Tadashi Takayanagi

Profile Information

Affiliation: Kyoto University

J-GLOBAL ID: 201401055562393606
researchmap Member ID: 7000009213

Research Interests

Research Areas

Natural sciences / Theoretical studies related to particle-, nuclear-, cosmic ray and astro-physics /

Research History

Apr, 2012 - Present

Professor, Yukawa Institute for Theoretical Physics, Kyoto University
Sep, 2008 - Mar, 2012

Project Associate Prof., Kavli Institute for the Physics and Mathematics of the Universe (IPMU), the University of Tokyo
Apr, 2006 - Aug, 2008

Assistant Prof., Faculty of Science, Kyoto University
Sep, 2005 - Mar, 2006

Post-doc Fellow, Kavli Institute for Theoretical Physics, University of California, Santa Barbara
Jul, 2002 - Aug, 2005

Post-doc fellow, Jefferson Lab., Harvard University

Education

Apr, 2000 - Jun, 2002

Physics (Ph.D), Faculty of Science, the University of Tokyo
Apr, 1998 - Mar, 2000

physics(Master), Faculty of Science, the University of Tokyo
Apr, 1994 - Mar, 1998

Physics(Bachelor), Faculty of Science, the University of Tokyo

Awards

Dec, 2016

Nishina Memorial Award, “Discovery and development of the holographic entanglement entropy formula, Nishina Memorial Foundation

Tadashi Takayanagi
Nov, 2014

New Horizons in Physics Prizes, For fundamental ideas about entropy in quantum field theory and quantum gravity, The Breakthrough Prize Foundation

Tadashi Takayanagi
Nov, 2013

Nishinomiya-Yukawa Prize, Studied of Quantum Entanglement Via Holographic Principle, Nishinomiya City

Tadashi Takayanagi
Jan, 2011

Yukawa-Kimura prize, Holography in String Theory and Tachyon Condensation, Yukawa Memorial Foundation

Tadashi Takayanagi

Major Papers

177

BCFT and Islands in two dimensions

Kenta Suzuki, Tadashi Takayanagi

Journal of High Energy Physics, 2022(6), Jun, 2022
Holographic local operator quenches in BCFTs

Taishi Kawamoto, Takato Mori, Yu ki Suzuki, Tadashi Takayanagi, Tomonori Ugajin

Journal of High Energy Physics, 2022(5), May, 2022
CFT duals of three-dimensional de Sitter gravity

Yasuaki Hikida, Tatsuma Nishioka, Tadashi Takayanagi, Yusuke Taki

Journal of High Energy Physics, 2022(5), May, 2022
Holographic moving mirrors

Ibrahim Akal, Yuya Kusuki, Noburo Shiba, Tadashi Takayanagi, Zixia Wei

CLASSICAL AND QUANTUM GRAVITY, 38(22), Nov, 2021 Peer-reviewed
JT gravity limit of Liouville CFT and matrix model

Kenta Suzuki, Tadashi Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS, (11), Nov, 2021 Peer-reviewed
Aspects of pseudoentropy in field theories

Ali Mollabashi, Noburo Shiba, Tadashi Takayanagi, Kotaro Tamaoka, Zixia Wei

PHYSICAL REVIEW RESEARCH, 3(3), Sep, 2021 Peer-reviewed
Topological pseudo entropy

Tatsuma Nishioka, Tadashi Takayanagi, Yusuke Taki

JOURNAL OF HIGH ENERGY PHYSICS, (9), Sep, 2021 Peer-reviewed
Holographic path-integral optimization

Jan Boruch, Pawel Caputa, Dongsheng Ge, Tadashi Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS, (7), Jul, 2021 Peer-reviewed
Spectrum of end of the world branes in holographic BCFTs

Masamichi Miyaji, Tadashi Takayanagi, Tomonori Ugajin

Journal of High Energy Physics, 2021(6), Jun, 2021 Peer-reviewed
Chern-Simons gravity dual of BCFT

Tadashi Takayanagi, Takahiro Uetoko

Journal of High Energy Physics, 2021(4), Apr, 2021 Peer-reviewed
Entanglement and complexity of purification in (1+1)-dimensional free conformal field theories

Hugo A. Camargo, Lucas Hackl, Michal P. Heller, Alexander Jahn, Tadashi Takayanagi, Bennet Windt

PHYSICAL REVIEW RESEARCH, 3(1), Mar, 2021 Peer-reviewed
Pseudo-Entropy in Free Quantum Field Theories

Ali Mollabashi, Noburo Shiba, Tadashi Takayanagi, Kotaro Tamaoka, Zixia Wei

Physical Review Letters, 126(8), Feb 26, 2021 Peer-reviewed
Entanglement Entropy in a Holographic Moving Mirror and the Page Curve

Ibrahim Akal, Yuya Kusuki, Noburo Shiba, Tadashi Takayanagi, Zixia Wei

Physical Review Letters, 126(6), Feb 12, 2021 Peer-reviewed
New holographic generalization of entanglement entropy

Yoshifumi Nakata, Tadashi Takayanagi, Yusuke Taki, Kotaro Tamaoka, Zixia Wei

Physical Review D, 103(2), Jan 11, 2021 Peer-reviewed
Codimension-two holography for wedges

Ibrahim Akal, Yuya Kusuki, Tadashi Takayanagi, Zixia Wei

PHYSICAL REVIEW D, 102(12), Dec, 2020 Peer-reviewed
Looking at shadows of entanglement wedges

Yuya Kusuki, Yuki Suzuki, Tadashi Takayanagi, Koji Umemoto

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS, 2020(11), Nov, 2020 Peer-reviewed
Entanglement Wedges from the Information Metric in Conformal Field Theories

Suzuki Yuki, Takayanagi Tadashi, Umemoto Koji

PHYSICAL REVIEW LETTERS, 123(22), Nov 26, 2019 Peer-reviewed
Entanglement of Purification in Many Body Systems and Symmetry Breaking

Bhattacharyya Arpan, Jahn Alexander, Takayanagi Tadashi, Umemoto Koji

PHYSICAL REVIEW LETTERS, 122(20), May 22, 2019 Peer-reviewed
Holographic Entanglement of Purification from Conformal Field Theories

Caputa Pawel, Miyaji Masamichi, Takayanagi Tadashi, Umemoto Koji

PHYSICAL REVIEW LETTERS, 122(11), Mar 21, 2019 Peer-reviewed
Entanglement of purification through holographic duality

Koji Umemoto, Tadashi Takayanagi

Nature Physics, 14(6) 1-5, Mar 26, 2018 Peer-reviewed
Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

Pawel Caputa, Nilay Kundu, Masamichi Miyaji, Tadashi Takayanagi, Kento Watanabe

JOURNAL OF HIGH ENERGY PHYSICS, (11), Nov, 2017 Peer-reviewed
Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories

Pawel Caputa, Nilay Kundu, Masamichi Miyaji, Tadashi Takayanagi, Kento Watanabe

PHYSICAL REVIEW LETTERS, 119(7), Aug, 2017 Peer-reviewed
Holographic entanglement entropy

Mukund Rangamani, Tadashi Takayanagi

Lecture Notes in Physics, 931 35-47, 2017 Peer-reviewed
Continuous Multiscale Entanglement Renormalization Ansatz as Holographic Surface-State Correspondence

Masamichi Miyaji, Tokiro Numasawa, Noburo Shiba, Tadashi Takayanagi, Kento Watanabe

PHYSICAL REVIEW LETTERS, 115(17), Oct, 2015 Peer-reviewed
Surface/state correspondence as a generalized holography

Masamichi Miyaji, Tadashi Takayanagi

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS, 2015(7), Jul, 2015 Peer-reviewed
Entanglement of local operators in large-N conformal field theories

Pawel Caputa, Masahiro Nozaki, Tadashi Takayanagi

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS, 2014(9), Sep, 2014 Peer-reviewed
Quantum dimension as entanglement entropy in two dimensional conformal field theories

Song He, Tokiro Numasawa, Tadashi Takayanagi, Kento Watanabe

PHYSICAL REVIEW D, 90(4) 041701, Aug, 2014 Peer-reviewed
Quantum Entanglement of Local Operators in Conformal Field Theories

Masahiro Nozaki, Tokiro Numasawa, Tadashi Takayanagi

PHYSICAL REVIEW LETTERS, 112(11), Mar, 2014 Peer-reviewed
Dynamics of entanglement entropy from Einstein equation

Masahiro Nozaki, Tokiro Numasawa, Andrea Prudenziati, Tadashi Takayanagi

Physical Review D - Particles, Fields, Gravitation and Cosmology, 88(2), Jul 18, 2013 Peer-reviewed
Holographic local quenches and entanglement density

Masahiro Nozaki, Tokiro Numasawa, Tadashi Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS, 2013(5), May, 2013 Peer-reviewed
Thermodynamical Property of Entanglement Entropy for Excited States

Jyotirmoy Bhattacharya, Masahiro Nozaki, Tadashi Takayanagi, Tomonori Ugajin

PHYSICAL REVIEW LETTERS, 110(9), Mar, 2013 Peer-reviewed
Holographic geometry of entanglement renormalization in quantum field theories

Masahiro Nozaki, Shinsei Ryu, Tadashi Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS, 2012(10), Oct, 2012 Peer-reviewed
Holographic Fermi surfaces and entanglement entropy

Noriaki Ogawa, Tadashi Takayanagi, Tomonori Ugajin

JOURNAL OF HIGH ENERGY PHYSICS, 2012(1), Jan, 2012 Peer-reviewed
Aspects of AdS/BCFT

Mitsutoshi Fujita, Tadashi Takayanagi, Erik Tonni

JOURNAL OF HIGH ENERGY PHYSICS, 2011(11), Nov, 2011 Peer-reviewed
Holographic Dual of a Boundary Conformal Field Theory

Tadashi Takayanagi

PHYSICAL REVIEW LETTERS, 107(10), Aug, 2011 Peer-reviewed
Holographic superconductor/insulator transition at zero temperature

Tatsuma Nishioka, Shinsei Ryu, Tadashi Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS, 2010(3), Mar, 2010 Peer-reviewed
Holographic entanglement entropy: an overview

Tatsuma Nishioka, Shinsei Ryu, Tadashi Takayanagi

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 42(50), Dec, 2009 Peer-reviewed
ABJM with flavors and FQHE

Yasuaki Hikida, Wei Li, Tadashi Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS, 2009(7), Jul, 2009 Peer-reviewed
Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy

Mitsutoshi Fujita, Wei Li, Shinsei Ryu, Tadashi Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS, 2009(6), Jun, 2009 Peer-reviewed
On string theory duals of Lifshitz-like fixed points

Tatsuo Azeyanagi, Wei Li, Tadashi Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS, 2009(6), Jun, 2009 Peer-reviewed
On type IIA Penrose limit and N=6 Chern-Simons theories

Tatsuma Nishioka, Tadashi Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS, 2008(8), Aug, 2008 Peer-reviewed
Near extremal black hole entropy as entanglement entropy via AdS2/CFT1

Tatsuo Azeyanagi, Tatsuma Nishioka, Tadashi Takayanagi

Physical Review D - Particles, Fields, Gravitation and Cosmology, 77(6), Mar 5, 2008 Peer-reviewed
Holographic proof of the strong subadditivity of entanglement entropy

Matthew Headrick, Tadashi Takayanagi

PHYSICAL REVIEW D, 76(10), Nov, 2007 Peer-reviewed
A covariant holographic entanglement entropy proposal

Veronika E. Hubeny, Mukund Rangamani, Tadashi Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS, 2007(7), Jul, 2007 Peer-reviewed
Aspects of holographic entanglement entropy

Shinsei Ryu, Tadashi Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS, 2006(8), Aug, 2006 Peer-reviewed
Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence

S Ryu, T Takayanagi

PHYSICAL REVIEW LETTERS, 96(18), May, 2006 Peer-reviewed
Ghost D-branes

T Okuda, T Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS, (3) 4517-4555, Mar, 2006 Peer-reviewed
Flux backgrounds in 2D string theory

S Gukov, T Takayanagi, N Toumbas

JOURNAL OF HIGH ENERGY PHYSICS, 8(3) 391-420, Mar, 2004 Peer-reviewed
A matrix model dual of type 0B string theory in two dimensions

T Takayanagi, N Toumbas

JOURNAL OF HIGH ENERGY PHYSICS, 7(7) 1569-1586, Jul, 2003 Peer-reviewed
Correlators in Timelike Bulk Liouville Theory

Andrew Strominger, Tadashi Takayanagi

ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS, 7(2) 369-379, 2003 Peer-reviewed

Major Misc.

Quantum connections

Sean Hartnoll, Subir Sachdev, Tadashi Takayanagi, Xie Chen, Eva Silverstein, Julian Sonner

Nature Reviews Physics, 3(6) 391-393, 2021 Peer-reviewedInvited
Entanglement entropy and gravity/condensed matter correspondence

Tadashi Takayanagi

GENERAL RELATIVITY AND GRAVITATION, 46(5), May, 2014 Peer-reviewed
Holographic Entanglement Entropy, Fractional Quantum Hall Effect and Lifshitz-like Fixed Point

Tadashi Takayanagi

6TH INTERNATIONAL SYMPOSIUM ON QUANTUM THEORY AND SYMMETRIES (QTS6), 462(1), 2013 Peer-reviewed
30 Years of Mathematical Methods in High Energy Physics - In Honor of Professor Tohru Eguchi's 60th Birthday - March 17-19, 2008 Kyoto, Japan Preface

Tadashi Takayanagi, Shigeaki Yahikozawa

PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT, (177) I-I, 2009
30 years of Mathematical Methods in High Energy Physics

Shigeaki Yahikozawa, Hiroshi Kunitomo, Hirosi Ooguri, Akishi Kato, Spenta Wadia, Tadashi Takayanagi, Sinya Aoki

YITP-W-07-20 30 years of Mathematical Methods in High Energy Physics, Mar 17 - Mar 19, 2008. Shigeaki Yahikozawa, Hiroshi Kunitomo, Hirosi Ooguri, Akishi Kato, Spenta Wadia, Tadashi Takayanagi, Sinya Aoki, 300- participants,, 2008 Peer-reviewed

Books and Other Publications

Emergence of the Universe from Quantum Entanglement

Tadashi Takayanagi

Sep, 2020
Holographic Entanglement Entropy

Tadashi Takayanagi (Role: Joint author)

Springer, Aug, 2017 (ISBN: 9783319525730)
Holographic Principle and Quantum Entanglement

Tadashi Takayanagi

Saiensu-sha Co.,Ltd. Publishers, Apr, 2014

Presentations

108

Holographic Pseudo Entropy and Emergent Spacetime

Tadashi Takayanagi

Quantum Complexity: Quantum PCP, Area Laws, and Quantum Gravity, Simons Institute, UC Berkeley, USA, Mar 21, 2024 Invited
Is Spacetime an Illusion? The Mysterious Tale of Quantum Mechanics and Black Holes

Tadashi Takayanagi

Kinchakai, KEK, Tsukuba, Dec 15, 2023 Invited
On Holography in de Sitter Space

Tadashi Takayanagi

The 32nd Workshop on General Relativity and Gravitation in Japan (JGRG32), Nagoya, Japan, Dec 1, 2023 Invited
On Holography in de Sitter Space

Tadashi Takayanagi

KEK Theory Workshop 2023, Tsukuba, Japan, Nov 30, 2023 Invited
Pseudo Entropy and Celestial Holography

Tadashi Takayanagi

Celestial Kick off, Harvard, USA, Oct 28, 2023 Invited
Holographic Entanglement and Beyond

Tadashi Takayanagi

The first International Congress of Basic Science (ICBS), Beijing, Jul 18, 2023 Invited
Holographic Universe from Quantum Information

Tadashi Takayanagi

The KMI colloquium, Nagoya U., Jul 13, 2023 Invited
Emergence of Extreme Universe from Quantum Information

Tadashi Takayanagi

iTHEMS colloquium, Riken, Wako, Apr 17, 2023 Invited
Holography with End-of-the-World Branes and Quantum Entanglement

Tadashi Takayanagi

Eastern Hemisphere Colloquium of Geometry and Physics, IBS-CGP, Mar 22, 2023 Invited
Holography with End-of-the-World Branes and Quantum Entanglement

Tadashi Takayanagi

Princeton University Donald R. Hamilton Colloquium, Feb 28, 2023 Invited
Emergent holographic spacetimes from quantum information

Tadashi Takayanagi

13th Conference on Physics of Particles and Fields, the Physics Society of Iran, Feb 8, 2023 Invited
Wedge Holography in Flat Space and Celestial Holography

Tadashi Takayanagi

Taiwan String Workshop 2022, NTU, Dec 22, 2022 Invited
Pseudo Entropy and AdS(dS)/CFT

Tadashi Takayanagi

2022 Simons Collaboration on It from Qubit Annual Meeting, Simons Foundation, New York,, Dec 8, 2022
A New Generalization of Entanglement Entropy

Tadashi Takayanagi

2nd Symposium on Trans-scale Quantum Science, U. of Tokyo, Nov 8, 2022 Invited
CFT Dual of dS3 and Pseudo Entropy

Tadashi Takayanagi

HirosiFest, Kavli IPMU, U.of Tokyo, Oct 21, 2022 Invited
CFT Dual of De Sitter Space in Three Dimensions

Tadashi Takayanagi

Quantum Information in QFT and AdS/CFT-III, online (IITGN, IITH), Sep 17, 2022 Invited
Wedge Holography in Flat Space and Celestial Holography

Tadashi Takayanagi

Workshop on celestial amplitudes and flat space holography, Corfu, Sep 15, 2022 Invited
Holographic Moving Mirrors

Tadashi Takayanagi

Fundamental aspects of gravity, Imperial College London, Aug 8, 2022 Invited
Moving Mirror and Page Curve

Tadashi Takayanagi

Current challenges in black hole physics and cosmology@ YITP, Kyoto, Jun 22, 2022 Invited
CFT Dual of De Sitter Gravity in Three Dimensions

Tadashi Takayanagi

Informational Architecture of Spacetime Workshop, OIST, May 30, 2022 Invited

Research Projects

Research on AdS/CFT correspondence by the generalized flow method

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (A), Japan Society for the Promotion of Science, Apr, 2022 - Mar, 2027
The Natural Laws of Extreme Universe--A New Paradigm for Spacetime and Matter from Quantum Information

Grants-in-Aid for Scientific Research, Grant-in-Aid for Transformative Research Areas (A), Japan Society for the Promotion of Science, Sep, 2021 - Mar, 2026
The Natural Laws of Extreme Universe--A New Paradigm for Spacetime and Matter from Quantum Information

Grants-in-Aid for Scientific Research Grant-in-Aid for Transformative Research Areas (A), Grant-in-Aid for Transformative Research Areas (A), Japan Society for the Promotion of Science, Sep, 2021 - Mar, 2026
Fundamental Theory of Quantum Cosmology via Quantum Information

Grants-in-Aid for Scientific Research, Grant-in-Aid for Transformative Research Areas (A), Japan Society for the Promotion of Science, Sep, 2021 - Mar, 2026
Studies of String Theory via Quantum Information Theory

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A), Grant-in-Aid for Scientific Research (A), Japan Society for the Promotion of Science, Apr, 2021 - Mar, 2025
Applications of Quantum Informatiom Theoretic Methods in Quantum Field Theories

Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows, Grant-in-Aid for JSPS Fellows, Japan Society for the Promotion of Science, Nov, 2019 - Mar, 2022
Gravity Dynamics via Path-integral Optimizations of Quantum Field Theories

Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Research (Exploratory), Grant-in-Aid for Challenging Research (Exploratory), Japan Society for the Promotion of Science, Jun, 2018 - Mar, 2022

Tadashi Takayanagi
Studies of AdS/CFT via Entanglement Entropy

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A), Grant-in-Aid for Scientific Research (A), Japan Society for the Promotion of Science, Apr, 2016 - Mar, 2021

Takayanagi Tadashi
Studies of Gravity from the viewpoint of Quantum Entanglement

Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows, Grant-in-Aid for JSPS Fellows, Japan Society for the Promotion of Science, Oct, 2017 - Mar, 2020
Microstructure of Black Holes and String Theory

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, Apr, 2016 - Mar, 2020

Shigemori Masaki
量子色力学のエンタングルメント・エントロピーを用いた研究

科学研究費助成事業特別研究員奨励費, 特別研究員奨励費, 日本学術振興会, Apr, 2013 - Mar, 2016

高柳匡, HE SONG, HE Song
Studies of AdS/CFT via Entanglement Entropy

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, Apr, 2013 - Mar, 2016

Takayanagi Tadashi, RYU Shinsei, SHIBA Noburo
From Telascale Physics to String Theory

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area), Japan Society for the Promotion of Science, Apr, 2011 - Mar, 2016

Watari Taizan, OOKOUCHI Yutaka, TAKAYANAGI Tadashi, Chung Yu-Chieh, Kehayias John, NISHIO Ryoichi, Gang Dong-Min, Weissenbacher Matthias
A New Formulation of Quantum Gravity via Quantum Entanglement

Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research, Grant-in-Aid for Challenging Exploratory Research, Japan Society for the Promotion of Science, Apr, 2012 - Mar, 2015

TAKAYANAGI Tadashi, RYU Shinsei
開いた位相的弦理論の研究

科学研究費助成事業特別研究員奨励費, 特別研究員奨励費, 日本学術振興会, 2011 - 2013

高柳匡, 江口徹, PRUDENZIATI Andrea
Study of Spacetime Structure via Holography in Superstring Theory

Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B), Grant-in-Aid for Young Scientists (B), Japan Society for the Promotion of Science, 2008 - 2011

TAKAYANAGI Tadashi
Superstring Theory and Creation of Universe

Grants-in-Aid for Scientific Research Grant-in-Aid for Creative Scientific Research, Grant-in-Aid for Creative Scientific Research, Japan Society for the Promotion of Science, 2007 - 2011

EGUCHI Toru, SASAKI Misao, SUGIMOTO Shigeki, SHIROMIZU Tetsuya, TAKAYANAGI Tadashi, MUKOHYAMA Shinji, HOSOMICHI Kazuo
ゲージ理論と重力理論の双対性の力学的側面

科学研究費助成事業若手研究(スタートアップ), 若手研究(スタートアップ), 日本学術振興会, 2006 - 2007

高柳匡
少ない超対称性をもつ超弦理論の非摂動的力学の研究

科学研究費助成事業特別研究員奨励費, 特別研究員奨励費, 日本学術振興会, 2000 - 2002

高柳匡

Profile Information

Research Interests

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Research History

Education

Awards

Major Papers

Major Misc.

Books and Other Publications

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