

Geometrical finiteness in strictly convex projective geometry
De Pierre-Louis Blayac


Local minimization of fuzziness under high symmetry
De Franco Vargas Pallete


The shape of the limit cone for positive representations
De Jeffrey Danciger
Apparaît dans la collection : Complex Hyperbolic Geometry and Related Topics / Autour de la géométrie hyperbolique complexe
I will report on progress with Daniel Allcock on the ”Monstrous Proposal”, namely the conjecture: Complex hyperbolic 13-space, modulo a particular discrete group, and with orbifold structure changed in a simple way, has fundamental group equal to (MxM)(semidirect)2, where M is the Monster finite simple group. Our progress is a proof that this orbifold fundamental group has generators that satisfy defining relations for (MxM)(semidirect) 2. It follows that either the monstrous proposal is true, or else the orbifold fundamental group collapses to Z/2. The generators and relations are extremely natural from the complex hyperbolic perspective, keeping hopes high for the conjecture.