Life around the scallop theorem

Around the Pcp Theorem

jeev Arora, from Princeton, was the guest speaker. The participants thus had a unique occasion to hear about what is arguably the most spectacular result in the history of computational complexity from someone who was deeply involved in its development. Many thanks to the note-takers, and very, very special thank you to Sanjeev who was so generous with his time and energy.

Generalized Scallop Theorem for Linear Swimmers

In this article, we are interested in studying locomotion strategies for a class of shape-changing bodies swimming in a fluid. This class consists of swimmers subject to a particular linear dynamics, which includes the two most investigated limit models in the literature: swimmers at low and high Reynolds numbers. Our first contribution is to prove that although for these two models the locomot...

Around the Complete Intersection Theorem

A Coordinate-Based Proof of the Scallop Theorem

We reconsider fluid dynamics for a self-propulsive swimmer in Stokes flow. With an exact definition of deformation of a swimmer, a coordinate-based proof is first given to Purcell’s scallop theorem including the body rotation.

Around the tangent cone theorem

A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several cl...