Myriam Fradon (Lille)
What is the closest packing for a finite number of non-overlapping spheres with equal radius ? The answer to this apparently simple question in only known for very small systems, despite the existence of many applications in physics, storage, communication, engineering, and so on. We present a probabilistic approximation to the closest packing problem using reflected stochastic differential equations.
During the first part of the talk we will present the sphere packing problem and the corresponding reflected equation. We focus on the regularity of the boundary of the set of hard sphere configurations, the solvability of the equation and the construction of its solution, i.e. the existence of the Brownian hard sphere dynamics.
The second part of the talk will be devoted to the concentration of the solution at large time on a set of configurations with minimal energy. A sketch of the proof will be presented as well as many open questions about this topics.
