Forms [招待あり] Analytic Torsion and Automorphic Forms [招待あり] Pacific Rim Complex Geometry Conference Pacific Rim Complex Geometry Conference Pacific Rim Complex Geometry Conference 2008/08 英語 口頭発表(招待・特別)
Analytic Torsion and Automorphic Forms[招待あり] Analytic Torsion and Automorphic Forms [招待あり] Analytic Torsion and Automorphic Forms [招待あり] Tosion and Eta Forms, Universit¥"at zu K¥"oln Tosion and Eta Forms, Universit¥"at zu K¥"oln Tosion and Eta Forms, Universit¥"at zu K¥"oln 2008/06 英語 口頭発表(招待・特別)
Analytic Torsion and Automorphic Forms[招待あり] Analytic Torsion and Automorphic Forms [招待あり] Analytic Torsion and Automorphic Forms [招待あり] International Conference on Geometry and Analysis on Manifolds, University of California Santa Barbara International Conference on Geometry and Analysis on Manifolds, University of California Santa Barbara International Conference on Geometry and Analysis on Manifolds, University of California Santa Barbara 2008/03 英語 口頭発表(招待・特別)

Analytic Torsion and Automorphic Forms[招待あり] Analytic Torsion and Automorphic Forms [招待あり] Analytic Torsion and Automorphic Forms [招待あり] 15th Southern California Geometric Analysis Seminar 15th Southern California Geometric Analysis Seminar 15th Southern California Geometric Analysis Seminar 2008/02 英語 口頭発表(招待・特別)
$K3$ Surfaces, Analytic Torsion and Automorphic Forms[招待あり] $K3$ Surfaces, Analytic Torsion and Automorphic Forms [招待あり] $K3$ Surfaces, Analytic Torsion and Automorphic Forms [招待あり] Short Program on Moduli Spaces of Riemann Surfaces and Related Topics, Centre de Recherches Math¥'ematiques Short Program on Moduli Spaces of Riemann Surfaces and Related Topics, Centre de Recherches Math¥'ematiques Short Program on Moduli Spaces of Riemann Surfaces and Related Topics, Centre de Recherches Math¥'ematiques 2007/07 英語 口頭発表(招待・特別)
$K3$ Surfaces, Analytic Torsion and Automorphic Forms[招待あり] $K3$ Surfaces, Analytic Torsion and Automorphic Forms [招待あり] $K3$ Surfaces, Analytic Torsion and Automorphic Forms [招待あり] Modular Forms and Moduli Spaces, Euler International Mathematical Institute Modular Forms and Moduli Spaces, Euler International Mathematical Institute Modular Forms and Moduli Spaces, Euler International Mathematical Institute 2007/07 英語 口頭発表(招待・特別)
A duality between Del Pezzo and $K3$ surfaces?[招待あり] A duality between Del Pezzo and $K3$ surfaces? [招待あり] A duality between Del Pezzo and $K3$ surfaces? [招待あり] International Conference on Geometry and Analysis on Manifolds, Chern Institute of Mathematics International Conference on Geometry and Analysis on Manifolds, Chern Institute of Mathematics International Conference on Geometry and Analysis on Manifolds, Chern Institute of Mathematics 2007/04 英語 口頭発表(招待・特別)
Analytic torsion for Calabi--Yau threefolds[招待あり] Analytic torsion for Calabi--Yau threefolds [招待あり] Analytic torsion for Calabi--Yau threefolds [招待あり] Arakelov Geometry, Mathematisches Forschungsinstitut Oberwolfach Arakelov Geometry, Mathematisches Forschungsinstitut Oberwolfach Arakelov Geometry, Mathematisches Forschungsinstitut Oberwolfach 2005/09 英語 口頭発表(招待・特別)
Analytic torsion for Calabi--Yau threefolds[招待あり] Analytic torsion for Calabi--Yau threefolds [招待あり] Analytic torsion for Calabi--Yau threefolds [招待あり] the XXIII International Conference of Differential Geometric Methods in Theoretical Physics the XXIII International Conference of Differential Geometric Methods in Theoretical Physics the XXIII International Conference of Differential Geometric Methods in Theoretical Physics 2005/08 英語 口頭発表(招待・特別)
Discriminants of certain $K3$ surfaces[招待あり] Discriminants of certain $K3$ surfaces [招待あり] Discriminants of certain $K3$ surfaces [招待あり] International Symposium on Representation Theory and Automorphic Forms International Symposium on Representation Theory and Automorphic Forms International Symposium on Representation Theory and Automorphic Forms 2005/02 英語 口頭発表(招待・特別)
On the singularity of Quillen metrics[招待あり] On the singularity of Quillen metrics [招待あり] On the singularity of Quillen metrics [招待あり] Hayama Symposium on Several Complex Variables Hayama Symposium on Several Complex Variables Hayama Symposium on Several Complex Variables 2004/12 英語 口頭発表(招待・特別)
$K3$ 曲面と解析的トーション[招待あり] $K3$ 曲面と解析的トーション [招待あり] $K3$ 曲面と解析的トーション [招待あり] 日本数学会函数論分科会 日本数学会函数論分科会 日本数学会函数論分科会 2004/03 日本語 口頭発表(招待・特別)
Calabi-Yau hypersurfaces, discriminants, and Quillen metrics[招待あり] Calabi-Yau hypersurfaces, discriminants, and Quillen metrics [招待あり] Calabi-Yau hypersurfaces, discriminants, and Quillen metrics [招待あり] Reelle Methoden der Komplexen Analysis, Mathematisches Forschungsinstitut Oberwolfach Reelle Methoden der Komplexen Analysis, Mathematisches Forschungsinstitut Oberwolfach Reelle Methoden der Komplexen Analysis, Mathematisches Forschungsinstitut Oberwolfach 2003/02 英語 口頭発表(招待・特別)
Isolated critical points and adiabatic limit of Chern forms Isolated critical points and adiabatic limit of Chern forms Isolated critical points and adiabatic limit of Chern forms Singularit¥'es franco-japonaises, Centre International de Rencontres Math¥'ematiques Singularit¥'es franco-japonaises, Centre International de Rencontres Math¥'ematiques Singularit¥'es franco-japonaises, Centre International de Rencontres Math¥'ematiques 2002/09 英語 口頭発表(招待・特別)
$K3$ surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space[招待あり] $K3$ surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space [招待あり] $K3$ surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space [招待あり] Geometric Analysis and Singular Spaces, Mathematisches Forschungsinstitut Oberwolfach Geometric Analysis and Singular Spaces, Mathematisches Forschungsinstitut Oberwolfach Geometric Analysis and Singular Spaces, Mathematisches Forschungsinstitut Oberwolfach 2002/06 英語 口頭発表(招待・特別)
$K3$ surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space[招待あり] $K3$ surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space [招待あり] $K3$ surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space [招待あり] Memorial Conference of Kiyoshi Oka's Centennial Birthday on Complex Analysis in Several Variables Memorial Conference of Kiyoshi Oka's Centennial Birthday on Complex Analysis in Several Variables Memorial Conference of Kiyoshi Oka's Centennial Birthday on Complex Analysis in Several Variables 2001/11 英語 口頭発表(招待・特別)
$K3$ surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space[招待あり] $K3$ surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space [招待あり] $K3$ surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space [招待あり] Algebraic Geometry 2000 Algebraic Geometry 2000 Algebraic Geometry 2000 2000/07 英語 口頭発表(招待・特別)
Analytic torsion and automorphic forms on the moduli space[招待あり] Analytic torsion and automorphic forms on the moduli space [招待あり] Analytic torsion and automorphic forms on the moduli space [招待あり] Reelle Methoden der Komplexen Analysis, Mathematisches Forschungsinstitut Oberwolfach Reelle Methoden der Komplexen Analysis, Mathematisches Forschungsinstitut Oberwolfach Reelle Methoden der Komplexen Analysis, Mathematisches Forschungsinstitut Oberwolfach 1999/03 英語 口頭発表(招待・特別)
Analytic torsion and automorphic forms on the moduli space[招待あり] Analytic torsion and automorphic forms on the moduli space [招待あり] Analytic torsion and automorphic forms on the moduli space [招待あり] Activity on automorphic products, Max-Plank-Institut f¥"ur Mathematik Activity on automorphic products, Max-Plank-Institut f¥"ur Mathematik Activity on automorphic products, Max-Plank-Institut f¥"ur Mathematik 1999/03 英語 口頭発表(招待・特別)
Analytic torsion and automorphic forms on the moduli space[招待あり] Analytic torsion and automorphic forms on the moduli space [招待あり] Analytic torsion and automorphic forms on the moduli space [招待あり] Arakelov Theory, Values of \$L\$-functions, Issac Newton Institute for Mathematical Sciences Arakelov Theory, Values of \$L\$-functions, Issac Newton Institute for Mathematical Sciences Arakelov Theory, Values of \$L\$-functions, Issac Newton Institute for Mathematical Sciences 1998/07 英語 口頭発表(招待・特別)
Quillenの計量と判別式 Quillenの計量と判別式 Quillenの計量と判別式 日本数学会函数論分科会 日本数学会函数論分科会 日本数学会函数論分科会 1997/10 日本語 口頭発表(招待・特別)
On the spectral zeta functions of K¥"ahler varieties with conical singularities[招待あり] On the spectral zeta functions of K¥"ahler varieties with conical singularities [招待あり] On the spectral zeta functions of K¥"ahler varieties with conical singularities [招待あり] Geometric Complex Analysis, the Third International Research Institute of the Mathematical Society of Japan Geometric Complex Analysis, the Third International Research Institute of the Mathematical Society of Japan Geometric Complex Analysis, the Third International Research Institute of the Mathematical Society of Japan 1995/03 英語 口頭発表(招待・特別)

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