Conference on Symmetry, Invariants, and their Applications

North Carolina State University, Raleigh NC

Investigators

Abstract

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.