Version kählérienne d'une conjecture de Robert J. Zimmer
Holomorphic actions, Kummer examples, and Zimmer program
We classify compact Kähler manifolds of dimension on which acts a lattice of an almost simple real Lie group of rank . This provides a new line in the so-called Zimmer program, and characterizes certain complex tori as compact Kähler manifolds with large automorphisms groups.
Dynamics on Character Varieties and Malgrange irreducibility of Painlevé VI equation
We consider representations of the fundamental group of the four punctured sphere into . The moduli space of representations modulo conjugacy is the character variety. The Mapping Class Group of the punctured sphere acts on this space by symplectic polynomial automorphisms. This dynamical system can be interpreted as the monodromy of the Painlevé VI equation. Infinite bounded orbits are characterized: they come from -representations. We prove the absence of invariant affine structure (and invariant...
Estimates for simple random walks on fundamental groups of surfaces
Numerical estimates are given for the spectral radius of simple random walks on Cayley graphs. Emphasis is on the case of the fundamental group of a closed surface, for the usual system of generators.
Page 1