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Monthly Archives: December 2012
Notes of Genevieve Walsh’s lecture
Rightangled Coxeter groups, polyhedral complexes, and acute triangulations Joint work with SangHyan Kim. 1. Coxeter groups Given a simplicial graph , there is an associated rightangled Coxeter group, generated by vertices of , and two generators commute iff the corresponding … Continue reading
Notes of Marc Bourdon’s lecture
Some applications of cohomology to the boundaries of Gromov hyperbolic spaces Joint work with Bruce Kleiner. 1. cohomology 1.1. Definition Definition 1 Let be a contractible hyperbolic simplicial complex with bounded geometry. Its cohomology is the following quotient space, Theorem … Continue reading
Notes of Matias Carrasco’s lecture
Conformal dimension and canonical splittings of hyperbolic groups Can one characterize hyperbolic groups whose conformal dimension equals one ? For the definition of conformal dimension, see Haissinsky’s talk. 1. The Kleinian dimension For Kleinian groups, an other dimensionlike invariant arises, … Continue reading
Notes of Gilles Courtois’ lecture
Poincaré inequalities and Ricci curvature Joint work with G. Besson and S. Hersonsky. 1. Poincaré inequalities 1.1. Definition Definition 1 Say a metric measure space satisfies a Poincaré inequality if there exist constants , , such that for all , … Continue reading
Notes of Sa’ar Hersonsky’s lecture
Combinatorial harmonic coordinates Uniformizing combinatorial annuli. 1. Perspective Can a combinatorial structure determine a rigid geometry ? Here are interesting cases where this works. Theorem 1 (Thurston, RodinSullivan, SchrammHe, BeardonStephenson, Colin de Verdière…) Cover a planar domain with small equal … Continue reading
Notes of Peter Haissinsky’s lecture
Hyperbolic groups with planar ideal boundaries I will prove the following theorem. Theorem 1 Let be a word hyperbolic group whose boundary is homeomorphic to a proper subset of the 2sphere. Then the following are equivalent. is virually a convex … Continue reading