Categorical representation theory and its applications to gnerating functions, dynamical systems and algebraic statistics

• Project/Area Number: 25400001
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Hokusei Gakuen University (2015); Hokkaido University (2013-2014)
• Principal Investigator: YOSHIDA Tomoyui 北星学園大学, 経済学部, 教授 (30002265)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥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)
• 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

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.

Research Products

• [Journal Article] 等差数列の標準偏差の整数性とペル方程式 x^2-3y^2=1. (2016)
  • Author(s): 吉田知行
  • Journal Title: 北星論集 Volume: 55-2 Pages: 131-135
  • Acknowledgement Compliant
• [Journal Article] 鉛同位体法の数理(1) (2015)
  • Author(s): 吉田知行
  • Journal Title: 数学セミナー Volume: 54-8
  • NAID: 40020534025
  • Peer Reviewed
• [Journal Article] 鉛同位体法の数理(2) (2015)
  • Author(s): 吉田知行
  • Journal Title: 数学セミナー Volume: 54-9 Pages: 52-56
  • NAID: 40020559320
  • Peer Reviewed
• [Journal Article] 鉛同位体法の数理(3) (2015)
  • Author(s): 吉田知行
  • Journal Title: 数学セミナー Volume: 54-10 Pages: 48-52
  • NAID: 40020592697
  • Peer Reviewed
• [Journal Article] 鉛同位体法の数理(4) (2015)
  • Author(s): 吉田知行
  • Journal Title: 数学セミナー Volume: 54-11 Pages: 48-53
  • NAID: 40020614771
• [Journal Article] The Category of Elements and its applications (2014)
  • Author(s): Yoshida, Tomoyuki
  • Journal Title: RIMS Kôkyûroku Volume: 1926 Pages: 13-24
  • Peer Reviewed
• [Journal Article] The Burnside ring and the universal zeta function of finite dynamical systems. (2014)
  • Author(s): Tomoyuki Yoshida
  • Journal Title: 数理解析研究所講究録 Volume: 1872 Pages: 122-131
  • Peer Reviewed
• [Presentation] 抽象バーンサイド環とその単数群 (2016)
  • Author(s): 吉田知行
  • Organizer: 群論シンポジウム
  • Place of Presentation: 近畿大学
  • Year and Date: 2016-03-02
  • Invited
• [Presentation] Reconstruction conjecture fro graphs and finite groups (2015)
  • Author(s): 吉田知行
  • Organizer: 愛媛大学代数談話会
  • Place of Presentation: 愛媛大学
  • Year and Date: 2015-10-05
  • Invited
• [Presentation] Reconstruction conjecture fro graphs and finite groups (2015)
  • Author(s): 吉田知行
  • Organizer: 代数的組み合わせ論シンポジウム
  • Place of Presentation: 金沢大学
  • Year and Date: 2015-06-06
  • Invited
• [Presentation] 鉛同位体法の統計的研究 (2014)
  • Author(s): 吉田知行
  • Organizer: 多様な分野における統計科学の教育・理論・応用の新展開
  • Place of Presentation: 新潟大学（新潟市）
  • Year and Date: 2014-10-10
  • Invited
• [Presentation] The category of elements and its applications (2014)
  • Author(s): 吉田知行
  • Organizer: RIMS 研究集会「有限群とその表現、頂点作用素代数、代数的組合せ論の研究」
  • Place of Presentation: 京都大学数理解析研究所大講堂(京都市)
  • Invited