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The pursuit of ergodic Ramsey theory and metric number theory for infinite ergodic transformations

Research Project

Project/Area Number 25K07035
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionJapan Women's University

Principal Investigator

夏井 利恵  日本女子大学, 理学部, 教授 (60398633)

Project Period (FY) 2025-04-01 – 2029-03-31
Project Status Granted (Fiscal Year 2025)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2028: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2027: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2026: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2025: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsergodic theory / metric number theory / ergodic Ramsey theory
Outline of Research at the Start

無限大不変測度を持つ可測力学系においてrandomnessを捉える新しい不変量を発見することを目指す。研究全般を通して、具体的かつ多様な数論的変換に対する研究を地道に積み重ねて行く。そこで様々な数論的変換に対する多角的な研究アプローチから数の振舞いを探りながら、fibred systemに研究対象を広げて行く。ここでは従来の有限不変測度系から無限大不変測度系へと拡張して行く中でこの系特有の性質から新しい不変量を見出し、randomnessとdeterminismの違いを捉える。

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Published: 2025-04-17   Modified: 2025-06-20  

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