Convex Projective Manifold of finite volume

by Dr Ludovic Marquis (l'Ecole Normale Superieure de Lyon, France)

Thursday 11 Feb 2010, 16:00 → 17:00 Asia/Kolkata

AG-69 (Colaba Campus)

In my talk, I will explain how covex projective geometry is a generalisation of hyperbolic geometry. A convex projective manifold M is the quotient of a properly open convex $\omega$ set by a discrete group of projective transformation Gamma. The basic example of such manifold is the quotient of the hyperbolic space by a discrete group of isometry. This kind of manifold carry a natural measure. A lot of people have studied the case where the manifold M is compact. I will explain what is known when the dimension of M is 2 and how to construct such a manifold when $\omega$ is not the hyperbolic space. This will lead us, to the construction of discrete subgroup of $SL_n+1(\mathbb (R)$.