Geometry Days : Projective differential geometry and Teichmueller theory.

5 au 7 septembre 2016

Ivan Izmestiev , Dr. Corina Ciobotaru (Fribourg), Dr. Patrick Ghanaat (Fribourg), Prof. Marc Troyanov (EPFL)

Prof. Vladimir Matveev (Jena), Prof. Valentin Ovsienko (Reims), Prof. Athanase Papadopoulos (Strasbourg)

The school will consist of three mini-courses of three lectures each. One course is devoted to the metric theory of Teichmueller spaces. A Teichmueller space is the space of (equivalence classes of) complex structures on a surface; it plays an important role in the hyperbolic geometry and low-dimensional topology. Two other courses deal with two aspects of the projective differential geometry. On one hand, one may study projective invariants of smooth submanifolds of the (real or complex) projective space. Convexity is the simplest qualitative, and the cross-ratio is the simplest quantitative invariant. The simplest differential projective invariant is the Schwarzian derivative, that one may encounter in the Teichmüller theory and in the conformal field theory. On the other hand, one may look at intrinsic projective structures on smooth manifolds. The basic object is a connection and the set of its geodesics. Two connections are called projectively equivalent if they generate the same geodesics. The classical Beltrami problem is to describe all Riemannian metrics projectively equivalent to a given one. This field interacts with the modern theory of integrable systems

Université de Fribourg

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