Standard transversality techniques for nonlinear elliptic problems typically rely on the Sard-Smale theorem and some form of unique continuation property, e.g. in the study of J-holomorphic curves, the latter role is played by the similarity principle. In this talk I will describe which aspects of this story change when the goal is to study transversality equivariantly. The discussion leads naturally to a significant strengthening of the usual unique continuation property, known as Petri's condition, which turns out to be the fundamental ingredient in any equivariant transversality argument. I will explain what Petri's condition is, give a few examples, and then sketch a proof that it holds for generic real-linear Cauchy-Riemann type operators. This should be seen as the basic analytical reason why transversality for multiply covered J-holomorphic curves is sometimes possible.
Mittwoch, den 15. Januar 2020 um 11.00-13.00 Uhr, in Mathematikon, INF 205, SR 9 Mittwoch, den 15. Januar 2020 at 11.00-13.00 , in Mathematikon, INF 205, SR 9
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Peter Albers