Maximal representations (3 of 3)- Olivier Guichard

Conference Title: GEAR Junior Retreat 2012 Theme: Special Representations (6 of 6) Title: Maximal representations (3 of 3) Speaker: Olivier Guichard, Univ. Paris-Sud; Date and Time: Friday August 3, 13:45 Description: Maximal representations are a family of representations of surface groups (i.e. πsub1(Σsubg)) into the symplectic groups Sp(2n,R) (or, more generally, into Lie groups of Hermitian type). By many aspects, maximal representations generalize uniformization's representations and their moduli spaces generalizes the Teichmuller space. We will explain some of those aspects: discreteness and faithfulness of maximal representations, "limit circles", etc. A tentative plan for the 3 lectures is the following: 1) maximal representations into SL(2,R), PSL(2,R) and... Homeo+(Ssuper1); 2) maximal representations into Sp(2n,R); Toledo number; geometry of Sp(2n,R) and of the Lagrangian variety; and, 3) equivariant maps into the Lagrangian variety; positivity; discreteness and faithfulness of maximal representations. Sponsor: GEAR Network Local host: UIUC Department of Mathematics Funding provided by: National Science Foundation Research Networks in Mathematical Sciences programAbstract: Prof. Olivier Guichard, in this GEAR Junior Retreat 2012 mini-course on Special Representations, will discuss how maximal representations generalize uniformization's representations and their moduli spaces generalizes the Teichmuller space.