Quantum Topology and Modular Forms in Mathematical Physics

• Project/Area Number: 23340115
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Kyushu University
• Principal Investigator: HIKAMI Kazuhiro 九州大学, 数理(科)学研究科(研究院), 准教授 (60262151)
• Co-Investigator(Kenkyū-buntansha): EGUCHI Tohru 立教大学, 理学研究科, 特任教授 (20151970) ; MURAKAMI Hitoshi 東北大学, 情報科学研究科, 教授 (70192771) ; MURAKAMI Jun 早稲田大学, 理工学術院, 教授 (90157751)
• Co-Investigator(Renkei-kenkyūsha): KANEKO Masanobu 九州大学, 数理学研究院, 教授 (70202017)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥11,570,000 (Direct Cost: ¥8,900,000、Indirect Cost: ¥2,670,000); Fiscal Year 2014: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2013: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2012: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2011: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
• Keywords: 数理物理 / モジュラー形式 / 量子トポロジー / トポロジー / 量子不変量 / 結び目 / ムーンシャイン / 共形場理論 / 双曲体積

Outline of Final Research Achievements

Quantum invariants of knots and 3-manifolds has been developed since Jones and Witten. We have studied a geometric aspect of the colored Jones polynomial. Some of the colored Jones polynomial was shown to have a nearly-modular property.
We have applied a method of the Ramanujan mock theta function to the superconformal algebra. We have studied "moonshine" phenomena which suggests a strange relationship between Fourier coefficients of mock theta function and irreducible representation of finite groups.

Research Products

• [Journal Article] Torus knots and quantum modular forms (2015)
  • Author(s): K. Hikami and J. Lovejoy
  • Journal Title: Research in the Mathematical Sciences Volume: 2 Issue: 1 Pages: 1-15
  • DOI: 10.1186/s40687-014-0016-3
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Braids, complex volume, and cluster algebra (2015)
  • Author(s): K. Hikami and R. Inoue
  • Journal Title: Algebraic and Geoemtric Topology Volume: 未定
  • Peer Reviewed
• [Journal Article] Generalized Kashaev invariants for knots in three manifolds (2015)
  • Author(s): J. Murakami
  • Journal Title: Quantum Topology Volume: 未定
  • Peer Reviewed
• [Journal Article] The colored Jones polynomial, the Chern-Simons invariant, and the Reidemeister torsion of a twice-iterated torus knot (2015)
  • Author(s): H. Murakami
  • Journal Title: Acta Math. Vietnam Volume: 39 Issue: 4 Pages: 649-710
  • DOI: 10.1007/s40306-014-0084-x
  • Peer Reviewed
• [Journal Article] Braiding operator via quantum cluster algebra (2014)
  • Author(s): Kazuhiro Hikami, Rei Inoue
  • Journal Title: Journal of Physics A: Mathematical and Theoretical Volume: 47 Issue: 47 Pages: 1-21
  • DOI: 10.1088/1751-8113/47/47/474006
  • Peer Reviewed / Open Access
• [Journal Article] Lattice gauge theory and the large N reduction (2014)
  • Author(s): Tohru Eguchi
  • Journal Title: Int.J.Mod.Phys.A Volume: 29 Issue: 15 Pages: 1430036-1430036
  • DOI: 10.1142/s0217751x14300361
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Compact formulas for the completed mock modular forms (2014)
  • Author(s): T. Eguchi and Y. Sugawara
  • Journal Title: Journal of High Energy Physics Volume: 2014 Issue: 11 Pages: 1-28
  • DOI: 10.1007/jhep11(2014)156
  • Peer Reviewed / Open Access
• [Journal Article] Cluster Algebra and Complex Volume of Once-Punctured Torus Bundles and Two-Bridge Knots (2014)
  • Author(s): Kazuhiro Hikami and Rei Inoue
  • Journal Title: J. Knot Theory and Its Ramifications Volume: 23 Issue: 01 Pages: 1450006-1450006
  • DOI: 10.1142/s0218216514500060
  • Peer Reviewed
• [Journal Article] Enriques Moonshine (2013)
  • Author(s): Tohru Eguchi and Kazuhiro Hikami
  • Journal Title: J. Phys. A Volume: 46 Issue: 31 Pages: 312001-312001
  • DOI: 10.1088/1751-8113/46/31/312001
  • Peer Reviewed
• [Journal Article] Cluster algebra and complex volume (2013)
  • Author(s): Kazuhiro Hikami, Rei Inoue
  • Journal Title: RIMS Kokyuroku Volume: 1866
• [Journal Article] The coloured Jones polynomial, the Chern-Simons invariant, and the Reidemeister torsion of the figure-eight knot (2013)
  • Author(s): Hitoshi Murakami
  • Journal Title: J.Topology Volume: 6 Issue: 1 Pages: 193-216
  • DOI: 10.1112/jtopol/jts036
  • Peer Reviewed
• [Journal Article] Invariants of handlebody-knots via Yokota's invariants (2013)
  • Author(s): Atsuhiko Mizusawa, Jun Murakami
  • Journal Title: J. Knot Theory Ramifications Volume: 22 Issue: 11 Pages: 1350068-1350068
  • DOI: 10.1142/s0218216513500685
  • Peer Reviewed
• [Journal Article] Optimistic limits of the colored Jones polynomials (2013)
  • Author(s): Jinseok Cho, Jun Murakami
  • Journal Title: J. Korean Math. Soc. Volume: 85 Issue: 3 Pages: 641-693
  • DOI: 10.4134/jkms.2013.50.3.641
  • Peer Reviewed
• [Journal Article] On SL(2, C) quantum 6j-symbol and its relation to the hyperbolic volume (2013)
  • Author(s): Francesco Costantino, Jun Murakami
  • Journal Title: Quantum Topol. Volume: 4 Issue: 3 Pages: 303-351
  • DOI: 10.4171/qt/41
  • Peer Reviewed
• [Journal Article] Modular Forms and Second Order Ordinary Differential Equations : Applications to Vertex Operator Algebras (2013)
  • Author(s): Masanobu Kaneko, Kiyokazu Nagatomo, Yuichi Sakai
  • Journal Title: Letters in Mathematical Physics Volume: 103 (4) Issue: 4 Pages: 439-453
  • DOI: 10.1007/s11005-012-0602-5
  • NAID: 120005227214
  • URL: http://catalog.lib.kyushu-u.ac.jp/recordID/26122
  • Peer Reviewed
• [Journal Article] The Ramanujan-Serre differential operators and certain elliptic curves (2013)
  • Author(s): Masanobu Kaneko, Yuichi Sakai
  • Journal Title: Proceedings of the American Mathematical Society Volume: 141 (10) Issue: 10 Pages: 3421-3429
  • DOI: 10.1090/s0002-9939-2013-11917-9
  • NAID: 120005323553
  • URL: http://catalog.lib.kyushu-u.ac.jp/recordID/27241
  • Peer Reviewed
• [Journal Article] Double zeta values, double Eisenstein series, and modular forms of leve 12 (2013)
  • Author(s): M. Kaneko, K. Tasaka
  • Journal Title: Math. Ann Volume: 357(3) Issue: 3 Pages: 1091-1118
  • DOI: 10.1007/s00208-013-0930-5
  • URL: http://catalog.lib.kyushu-u.ac.jp/recordID/27531
  • Peer Reviewed
• [Journal Article] On SL(2, C) quantum 6j-symbol and its relation to the hyperbolic volume (2013)
  • Author(s): Francesco Costantino, Jun Murakami
  • Journal Title: Quantum Topology Volume: ?
  • Peer Reviewed
• [Journal Article] Volume of a doubly truncated hyperbolic tetra- hedron (2012)
  • Author(s): Kolpakov, Alexander ; Murakami,Jun
  • Journal Title: Aequat. Math Volume: 電子速報版 Issue: 3 Pages: 1-15
  • DOI: 10.1007/s00010-012-0153-y
  • Peer Reviewed
• [Journal Article] N=2 moonshine (2012)
  • Author(s): T. Eguchi, K. Hikami
  • Journal Title: Phys.Lett. B Volume: 717 Issue: 1-3 Pages: 266-273
  • DOI: 10.1016/j.physletb.2012.09.037
  • Peer Reviewed
• [Journal Article] Twisted Elliptic Genus and Borcherds Product (2012)
  • Author(s): T. Eguchi, K. Hikami
  • Journal Title: Lett. Math. Phys. Volume: 102 Issue: 2 Pages: 203-222
  • DOI: 10.1007/s11005-012-0569-2
  • Peer Reviewed
• [Journal Article] Volume formulas for a spherical tetrahedron (2012)
  • Author(s): Jun Murakami
  • Journal Title: Proceedings of American Mathematical Society Volume: 140 Pages: 3289-3295
  • Peer Reviewed
• [Journal Article] On Fourier coefficients of some meromorphic modular forms (2012)
  • Author(s): Yutaro Honda, Masanobu Kaneko
  • Journal Title: Bulletin of the Korean Mathematical Society Volume: 49(6) Issue: 6 Pages: 1349-1357
  • DOI: 10.4134/bkms.2012.49.6.1349
  • NAID: 120004951632
  • Peer Reviewed
• [Journal Article] The volume formulas for a spherical tetrahedron (2012)
  • Author(s): J.Murakami
  • Journal Title: Proceedings of American Mathematical Society Volume: (掲載決定)
  • Peer Reviewed
• [Journal Article] On SL(2,C) quantum 6j-symbol and its relation to the hyperbolic volume (2012)
  • Author(s): F.Costantino, J.Murakami
  • Journal Title: Quantum Topology Volume: (掲載決定)
  • Peer Reviewed
• [Journal Article] On Fourier coefficients of some meromorphic modular forms (2012)
  • Author(s): M.Kaneko, Y.Honda
  • Journal Title: Bulletin of the Korean Mathematical Society Volume: (掲載決定)
  • NAID: 120004951632
  • Peer Reviewed
• [Journal Article] Representations and the colored Jones polynomial of a torus knot (2011)
  • Author(s): K.Hikami, H.Murakami
  • Journal Title: AMS/IP Studies in Advanced Mathematics Volume: 50 Pages: 153-171
  • Peer Reviewed
• [Journal Article] Decomposition of Witten-Reshetikhin-Turaev invariant : linking pairing and modular forms (2011)
  • Author(s): K.Hikami
  • Journal Title: AMS/IP Studies in Advanced Mathematics Volume: 50 Pages: 131-151
  • Peer Reviewed
• [Journal Article] Non-holomorphic modular forms and SL(2,R)/U(1) Superconformal Fieldtheory (2011)
  • Author(s): T.Eguchi, Y.Sugawara
  • Journal Title: Journal of High Energy Physics Volume: 1103 Issue: 3
  • DOI: 10.1007/jhep03(2011)107
  • NAID: 120003437137
  • Peer Reviewed
• [Journal Article] Note on twisted elliptic genus of K3 surface (2011)
  • Author(s): Tohru Eguchi and Kazuhiro Hikami
  • Journal Title: Physics Letters B Volume: 694 Issue: 4-5 Pages: 446-455
  • DOI: 10.1016/j.physletb.2010.10.017
  • Peer Reviewed
• [Journal Article] Notes on the K3 surface and the Mathieu group M24 (2011)
  • Author(s): Tohru Eguchi, Hirosi Ooguri and Yuji Tachikawa
  • Journal Title: Experimental Mathematics Volume: 20 Issue: 1 Pages: 91-96
  • DOI: 10.1080/10586458.2011.544585
  • Peer Reviewed
• [Journal Article] An introduction to the volume conjecture (2011)
  • Author(s): H.Murakami
  • Journal Title: Contemporary Mathematics Volume: 541 Pages: 1-40
  • Peer Reviewed
• [Journal Article] Elliptic curves and Fibonacci numbers arising from Lindenmayer system with Symbolic Computation (2011)
  • Author(s): Hiroshi Yoshida, Yoshihiro Miwa, Masanobu Kaneko
  • Journal Title: Applicable Algebra in Engineering, Communication and Computing Volume: 22 Issue: 2 Pages: 147-164
  • DOI: 10.1007/s00200-011-0143-7
  • NAID: 120003783219
  • Peer Reviewed
• [Journal Article] Congruences modulo 4 of calibers of real quadratic fields (2011)
  • Author(s): M.Kaneko, K.Mori
  • Journal Title: Ann.Sci.Math.Quebec Volume: 35(2) Pages: 185-195
  • NAID: 120003734031
  • Peer Reviewed
• [Journal Article] On the SO(N) and Sp(N) free energy of a rational homology 3-sphere (2011)
  • Author(s): 高田敏恵
  • Journal Title: International Joounal of Mathematics Volume: 22 Issue: 04 Pages: 465-482
  • DOI: 10.1142/s0129167x11006866
  • Peer Reviewed
• [Presentation] K3 surface and Mathie moonshine (2015)
  • Author(s): 江口
  • Organizer: Moduli Space, Conformal Field Theory and Matrix Model
  • Place of Presentation: 沖縄OIST
  • Year and Date: 2015-03-16
  • Invited
• [Presentation] モックテータ函数の周辺 (2015)
  • Author(s): 樋上
  • Organizer: 東北大学 情報科学研究科 談話会
  • Place of Presentation: 東北大学
  • Year and Date: 2015-01-16
  • Invited
• [Presentation] K3 Surface and Mathieu moonshine (2014)
  • Author(s): 江口
  • Organizer: 岡潔シンポジウム
  • Place of Presentation: 奈良女子大学
  • Year and Date: 2014-12-08
  • Invited
• [Presentation] Logarithmic invariants of links (2014)
  • Author(s): J. Murakami
  • Organizer: Quantum Topology and Physics 2014 in Fukuoka
  • Place of Presentation: 九州大学
  • Year and Date: 2014-09-18
  • Invited
• [Presentation] Logarithmic knot invariants and hyperbolic volumes (2014)
  • Author(s): J. Murakami
  • Organizer: Knots and Low Dimensional Manifolds
  • Place of Presentation: BEXCO Convention & Exivition Center II, Korea
  • Year and Date: 2014-08-25
  • Invited
• [Presentation] Quantum modular form from torus knots (2014)
  • Author(s): K. Hikami
  • Organizer: Low-Dimensional Topology and Number Theory
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach, Germany
  • Year and Date: 2014-08-22
  • Invited
• [Presentation] The colored Jones polynomial, the Chern-Simons invariant, and the Reidemeister torsion of a cable knot (2014)
  • Author(s): H. Murakami
  • Organizer: Low-Dimensional Topology and Number Theory
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach, Germany
  • Year and Date: 2014-08-20
  • Invited
• [Presentation] On the volume conjecture and its generalizations (2014)
  • Author(s): H. Murakami
  • Organizer: The 2014 KMJ Conference for Accreditation Strategies
  • Place of Presentation: Kyungpook National University, Korea
  • Year and Date: 2014-08-08
  • Invited
• [Presentation] Logarithmic invariants of knots (2014)
  • Author(s): J. Murakami
  • Organizer: Quantum Curves and Quantum Knot Invariants
  • Place of Presentation: Banff International Research Station, Canada
  • Year and Date: 2014-06-19
  • Invited
• [Presentation] Volume conjecture for logarithmic invariant of knots (2014)
  • Author(s): J. Murakami
  • Organizer: Mini-Workshop on the Volume Conjecture
  • Place of Presentation: Korea Institute for Advanced Study, Korea
  • Year and Date: 2014-06-11
  • Invited
• [Presentation] Mathieu moonshine and superconformal algebra (2014)
  • Author(s): 江口
  • Organizer: workshop on string theory
  • Place of Presentation: 精華大学、台湾
  • Year and Date: 2014-05-15
  • Invited
• [Presentation] (mock) modular form and quantum invariant (2014)
  • Author(s): K. Hikami
  • Organizer: Mock Modular Forms and Physics: Black Holes, Moonshine, and Conformal Field Theory
  • Place of Presentation: The Institute of Mathematical Sciences, India
  • Year and Date: 2014-04-15
  • Invited
• [Presentation] Mock theta functions and moonshine (2013)
  • Author(s): Kazuhiro Hikami
  • Organizer: Lectures on q-series and modular forms
  • Place of Presentation: Korea Institute for Advanced Study
  • Invited
• [Presentation] Hyperbolic geometry and dilogarithm (2013)
  • Author(s): Kazuhiro Hikami
  • Organizer: Quantum dilogarithm, modular double, and representation theory
  • Place of Presentation: 大阪市立大学
  • Invited
• [Presentation] Congruences of Markoff numbers via Farey parametrization (2012)
  • Author(s): 金子昌信
  • Organizer: Special Session of the AMS 2012 Spring Western Section Meeting
  • Place of Presentation: University of Hawaii at Manoa(アメリカ)
  • Year and Date: 2012-03-04
• [Presentation] An algebraic formula of the Witten-Reshetikhin-Turaev invariant for 3-manifolds (2012)
  • Author(s): 高田敏恵
  • Organizer: The 8^<th> East Asian School of Knots and Related Topics
  • Place of Presentation: KATST(韓国)(招待講演)
  • Year and Date: 2012-01-09
• [Presentation] 3次元球面内の四面体の体積公式 (2011)
  • Author(s): 村上順
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-30
• [Presentation] Markoff numbers and Farey sequences (2011)
  • Author(s): 金子昌信
  • Organizer: The 1st International Congress on Natural Sciences (ICNS2011)
  • Place of Presentation: Pukyong National University(韓国)
  • Year and Date: 2011-08-26
• [Presentation] Ribbon Hopf algebrasと3次元多様体の量子不変量 (2011)
  • Author(s): 高田敏恵
  • Organizer: 結び目の量子不変量とそのカテゴリー化
  • Place of Presentation: 早稲田大学(東京)(招待講演)
  • Year and Date: 2011-08-24
• [Presentation] Ramanujan擬テータ函数とMathieu Moonshine (2011)
  • Author(s): 樋上和弘
  • Organizer: 福岡数論
  • Place of Presentation: 九州大学(福岡)(招待講演)
  • Year and Date: 2011-08-23
• [Presentation] Volume conjecture and quantum dilogarithm function (2011)
  • Author(s): 樋上和弘
  • Organizer: Simons Summer Workshop in Mathematics and Physics
  • Place of Presentation: Simons Center for Geometry and Physics(アメリカ)(招待講演)
  • Year and Date: 2011-08-12
• [Presentation] Hoffman予想(Brownの定理)をめぐって,いくつかの実験 (2011)
  • Author(s): 金子昌信
  • Organizer: 関西多重ゼータ研究会
  • Place of Presentation: 大阪工業大学大宮キャンパス(大阪市)(招待講演)
  • Year and Date: 2011-08-05
• [Presentation] K3 surface and Mathieu Group M24 (2011)
  • Author(s): 江口徹
  • Organizer: Branes, Strings and Supergravity
  • Place of Presentation: Istanbul(トルコ)(招待講演)
  • Year and Date: 2011-08-01
• [Presentation] Character decomposition of elliptic genus (2011)
  • Author(s): 樋上和弘
  • Organizer: Workshop on Mathieu Moonshine
  • Place of Presentation: ETH Zurich(スイス)(招待講演)
  • Year and Date: 2011-07-09
• [Presentation] K3 surface and Mathieu group M24 (2011)
  • Author(s): 江口徹
  • Organizer: Workshop on Mathieu Moonshine
  • Place of Presentation: ETH Zurich(スイス)(招待講演)
  • Year and Date: 2011-07-07
• [Presentation] K3 surface and Mathieu group M24 (2011)
  • Author(s): 江口徹
  • Organizer: 弦理論3世代研究会
  • Place of Presentation: IHES, Paris(フランス)(招待講演)
  • Year and Date: 2011-05-16
• [Presentation] Double Eisenstein series and modular forms (2011)
  • Author(s): 金子昌信
  • Organizer: Workshop on multiple zeta values, modular forms and elliptic motives
  • Place of Presentation: University of Bristol(イギリス)
  • Year and Date: 2011-05-03
• [Presentation] Cluster algebra and complex volume
  • Author(s): Kazuhiro Hikami
  • Organizer: Intelligence of Low-Dimensional Topology
  • Place of Presentation: 数理解析研究所、京都大学
  • Invited
• [Presentation] Moonshine and N=2/4 superconformal algebra
  • Author(s): Kazuhiro Hikami
  • Organizer: Mock modular forms, moonshine, and string theory
  • Place of Presentation: Simons Center for Geometry and Physics
  • Invited
• [Presentation] Quantum modular form and quantum invariant
  • Author(s): Kazuhiro Hikami
  • Organizer: Modular functions and quadratic forms --- number theoretic delights
  • Place of Presentation: 中之島センター、大阪大学
  • Invited
• [Presentation] Mathieu moonshine and K3 surface
  • Author(s): Tohru Eguchi
  • Organizer: Mock modular forms, moonshine, and string theory
  • Place of Presentation: Simons Center for Geometry and Physics, USA
  • Invited
• [Presentation] 超弦理論の進展
  • Author(s): 江口徹
  • Organizer: 基礎物理学研究所60周年記念シンポジウム
  • Place of Presentation: 基礎物理学研究所、京都大学
  • Invited
• [Presentation] Mathieu moonshine and superconformal algebra
  • Author(s): Tohru Eguchi
  • Organizer: Arithmetic and algebraic geometry 2014
  • Place of Presentation: 東京大学
  • Invited
• [Presentation] マシュームーンシャインと超共形代数
  • Author(s): 江口徹
  • Organizer: Superstring theory and VOA
  • Place of Presentation: 立教大学
  • Invited
• [Presentation] Mathieu moonshine and superconformal algebra
  • Author(s): Tohru Eguchi
  • Organizer: Peter Goddard Symposium
  • Place of Presentation: IPMU, University of Tokyo
  • Invited
• [Presentation] How much does the colored Jones polynomial of a knot know about representations of the fundamental group to SL(2; C)?
  • Author(s): Hitoshi Murakami
  • Organizer: Quantum topology and hyperbolic geometry
  • Place of Presentation: Nha Trang, Vietnam
  • Invited
• [Presentation] Survey of the volume conjecture
  • Author(s): Hitoshi Murakami
  • Organizer: Geometric topology in Cortona
  • Place of Presentation: Cortona, Italy
  • Invited
• [Presentation] The colored Jones polynomial of a knot and SL(2;C) representations of the fundamental group of its complement
  • Author(s): Hitoshi Murakami
  • Organizer: Knots and Physics workshop in Amsterdam
  • Place of Presentation: University of Amsterdam, Netherlands
  • Invited
• [Presentation] Volume formulas for a spherical tetrahedron
  • Author(s): Jun Murakami
  • Organizer: Geometric structures on low-dimensional manifolds
  • Place of Presentation: Korean Institute for Advanced Study, Korea
  • Invited
• [Presentation] Knots invariants coming from the small quantum group
  • Author(s): Jun Murakami
  • Organizer: 第58回代数学シンポジウム
  • Place of Presentation: 広島大学
  • Invited
• [Presentation] Generalized Kashaev invariants for knots in three-manifolds
  • Author(s): Jun Murakami
  • Organizer: Modern Trends in Topological Quantum Field Theory, Workshop II
  • Place of Presentation: Erwin Schr&#246;dinger International Institute for Mathematical Physics, Austria
  • Invited
• [Presentation] Finite multiple zeta values
  • Author(s): Masanobu Kaneko
  • Organizer: 28th Journ&#233;es Arithm&#233;tiques JA2013
  • Place of Presentation: Fourier Institute, Unive. Grenoble
• [Presentation] On the elliptic modular function j(tau)
  • Author(s): Masanobu Kaneko
  • Organizer: Modular functions and quadratic forms --number theoretic delights
  • Place of Presentation: Nakanoshima Center, Osaka University
  • Invited
• [Presentation] Moonshine from Character Decompositions of Elliptic Genera
  • Author(s): K. Hikami
  • Organizer: Workshop on Modular Forms
  • Place of Presentation: Kyushu University
  • Invited
• [Presentation] Superconformal algebra, mock theta functions, and moonshine
  • Author(s): K. Hikami
  • Organizer: Hypergeometric Series and Their Generalizations in Algebra, Geometry, Number Theory and Physics
  • Place of Presentation: Institut Henri Poincare, France
  • Invited
• [Presentation] Decomposition of elliptic genera in terms of superconformal characters
  • Author(s): K. Hikami
  • Organizer: Decomposition of elliptic genera in terms of superconformal characters
  • Place of Presentation: MFO, Germany
  • Invited
• [Presentation] Cluster algebra and complex volume of 2-bridge knots
  • Author(s): K. Hikami
  • Organizer: Facets of integrability: random patterns, stochastic processes, hydrodynamics, gauge theories and condensed matter systems
  • Place of Presentation: Simons Center for Geometry and Physics, USA
  • Invited
• [Presentation] On the Complex Volume of Knots
  • Author(s): K. Hikami
  • Organizer: Bethe Ansatz, Quantum Groups and Beyond
  • Place of Presentation: 数理解析研究所
  • Invited
• [Presentation] Superconformal algebra and Mathieu group
  • Author(s): T. Eguchi
  • Organizer: Algebraic Geometry, Modular Forms, and Applications to Physics
  • Place of Presentation: International Centre for Mathematical Sciences, Edinburgh, UK
  • Invited
• [Presentation] Superconformal algebra and moonshine phenomenon
  • Author(s): T. Eguchi
  • Organizer: Geometry and Physics
  • Place of Presentation: Max-Planck Institute for Physics, Munich, Germany
  • Invited
• [Presentation] `The colored Jones polynomial, the Chern-Simons invariant, and the Reidemeister torsion of a knot
  • Author(s): H. Murakami
  • Organizer: New Perspectives in Topological Field Theories
  • Place of Presentation: Center for Mathematical Physics, Hamburg, Germany
  • Invited
• [Presentation] On the logarithmic knot invariants and the hyperbolic volume
  • Author(s): J. Murakami
  • Organizer: Low Dimensional Topology and Number Theory V
  • Place of Presentation: Soft Research Park, Fukuoka, Japan
  • Invited
• [Presentation] Logarithmic invariants of knots in three manifolds
  • Author(s): J. Murakami
  • Organizer: Exact Results in SUSY Gauge Theories and Integrable Systems
  • Place of Presentation: Rikkyo University, Japan
  • Invited
• [Presentation] Quantum 6j-symbols for non-integral highest weight representations of Uq(sly) at root of unity
  • Author(s): J. Murakami
  • Organizer: 日本数学会 秋季総合分科会
  • Place of Presentation: 九州大学
• [Presentation] Logarithmic invariants for knots in three manifolds
  • Author(s): J. Murakami
  • Organizer: ホップ代数と量子群 -- 応用の可能性
  • Place of Presentation: 数理解析研究所、京都大学
• [Presentation] Quantum invariants of knots and the hyperbolic volume
  • Author(s): J. Murakami
  • Organizer: The 29th International Colloquium on Group-Theoretical Method in Physics
  • Place of Presentation: Chern Institute of Mathematics, China
  • Invited