Jerusalem Mathematics Colloquium

Thursday, 7 May 1998, 4:00 pm
Mathematics Bldg., lecture hall 2

Marina Ville (Ecole Polytechnique)

"Minimal surfaces, pseudo-holomorphic curves and al."

One of the beautiful features of geometry in the complex projective plane CP2 is the interplay between the metric and the complex structures: for instance, complex curves in CP2 minimize the area in their homology class.
So, analogues of these complex curves in a more general manifold will be of two kinds. First, in an almost complex manifold: we have the theory of pseudo-holomorphic curves. These objects, previously almost ignored, became very important with Gromov's groundbreaking work on symplectic topology.
On the other hand, so to speak "metric analogues" of complex curves in CP2, namely area-minimizing surfaces, minimal surfaces etc... have been intensively studied for quite a few decades. And yet many basic questions remain unanswered.
We will ask: given a pseudo-holomorphic curve, a minimal surface ... how much does it look like an honest complex curve in CP2?

Coffee, Cookies at the faculty lounge at 3:30.

"After colloquium coffee chat": after the colloquium, in Beit-Belgia.

List of talks, 1997-98