Université libre de Bruxelles, 20/09/19
“Compactness issues for Willmore surfaces”
We will start by introducing the general framework of Willmore surfaces and the analytic tools devoted to their study. Then we will focus on the question of weak compactness for sequences of Willmore surfaces. Especially we are going to be interested in the case when the conformal class degenerates. This will allows me to introduce the residues issue from conservation laws. Then using those residues I will give some compactness results, notably that sequences of Willmore tori are compact below 12 pi.
“Willmore spheres are unstable”
I will explain what the Willmore Morse Index of unbranched Willmore spheres in Euclidean three-space is and how to compute it. A consequence of the computation is that all unbranched Willmore spheres are unstable (except for the Round sphere). This talk is based on joint work with Jonas Hirsch.
“Immersed 2 Spheres in R^3: A Morse Theoretic Approach”