10:00 to 11:00 Domains of Discontinuity for Anosov Representations and Generalized Teichmüller Spaces Many representations of surface groups (in particular those belonging to "generalized" Teichmüller spaces) are known to satisfy a strong dynamical property: they are Anosov representations. We shall first explain more fully this notion due to F. Labourie. Secondly we will explain how an Anosov representation $\Gamma \to G$ (for any group $\Gamma$) can be interpreted as the holonomy representation of a geometric structure by constructing a domain of discontinuity with compact quotient for $\Gamma$ into a homogenous $G$-space. At last we shall see to what extent this construction can be used in interpreting the generalized Teichmüller spaces as moduli of geometric structures. This is a joint work with Anna Wienhard. 11:00 to 11:30 Morning Coffee at Mathematical Institute 11:30 to 12:30 D Toledo ([Utah])Convexity Properties of Energy on Teichmüller Space Let M be a closed surface of genus at least two, N a manifold of non-positive Hermitian curvature (the Siu-Sampson condition) and fix a homotopy class of maps from M to N (or a representation of the fundamental group of M in the group of isometries of N). For each complex structure J on M there is a harmonic map f:M->N (or an equivariant harmonic map of the universal covers). In situations where this map is unique it depends smoothly on J and its energy E defines a smooth function on the Teichmüller space of M. We prove that this function is plurisubharmonic, and study conditions when it is strictly plurisubharmonic. This result was suggested by Gromov as an alternative way of developing and strengthening the Siu-Sampson rigidity theory. Indications of these applications will be given as time permits. 13:00 to 14:00 Lunch served at Wadham College 14:00 to 15:00 Free time 15:00 to 16:00 Local rigidity for complex hyperbolic lattices I will explain how Hodge theory can be used to prove local rigidity results for complex hyperbolic lattices. 16:00 to 16:30 Afternoon Tea at Mathematical Institute 16:30 to 17:30 Linear coverings of complex projective manifolds This talk will survey the methods and applications of our joint work with Katzarkov Pantev and Ramachandran arxiv/0409.0693.
 10:00 to 11:00 A Iozzi (ETH Zürich)Surfaces and bounded cohomology We introduce the notion of causal representation of a surface group and relate it to that of maximal representation and of tight homomorphism. When the target is SL(2,R) we show that these are hyperbolizations. In the process we define and study the bounded fundamental class of a compact surface (with or without boundary) and establish a result characterizing it among all bounded classes. We relate this to the winding number of Chillingsworth and to work of Calegari on stable commutator length. 11:00 to 11:30 Morning Coffee at Mathematical Institute 11:30 to 12:30 M Burger (ETH Zürich)Causal representations of surface groups In this talk we will present a structure theorem concerning causal representations; in particular we will discuss the rationality of the Toledo invariant in the non compact case and explain its relation to the characterisation of non tube type domains in terms of the hermitian triple product. 13:00 to 14:00 Lunch served at Wadham College 14:00 to 15:00 Free time 15:00 to 16:00 Asymptotics in TQFT We will via the geometric quantization of moduli spaces of flat connections discuss various asymptotic properties of the associated representations of the mapping class groups. 16:00 to 16:30 Afternoon Tea at Mathematical Institute 16:30 to 17:30 S Choi & K Choi ([Korea Advanced Institute of Science and Technology])Deforming convex real projective 3-orbifolds A convex real projective 3-orbifold is the quotient orbifold of a convex domain in $RP^3$ by a discrete group of projective automorphisms in $PGL(4, R)$. Hyperbolic 3-orbifolds form a subclass. The convex real projective 3-manifolds were begun to be studied by Cooper, Long, and Thistlethwaite. We will summarize some of the recent results on deforming convex real projective structures on 3-dimensional orbifolds, including those of Benoist, myself, Marquis, Lee, Hodgson, Cooper, Tillman, and so on. In particular, a numerical study of real projective structures on Coxeter orbifolds is included. Finally, we discuss open problems in this area. Our topic is related to understanding the deformations of $SL(4,R)$-representations of discrete groups. 18:45 to 19:30 Wine reception at Wadham College (sponsored by Oxford University Press) 19:30 to 21:00 Conference dinner at Wadham College
 10:00 to 11:00 P Boalch ([ENS])Irregular connections, Dynkin diagrams and fission I'll survey some results (both old and new) related to the geometry of moduli spaces of irregular connections on curves. If time permits this will include: 1) new nonlinear geometric braid group actions, 2) new complete hyperkahler manifolds (including some gravitational instantons) [in work with O. Biquard], and 3) new ways to glue Riemann surfaces together to obtain (symplectic) generalisations of the complex character varieties of surface groups. 11:00 to 11:30 Morning Coffee at Mathematical Institute 11:30 to 12:30 Fibrations on the moduli of parabolic connections on P^1 minus 4 points This reports on joint work with Frank Loray and Masa-Hiko Saito. Given a connection with parabolic structure, one can look at the limit as $t\rightarrow 0$ in Hitchin's twistor space. The limit is a $C^*$-fixed Higgs bundle. Breaking up the moduli space according to the isomorphism class of the limit leads to a decomposition in locally closed subvarieties. In the case of rank $2$ connections on $P^1-\{ t_1,t_2,t_3,t_4\}$ we are able to show that the subvarieties are closed. They are the fibers of fibrations, depending on the parabolic weights, which are already known: appearing for example in work of Arinkin and Lysenko, and of Iwasaki, Inaba, Saito. Katz's middle convolution is one of Okamoto's symmetries exchanging the different types of fibrations. 13:00 to 14:00 Lunch served at Wadham College 14:00 to 17:30 Free afternoon