Motivic Galois group(Fostering Joint International Research)

2019 Fiscal Year Final Research Report

• Project/Area Number: 15KK0159
• Research Category: Fund for the Promotion of Joint International Research (Fostering Joint International Research)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Nagoya University
• Principal Investigator: FURUSHO HIDEKAZU 名古屋大学, 多元数理科学研究科, 教授 (60377976)
• Project Period (FY): 2016 – 2019
• Keywords: モチヴィックガロア群 / 多重ゼータ値 / associators / double shuffle関係式

Outline of Final Research Achievements

To make clearer a relationship of the motivic Galois group with various fields of mathematics, I conducted researches, particularly on multiple zeta values and associators, and obtained the following results:
geometric interpretation of the harmonic coproduct of multiple zeta values and constructions of its Betti counterpart, a method to calculate coefficients of the Alekseev-Torossian associator, relationship of associator relations and relations among multiple zeta values obtained in knot theory, relations between p-adic multiple L-functions and cyclotomic multiple harmonic values.

Free Research Field

代数学

Academic Significance and Societal Importance of the Research Achievements

モチヴィックガロア群の研究は数論幾何学のみならず、様々な分野と関連していることが概念的に指摘されている。多重ゼータ値等の非常に具体的な対象を通じて研究することで、この繋がりはより直接的になり、またより明らかなものになる。