Title: What is the best shape? Geometric
problems arising in aggregation models
Abstract: How do pair interactions shape the large-scale
behaviour of a cloud of particles (animals,
social agents …) ? In the most basic
models, the shape of the cloud is determined
by minimizing an attractive-repulsive interaction
energy under suitable geometric constraints.
When can we expect aggregation to occur? what
is the shape of the resulting flock? I will
describe recent work on optimal shapes in capacitor
problems that occur as limiting cases.