Conference on Symmetry, Invariants, and their Applications

对称性、不变量及其应用会议

• 批准号: 2217293
• 负责人: Irina Kogan
• 金额: $ 3.59万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2217293&HistoricalAwards=false
• 关键词: Conference; Symmetry; Invariants; their; Applications

The conference "Symmetry, Invariants, and their Applications" will take place on August 3-5, 2022 at Dalhousie University in Nova Scotia, Canada, both in person and on line. The award funds will help defray travel and local expenses of US-based participants, prioritizing support for graduate students, postdocs, early-career researchers, and members of underrepresented groups. Symmetries are transformations that keep a geometric object invariant, that is, unchanged. Many biological, chemical, physical, and man-made structures exhibit symmetries as fundamental design principles or essential aspects of their functioning. In geometry, the Erlangen program set forward by Felix Klein in 1872 clearly identified the importance of symmetry and invariants in the geometrical study of manifolds. Symmetry group methods are among the most powerful techniques available for finding closed-form solutions to nonlinear differential equations appearing in physics, engineering, and economics. Symmetries are essential in our understanding of conservation laws in physics and occur in a wide variety of modern applications including computer vision, automatic assembly of broken objects such as eggshells, pottery, and bones, and more.One of the central themes of the conference is the application of Lie point symmetries and their extensions to obtain closed-form solutions of differential, finite difference, differential-difference, integro-differential, stochastic, and fractional differential equations. This theme intertwines with the investigation of differential, integral, and joint invariants together with their applications in general relativity, computer vision, automated assembly problems, geometric numerical integration, and other fields. These invariants can be computed using the method of moving frames where the recurrence relations unlock the structure of the algebra of invariants. Moving frames play a crucial role in solving equivalence problems and studying geometric spaces, invariant geometric flows, and integrable systems.Conference website: https://www.math.mun.ca/movingframes2022/This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

会议“对称性，不变量及其应用”将于2022年8月3日至5日在加拿大新斯科舍省的达尔豪西大学举行，无论是亲自还是在线。该奖项的资金将帮助支付美国参与者的旅行和当地费用，优先支持研究生，博士后，早期职业研究人员和代表性不足的群体成员。 对称是保持几何对象不变（即不变）的变换。 许多生物、化学、物理和人造结构都表现出对称性，作为其基本设计原则或功能的基本方面。 在几何学中，埃尔兰根计划提出的费利克斯克莱因在1872年明确指出了重要性的对称性和不变量的几何研究的流形。 对称群方法是在物理学、工程学和经济学中发现非线性微分方程的封闭形式解的最强大的技术之一。对称性是我们理解物理学中守恒定律的基础，并且在各种各样的现代应用中出现，包括计算机视觉，蛋壳，陶器和骨头等破碎物体的自动组装等等。会议的中心主题之一是应用Lie点对称性及其扩展来获得微分，有限差分，微分差分，积分微分、随机和分数阶微分方程。这一主题与微分，积分和联合不变量及其在广义相对论，计算机视觉，自动装配问题，几何数值积分和其他领域的应用研究交织在一起。这些不变量可以使用移动标架的方法来计算，其中递归关系解锁了不变量代数的结构。 活动标架在解决等价问题和研究几何空间、不变几何流和可积系统中起着至关重要的作用。会议网站：https://www.math.mun.ca/movingframes2022/This奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。