Monthly Archives: December 2012

Notes of Genevieve Walsh’s lecture

Right-angled Coxeter groups, polyhedral complexes, and acute triangulations Joint work with Sang-Hyan Kim. 1. Coxeter groups Given a simplicial graph , there is an associated right-angled Coxeter group, generated by vertices of , and two generators commute iff the corresponding … Continue reading

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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

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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 dimension-like invariant arises, … Continue reading

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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

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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, Rodin-Sullivan, Schramm-He, Beardon-Stephenson, Colin de Verdière…) Cover a planar domain with small equal … Continue reading

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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 2-sphere. Then the following are equivalent. is virually a convex … Continue reading

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