2022 Fiscal Year Final Research Report
Algebraic combinatorics and its ties with other areas
| Project/Area Number |
20K03551
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Tohoku University |
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Principal Investigator |
Tanaka Hajime 東北大学, 情報科学研究科, 准教授 (50466546)
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| Project Period (FY) |
2020-04-01 – 2023-03-31
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| Keywords | 距離正則グラフ / アソシエーションスキーム / Terwilliger 代数 / グラフのスペクトル / 量子ウォーク / 量子中心極限定理 |
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| Outline of Final Research Achievements |
I explored applications of the representation theory of noncommutative semisimple matrix algebras associated with a graph and obtained results, such as vertex search algorithms on graphs based on quantum walks and quantum central limit theorems on graphs. Besides, I worked on research on graphs from the viewpoint of quantum probability theory and partial proof of a conjecture about the duality of association schemes, etc. At around the end of the period of the research plan, I was also involved with multiple projects on certain quantum algorithms and graphic rendering, etc., and I plan to publicize the outcomes as soon as they are ready.
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| Free Research Field |
代数的組合せ論・代数的グラフ理論
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| Academic Significance and Societal Importance of the Research Achievements |
代数的グラフ理論或いはグラフのスペクトル理論はそもそも情報理論等の工学的分野とも直接関わって発展してきたが、本研究計画では量子情報理論や量子確率論、さらには工学の分野 (グラフィックレンダリング) についても成果を上げることができ、数学の理論・応用の両側面について十分な貢献を行うことができたものと考える。特に、量子情報理論の研究は2018年頃より構想を進めてきたものであり、本研究計画期間中に予定通り実施できたのは大きな進展である。
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