Conference on Symmetry, Invariants, and their Applications

“对称、不变量及其应用”会议将于2022年8月3日至5日在加拿大新斯科舍省达尔豪斯大学举行，现场和网上均可参加。该奖励基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的变换，也就是说，不变。许多生物、化学、物理和人造结构都以对称为基本设计原则或其功能的基本方面。在几何学中，费利克斯·克莱因在1872年提出的埃尔兰根计划清楚地指出了对称和不变量在流形几何研究中的重要性。对称群方法是在物理学、工程学和经济学中寻找非线性微分方程的闭形式解的最强大的技术之一。对称在我们对物理守恒定律的理解中是必不可少的，并且在各种现代应用中都有应用，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李点对称及其扩展在微分、有限差分、微分-差分、积分-微分、随机和分数阶微分方程的闭型解中的应用。这个主题与微分、积分和联合不变量的研究交织在一起，以及它们在广义相对论、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。这些不变量可以使用移动帧的方法来计算，其中递归关系解开了不变量代数的结构。运动框架在求解等价问题、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。该奖项反映了美国国家科学基金会的法定使命，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，认为值得支持。

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.