Brought to maturity by Élie Cartan, the method of moving frames has been in the mathematical landscape for more than a century. From the Frenet-Serret frame to Cartan's "repère mobile" and beyond, moving-frame techniques have proven indispensable in the study of symmetries, invariants, and other intrinsic properties of geometrical objects. Explicit applications of moving-frame techniques range from classical differential geometry to integrable systems, and on toward control theory and computer vision.
The objective of this workshop is to discuss recent applications and theoretical advances of these techniques. Several particular topics will be covered regarding contemporary applications of both Cartan's equivalence method and equivariant moving frames in geometry and analysis, such as the geometry of differential equations and conservation laws, geometric submanifold flows, and classification problems in differential and algebraic geometry.
Each topic will begin with a one-hour general overview of the subject given by one of the primary speakers. It will be followed by more traditional contributed research talks of 30 to 45 minutes. Coverage of topics will conclude with discussion periods outlining theoretical developments and new applications worth pursuing in the years to come. The overall goal is to gain a collective view of recent advances in this field while also generating new ideas and fostering new collaborations.