Monday, December 9 |
07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
08:45 - 09:00 |
Introduction and Welcome by BIRS Staff ↓ A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions. (TCPL 201) |
09:00 - 09:50 |
Jeffrey Danciger: Affine actions with Hitchin linear part ↓ Properly discontinuous actions of a surface group on Rd by affine transformations were shown to exist by Danciger-Gueritaud-Kassel. We show, however, that if the linear part of an affine surface group action is in the Hitchin component, then the affine action is not properly discontinuous. The key case is that of linear part in SO(n,n−1), so that Rd=Rn,n−1 is the model for flat psuedo-Riemannian geometry of signature (n,n−1). Here, the translational parts determine a deformation of the linear part into SO(n,n) Hitchin representations and the crucial step is to show that such representations are not Anosov in SL(2n,R) with respect to the stabilizer of an n-plane. Joint with Tengren Zhang. (TCPL 201) |
10:00 - 10:30 |
Coffee Break (TCPL Foyer) |
10:30 - 10:55 |
Giuseppe Martone: Sequences of Hitchin representations of Tree-Type ↓ In this talk we describe non-trivial sufficient conditions on a diverging sequence of Hitchin representations so that its limit in the Parreau boundary can be described as an action on a tree. These non-trivial conditions are given in terms of Fock-Goncharov coordinates on moduli spaces of positive tuples of flags. (TCPL 201) |
11:00 - 11:25 |
Joan Porti: Twisted Alexander polynomials and hyperbolic volume for three-manifolds ↓ Given a hyperbolic 3-manifold with cusps, we consider the composition of a lift of its holonomy in SL(2,C) with the irreducible representation in SL(n,C), that yields a twisted Alexander polynomial An(t), for each natural n. We prove that, for a complex number z with norm one log|An(z)|/n2 converges to the hyperbolic volume of the manifold divided by 4π, as n→∞. This generalizes and uses a theorem of W.Mueller for closed manifolds on analytic torsion. This is joint work with L.Bénard, J.Dubois and M.Heusener. (TCPL 201) |
11:30 - 13:00 |
Lunch ↓ Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
13:00 - 14:00 |
Guided Tour of The Banff Centre ↓ Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus. (Corbett Hall Lounge (CH 2110)) |
14:00 - 14:50 |
Sara Maloni: The geometry of quasi-Hitchin symplectic Anosov representations ↓ In this talk we will discuss quasi-Hitchin representations in Sp(4,C), which are deformations of Fuchsian (and Hitchin) representations which remain Anosov. These representations acts on the space Lag(C4) of complex lagrangian grassmanian subspaces of C4. This theory generalises the classical and important theory of quasi-Fuchsian representations and their action on the Riemann sphere CP1=Lag(C2). In the talk, after reviewing the classical theory, we will define Anosov and quasi-Hitchin representations and we will discuss their geometry. In particular, we show that the quotient of the domain of discontinuity for this action is a fiber bundle over the surface and we will describe the fiber. The projection map comes from an interesting parametrization of Lag(C4) as the space of regular ideal hyperbolic tetrahedra and their degenerations. (This is joint work with D.Alessandrini and A.Wienhard.) (TCPL 201) |
15:00 - 15:30 |
Coffee Break (TCPL Foyer) |
16:00 - 16:25 |
Tengren Zhang: Regularity of limit curves of Anosov representations ↓ Anosov representations are representations of a hyperbolic group to a non-compact semisimple Lie group that are ``geometrically well-behaved''. In the case when the target Lie group is PGL(d,R), these representations admit a limit set in d−1 dimensional projective space that is homeomorphic to the boundary of the group. Under some irreducibility conditions, we give necessary and sufficient conditions for when this limit set is a C1,a sub manifold. This is joint work with A.Zimmer. (TCPL 201) |
16:30 - 16:55 |
Konstantinos Tsouvalas: Characterizing Benoist representations by limit maps ↓ Anosov representations of word hyperbolic groups form a rich class of discrete subgroups of semisimple Lie groups, generalizing classical convex cocompact groups of real rank one Lie groups. A large class of projective Anosov representations are Benoist representations. In this talk, we are going to give a characterization of Benoist representations in terms of the existence of limit maps. This is joint work with Richard Canary. (TCPL 201) |
17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
19:30 - 21:00 |
Problem Session (TCPL 201) |