2022 Fiscal Year Final Research Report
Studies on Mock Modular Forms and Quantum Invariants
| Project/Area Number |
16H03927
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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 |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
村上 斉 東北大学, 情報科学研究科, 教授 (70192771)
藤 博之 大阪工業大学, 情報科学部, 教授 (50391719)
山崎 玲 (井上玲) 千葉大学, 大学院理学研究院, 教授 (30431901)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Keywords | 数理物理 / 量子トポロジー / モジュラー形式 |
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| Outline of Final Research Achievements |
A mock modular form is defined as a holomorphic part of the harmonic Maass forms. A typical example is the Ramanujan mock theta function, which has a weight 1/2 mock modular form. It is originally related to the integer partition. Recently it is recognized that mock modular form plays an important role in quantum topology. In the present research, we studied quantum modular form by use of the cluster algebra and the double affine Hecke algebra, and clarified new aspects of quantum invariants.
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| Free Research Field |
数理物理
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| Academic Significance and Societal Importance of the Research Achievements |
量子トポロジーの研究は，量子計算，特にトポロジカル量子計算の応用研究につながる．結び目や3次元多様体の量子不変量の性質，特にモジュラー形式との関係はじめ数論的性質を明らかにしようとする研究課題は比較的新しいものであり，今後の応用・発展につながることが期待できる．
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