# 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."

** Abstract: **

One of the beautiful features of geometry in the complex projective
plane CP^{2} is the interplay between the metric and the complex
structures: for instance, complex curves in CP^{2} 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 CP^{2}, 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 CP^{2}?

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

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

List of talks, 1997-98