Categorical representation theory and its applications to gnerating functions, dynamical systems and algebraic statistics
| Project/Area Number |
25400001
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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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| Research Field |
Algebra
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| Research Institution | Hokusei Gakuen University (2015)
Hokkaido University (2013-2014) |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 有限群の表現論 / 圏論 / バーンサイド環 / マッキー関手 / 代数学の応用 / 公理的表現論 / ヘッケカテゴリー / 抽象バーンサイド環 / カテゴリー論の応用 / 鉛同位体法 / MCMC法 / 有限群のゼータ関数 / 圏の普遍ゼータ関数 / 力学系のゼータ関数 / 再構成予想 / 単項バーンサイド環 / 高次元分割表 / 人文学における数理方法 / エレメントの圏 |
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| Outline of Final Research Achievements |
(1) Categorical representation theory is abstract theory in mathematics. But it has many application in math. Many results have been published or so will be.
(2) Universal zeta funcitons of categories have relations with much area of math, e.g., reconstruction conjecure for graphs and Yoneda's lemma.
(3) A new appplication of group theory to algebraic statistics was discovered. Camberra metric which appeared in lead isotopo method is also related to Numerical analysis.
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Report
(4 results)
Research Products
(12 results)
