Benoît Daniel (Université de Lorraine  Nancy, France)
Oussama Hijazi (Université de Lorraine  Nancy, France)
Sebastián Montiel (Universidad de Granada, Spain)
The talks will take place in Salle de Conférences (2nd floor), except those of Tuesday morning (in Salle Döblin, 4th floor).
Monday, May 13
 11:00

Harold Rosenberg (IMPA  Rio de Janeiro, Brazil)
 Properly immersed minimal surfaces in hyperbolic 3manifolds of finite volume, and in M × S^{1}, M a hyperbolic complete surface of finite area
 I will discuss work done with Pascal Collin and Laurent Hauswirth. We prove a minimal surface
of finite topology as described in the title, has finite total curvature equal to 2π times the Euler characteristic. We also describe the asymptotic geometry of the ends of the surface.
Examples will be discussed; in particular, in the complement of the figure eight knot with a hyperbolic structure.
 14:15

Andrei Moroianu (CNRS  Université de Versailles, France)
 Generalized Killing spinors on Einstein manifolds
 In this talk (based on joint work with Uwe Semmelmann) I will discuss the issue of generalized Killing spinors on compact Einstein manifolds with positive scalar curvature. This problem is related to the existence compact Einstein hypersurfaces in manifolds with parallel spinors, or equivalently, in Riemannian products of flat spaces, CalabiYau, hyperkähler, G_{2} and Spin(7) manifolds.
 15:45

Josef Dorfmeister (Technische Universität München, Germany)
 Minimal surfaces in Nil_{3} via loop groups
 We will discuss surfaces in Nil_{3} in the spirit of the work of Taimanov and Berdinskii. Starting from Berdinskii's system of equations for conformal immersions into Nil_{3} we chracaterize constant mean curvature surfaces by flat connections and equivalently by the harmonicity of some map.
In this context we clarify what t means for an arbitrary conformal surface to have a holomorphic AbreschRosenberg differential.
It turns out that the Berdinskii system produces "associate families" of surfaces, but, in general, only for a few values of the family parameter the corresponding surface can have constant mean curvature.
If the mean curvature H vanishes, however, a complete loop group method is avialble. In particular, every minimal surface in Nil_{3} can be constructed starting from some holomorphic (and unconstrained) data.
Tuesday, May 14
 09:15 (Salle Döblin)

Nicolas Ginoux (Universität Regensburg, Germany)
 Diracharmonic maps from index theory
 Joint work with Bernd Ammann. Diracharmonic maps are
critical points of some kind of energy functional coupling a map between
Riemannian manifolds and a section of a twisted spinor bundle. Their
characterizing equation involves a twisted Dirac operator.
In this talk, I will explain how the nonvanishing of its index allows
to produce Diracharmonic maps out of harmonic ones.
 10:30 (Salle Döblin)

Simon Raulot (Université de Rouen, France)
 The Dirac operator on untrapped surfaces
 In this talk, we establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to rigidity results for the constraint equations with spherical boundary as well as uniqueness results for surfaces with constant mean curvature vector field in Minkowski space.
 14:00

Andrea Mondino (Scuola Normale Superiore  Pisa, Italy)
 Willmore spheres in Riemannian manifolds
 Given an immersion f of the 2sphere in a Riemannian manifold (M,g) we study quadratic curvature functionals of the type
∫_{f(S2)} H^{2},
∫_{f(S2)} A^{2},
∫_{f(S2)} A^{o}^{2},
where H is the mean curvature, A is the second fundamental form, and A^{o} is the tracefree second fundamental form.
Minimizers, and more generally critical points of such functionals can be seen respectively as GENERALIZED minimal, totally geodesic and totally umbilical immersions. In the seminar I will review some results (obtained in collaboration with Kuwert, Rivière and Schygulla) regarding the existence and the regularity of minimizers of such functionals. An interesting observation regarding the results obtained with Rivière is that the theory of Willmore surfaces can be usesful to complete the theory of minimal surfaces (in particular in relation to the existence of canonical smooth representatives in homotopy classes, a classical program started by Sacks and Uhlenbeck).
 15:30

Laurent Mazet (CNRS  Université ParisEst Créteil, France)
 Cyllindrically bounded cmc annuli in H^{2} × R
 In this talk, I will recall some known results about the classification of constant mean curvature annuli in R^{3}. Then I will explain how similar results can be proved in H^{2} × R with "less symmetries".
Wednesday, May 15
 9:15

Laurent Hauswirth (Université ParisEst MarnelaVallée, France)
 The Lawson conjecture via integrable systems
 In 2012, Brendle and AndrewsLi proved with analytic argument
that embedded constant mean curvature tori in the 3dimensional sphere are
rotational surfaces.
We prove this theorem using algebraic method. We consider the space moduli
of CMC Alexandrov embedded annuli covering CMC embedded torus. The path
connected property and isolated property reformulate via
integrable systems in an algebraic problem in the space moduli of
hyperelliptic Riemann surfaces with an abelian differential form.
 10:30

Joaquin Pérez (Universidad de Granada, Spain)
 Isoperimetric domains with large volume in simply connected homogeneous 3manifolds
 We will study the relationship between three natural notions related to constant mean curvature surfaces in
a noncompact, simply connected homogeneous 3manifold X: The Cheeger constant Ch(X), the critical mean curvature H(X)
and the geometry of isoperimetric domains. We will see that the first two numbers are essentially the same, and
that if Ch(X)>0, then there exists a product foliation F of X by pairwise congruent leaves with constant mean curvature H(X)
such that the boundaries of isoperimetric domains of large volume are wellapproximated in a natural sense by the leaves of F.