Quantum Topology and Modular Forms in Mathematical Physics
| Project/Area Number |
23340115
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kyushu University |
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Principal Investigator |
HIKAMI Kazuhiro 九州大学, 数理(科)学研究科(研究院), 准教授 (60262151)
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| 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)
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| Co-Investigator(Renkei-kenkyūsha) |
KANEKO Masanobu 九州大学, 数理学研究院, 教授 (70202017)
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| Project Period (FY) |
2011-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥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)
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| 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 |
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| 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.
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Report
(5 results)
Research Products
(91 results)
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[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
Related Report
Invited
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