Rchr
J-GLOBAL ID：200901089776199400
Update date: Sep. 19, 2024
Murakami Jun
ムラカミ ジュン | Murakami Jun
Affiliation and department：
Job title：
Professor
Homepage URL (2)：
https://murakami.w.waseda.jp/jun-home-j.html
,
https://murakami.w.waseda.jp/index.html
Research field (3)：
Mathematical analysis
, Algebra
, Geometry
Research keywords (1)：
3-manifold, knot theory, quantum invariant, representation theory
Research theme for competitive and other funds (52)：
- 2020 - 2025 Study of the geometric structure of three manifolds by using quantum invariants
- 2020 - 2023 Research on a complexification of hyperbolic tetrahedra
- 2019 - 2022 Diagramatic construction of non-semisimple TQFT
- 2017 - 2020 Quantization of the fundamental group by dual quantum group
- 2017 - 2020 双対量子群による基本群の量子化
- 2013 - 2017 Discrete quantization of low-dimensional geometry with quantum invariants
- 2013 - 2016 Study in phantom of the quantum groups
- 2011 - 2016 Study of modular/quasimodular forms and multiple zeta values appearing in various aspects of mathematics and physics
- 2011 - 2015 Iterated integrals, geometric structures of configuration spaces and applications to quantum topological invariants
- 2011 - 2015 Quantum Topology and Modular Forms in Mathematical Physics
- 2010 - 2013 Representations of the quantum groups at roots of unity and its application to knot theory
- 2009 - 2011 結び目の体積予想の研究
- 2007 - 2009 Noether's Problem for Cremona Groups over algebraic number fields and its application to Number theory
- 2007 - 2008 Volume conjecture for knots and 3-manifolds
- 2005 - 2006 General research of the volume conjecture of knots
- 2003 - 2005 Construction of Generic Polynomials in Galois Theory and application to Number Theory
- 2000 - 2003 De Rham Theory of Loop Spaces and Quantum Topological Invariants
- 2001 - 2002 低次元トポロジーの総合的研究
- 2000 - 2001 Representation theory of Algebraic Groups and Quantum Groups
- 1999 - 2001 共形場理論におけるモノドロミーのガロア表現への応用
- 1999 - 2001 ウェブ図の代数的研究
- 1998 - 2001 Representation theory of the quantized enveloping algebras and the quantized enveloping superalgebras
- 1998 - 2000 STRUCTURE OF THE MAPPING CLASS GROUP AND GEOMETRY OF THE MODULI SPACE OF RIEMANN SURFACES
- 1998 - 2000 Quantum structure of Riemann surfaces and its application to low-climensional topology
- 1998 - 2000 結び目の解消トンネルと双曲構造
- 1997 - 1999 Topological Field Theory and Related Geometry
- 1997 - 1999 Heegaand spliffings and hyperbolic structures of 3-manifolds
- 1997 - 1999 Rational Curves on Algebraic Varieties
- 1997 - 1998 Learning Baysian Networks based on the MDL principle
- 1997 - 1998 Completely integrable systema and representation theory of infinite dimen-sional algebras
- 1997 - 1998 表現論における新手法の研究
- 1996 - 1997 Experimental Method of Mathematics
- 1996 - 1996 有限半順序集合の組合せ論における代数的基礎理論の研究
- 1996 - 1996 頂点作用素代数の数理物理学への応用
- 1996 - 1996 ファインマン図を用いた幾何や数理物理の新しい手法とその応用
- 1995 - 1996 Geometric Study of Algebraic Systems
- 1995 - 1995 結び目や3次元多様体の表現論的な手法を用いた分類
- 1995 - 1995 単項式イデアルの極小自由分解の研究
- 1994 - 1995 Arithmetics on Jacobian Varieties
- 1994 - 1994 ブレイド群の表現論
- 1993 - 1994 Fixed point theorems and cobordism
- 1992 - 1993 Representations of Groups, Lie Algebras, and Algebras
- 1991 - 1991 環境の動的構造を学習する神経回路網の研究
- 1990 - 1990 動的パタ-ンの神経回路網による認識と学習の機構
- 1990 - 1990 同変Sーコボルディズム理論と誘導定理
- 1990 - 1990 楕円曲線の整数論
- 1989 - 1989 ヘッケ環の表現論
- 1987 - 1988 有限群と代数群の表現論
- 1983 - 1983 Arrangement に作用する群の表現論
- Mapping Class Group of Surfaces and Geometry of Moduli Spaces
- Geometry of Groups and Moduli Spaces (2)
- Study on geometry of knots and three manifolds by using representation theory of quantum groups
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Papers (65)：
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Qingtao Chen, Jun Murakami. ASYMPTOTICS OF QUANTUM 6j SYMBOLS. Journal of Differential Geometry. 2023. 123. 1. 1-20
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Jun Murakami, Roland van der Veen. Quantized representations of knot groups. Quantum Topology. 2023. 14. 4. 659-692
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Marco De Renzi, Jun Murakami. Non-semisimple 3-manifold invariants derived from the Kauffman bracket. Quantum Topology. 2022. 13. 2. 255-333
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C. Blanchet, M. De Renzi, J. Murakami. DIAGRAMMATIC CONSTRUCTION OF REPRESENTATIONS OF SMALL QUANTUM sl 2. Transformation Groups. 2021
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Alexander Kolpakov, Jun Murakami. Combinatorial Decompositions, Kirillov-Reshetikhin Invariants, and the Volume Conjecture for Hyperbolic Polyhedra. Experimental Mathematics. 2018. 27. 2. 193-207
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MISC (1)：
-
村上 順. 可積分系や量子化と不変量 (特集 物理と数学をつなぐ結び目理論). 数理科学. 1997. 35. 12. 28-35
Books (15)：
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結び目と量子群
朝倉書店 2000
-
量子不変量
日本評論社 1999
-
現代数学序説 2
大阪大学出版会 1998
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Representation of mapping class groups via the universal perturbative invariant
Proceedings of Knots 96, ed. S. Suzuki, World Scientific 1997
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The Casson invariant for a knot in a 3-manifold
Geomatry and Physics (Ed. Anderson, Dupont Pedersen and Swan), Lecture notes in pure and applied mathematics 1996
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Lectures and oral presentations (51)：
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Volume conjecture for the logarithmic invariant
(Volume Conjecture in Tokyo 2018)
-
On a q-deformation of PSL(2) representation of knot groups
(Low dimensional topology and number theory X 2018)
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Presentation of knots by a braided Hopf algebra
(Modular Forms and Quantum Knot Invariants 2018)
-
Braided Wirtinger presentation of knots
(Representation Spaces, Teichmüller Theory, and their Relationship with 3-manifolds from the Classical and Quantum Viewpoints 2018)
-
On the volume conjecture of quantum knot invariants
(Low-dimensional Topology and Number Theory 2017)
ｍore...
Education (2)：
- - 1982 University of Tokyo Graduate School, Division of Science Mathematics
- - 1980 University of Tokyo Faculty of Science Department of Mathematics
Professional career (2)：
- Master of Science (University of Tokyo)
- Doctor of Science (Osaka University)
Work history (6)：
- 1993 - 2001 Osaka University, Associate Professor
- 2001 - Waseda Unviersity, Professor
- 1992 - 1993 Max-Plank Institute for Mathematics (Bonn, Germany), Researcher
- 1990 - 1993 Osaka University, Lecturer
- 1991 - 1992 Institute for Advanced Studies (Princeton, USA), Member
- 1982 - 1989 Osaka University, Research Assistant
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Awards (1)：
- 2021 - Mathematical Society of Japan MSJ Geometry Prize
Association Membership(s) (1)：
The Mathematical Society of Japan
