Course: The Etnyre-Ghrist mirror and embedding theorems under symmetries

This mini-course offered by Søren Dyhr will take place in person in the lab itself at the EPSEB. However, it will also be transmitted by videoconference and on the b-lab's youtube page. If you wish to get access to the videoconference please send us an e-mail.

There is no registration fee for this course and registration is only required for people attending at the videoconference.

Title: The Etnyre-Ghrist mirror and embedding theorems under symmetries.

Summary: The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. In recent papers several unknown facets of the Euler flows have been discovered, including universality properties of the stationary solutions to the Euler equations. The study of these universality features was suggested by Tao as a novel way to address the problem of global existence for Euler and Navier-Stokes]. Universality of the Euler equations was proved by Cardona-Miranda-Peralta-Salas- Presas for stationary solutions using a contact mirror which reflects a Beltrami flow as a Reeb vector field. This contact mirror permits the use of advanced geometric techniques in fluid dynamics. On the other hand, motivated by Tao's approach.

In the first part of the course we will rediscover Etnyre and Ghrist mirror and unveil its natural equivariant behavior under symmetries (Josep Fontana- joint work with Eva Miranda and Daniel Peralta-Salas). On the second part of the course Tao's approach to the embedding problem for Lie groups (Soren Dyhr in joint work with Angel Gonzalez, Eva Miranda and Daniel Peralta-Salas).