Yannick Herfray (ULB) will speak in the geometry seminar on Tuesday 29 January, at 1.30pm in the Salle de Profs. Yannick’s title is *Conformally invariant geodesics in asymptotically hyperbolic manifolds* and his abstract is below.

This talk will be on recent results in conformal geometry that Joel Fine and I obtained. In the first part of the talk I will try to review the main three standard tools in the field in a way that insists on their geometrical unity : tractor calculus, the so-called (n+2-dimensional) Ambient metric of Fefferman and Graham and the associated (n+1-dimensional) Poincaré-Einstein metric, best known for its ubiquity in holographic context.

I will then use these to discuss a natural conformally invariant version of geodesic lines. The tractor calculus description of these “conformal geodesics” has been known for a long time but the holographic (I.e Poincare) and ambient metric realisations are new. Essentially we proved that being a conformal geodesic is one-to-one correspondence with asymptotic vanishing of the extrinsic curvature of a “dual” minimal surface in the PE space.