Quantum Topology and Modular Forms in Mathematical Physics

2014 Fiscal Year Final Research Report

• 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
• Keywords: 数理物理 / モジュラー形式 / 量子トポロジー

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.

Free Research Field

数理物理