Equivariant Symplectic and Algebraic Geometry

等变辛和代数几何

• 批准号: 1000229278-2013
• 负责人: Harada, Megumi
• 金额: $ 3.64万
• 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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=653044
• 关键词: Equivariant; Symplectic; Algebraic; Geometry

Many problems in Mathematics involve solving a system of equations. Algebraic Geometry is precisely the study of the solutions to systems of algebraic equations, and is therefore a core area of Mathematics. Algebraic geometry also has applications in quantum computing, cryptography, and image and signal processing. Combinatorial geometry includes the study of polytopes, which are generalizations of figures in plane geometry such as trapezoids and parallelograms. The convex geometry of polytopes has applications in optimization theory. The objective of the proposed research is to develop the new theory of Okounkov bodies, which connects these research areas.

数学中的许多问题都涉及到解方程组。代数几何正是研究代数方程组的解决方案，因此是数学的核心领域。代数几何在量子计算、密码学、图像和信号处理中也有应用。组合几何学包括多面体的研究，多面体是平面几何中图形的推广，如长方体和平行四边形。多面体的凸几何在最优化理论中有应用。拟议的研究的目标是发展新的理论的Okounkov机构，连接这些研究领域。