Equivariant Symplectic And Algebraic Geometry

等变辛和代数几何

• 批准号: CRC-2018-00218
• 负责人: Harada, Megumi
• 金额: $ 7.29万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=730174
• 关键词: Equivariant; Symplectic; Algebraic; Geometry

Many problems in Mathematics involve systems of equations. Algebraic Geometry is the study of the solutions to such equations, and is a core area of Mathematics. Algebraic geometry has applications in quantum computing, cryptography, and signal processing. Combinatorial geometry includes the study of polytopes, which generalize plane figures such as trapezoids, and has applications in optimization theory. Combinatorics involves the study of graphs, which have applications in network theory and biology. The objective of the proposed research is to develop (1) the theory of Okounkov bodies and (2) the theory of Hessenberg varieties, both of which connect these research areas.

数学中的许多问题涉及方程组。代数几何是研究这些方程的解决方案，是数学的核心领域。代数几何在量子计算、密码学和信号处理中有应用。组合几何学包括多面体的研究，它概括了平面图形，如多面体，并在优化理论中有应用。组合数学涉及对图的研究，它在网络理论和生物学中有应用。建议的研究的目标是发展（1）Okounkov体的理论和（2）Hessenberg簇的理论，两者都连接这些研究领域。