Symmetric representation and the categorification of cluster structure on non-orientable surfaces

• Project/Area Number: 24K06666
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 11010:Algebra-related
• Research Institution: Nagoya University
• Principal Investigator: チャン アーロンケイヤム 名古屋大学, 高等研究院(多元), 特任助教 (50845039)
• Project Period (FY): 2024-04-01 – 2029-03-31
• Project Status: Granted (Fiscal Year 2024)
• Budget Amount: ¥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: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2026: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2025: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2024: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: representation theory / cluster structure / topological surfaces

Outline of Research at the Start

Cluster algebras are mathematical structures generated by variables that can change in specific ways. Our interest is in those that arise from the study of geometry of topological surfaces. Our aim is to study this by expanding some of the current algebraic methods called categorification.