# Workshop Programme

## for period 12 October 2005

### Mathematical aspects of BTZ black holdes

12 October 2005

Timetable

Wednesday 12 October | ||||

10:00-11:00 | Beguin, F (Paris-Sud) |
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AdS geometry and Mess' work | Sem 1 | |||

11:30-12:30 | Benedetti, R (Pisa) |
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Canonical Wick rotations in 3D gravity | Sem 1 | |||

We outline the main features of the theory (developed in arXiv.math.DG/0508485), by turning one's attention in particular to background and motivations (mostly in relation with the problem of constructing a 2+1 QFT pertinent to 3D gravity). |
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14:30-15:30 | Barbot, T (Lyon) |
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A geometric insight into BTZ multi black-holes | Sem 1 | |||

We give a global (classical) description of the family of BTZ multi black-holes, including the spinning case, as quotients of open domains of the anti-de Sitter space (AdS) by discrete groups of isometries. Fixing the topology, and fixing the mass and angular momenta, this family is parametrized by the pairs of elements of the Teichm\"{u}ller space of a given Rieman surface with prescribed holonomy on the boundary. |
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16:00-17:00 | Schlenker, J-M (Paul Sabatier) |
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Minimal surfaces in singular constant curvature manifolds | Sem 1 | |||

We use minimal surface techniques to show that the set of quasi-fuchsian hyperbolic manifolds containing a closed surface with principal curvatures less than 1 is parametrized by a subset of the cotangent of Teichmüller space. This also yields a parametrization of the space of all GHMC AdS manifolds by the whole cotangent of Teichmüller space. The same techniques work for hyperbolic or AdS manifolds with singular curvatures (physically, particles) and provides a description in terms of the Teichmüller space with marked points which should be well adapted to quantization. |