Seminar: Jellyfish exist

Time:

Venue/Location: Phòng C101, VIASM

Báo cáo viên: Prof. Glen Wheeler (University of Wollongong)

Tóm tắt: The search for homothetic solutions is a classical pursuit in geometric flows. It has long been known that the lemniscate of Bernoulli is homothetic under the curve diffusion and elastic flows, however, further examples have proven elusive; indeed, it’s a common belief that other examples do not exist, and rigidity has been sought. In this talk, I describe recent exciting work that shows there is to the contrary a wealth of examples. We exhibit in particular the jellyfish and epicyclic families of self-similar solutions, covering the elastic flow, curve diffusion flow, and ideal flow. These provide infinitely many geometrically distinct examples, and we believe only scratch the surface of the rich dynamical picture for these flows. To describe the full landscape of asymptotic shapes appears to be an extremely ambitious task. This is joint work with Ben Andrews (ANU).