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The goal of the forthcoming school is to present recent results in differential geometry related to nonlinear PDEs, mathematical physics, and moving frames.

The lectures will focus on Lie groups and pseudogroups which play an important role in these fields, and we will discuss different ways of studying their orbit spaces. Two main topics are Poisson algebras and differential invariants. The theory will be illustrated by examples from algebraic and differential geometry, fluid dynamics, and thermodynamics.

The third main topic is moving frames. The lectures will center on the basic theory, computational techniques, and applications of the new, equivariant approach to the method of moving frames, concentrating one the case of finite-dimensional Lie group actions. The methods will be illustrated by examples chosen from an ever-expanding range of applications, including differential geometry, partial differential equations, calculus of variations, geometric flows, integrable systems, classical invariant theory, numerical analysis, and image processing including the automatic reassembly of broken objects: jigsaw puzzles, egg shells, and bone fragments.

The school will provide young researchers with an opportunity to interact with their colleagues and well-known researchers in the field. Selected materials of the school and workshop will be published by Springer Nature.