Monthly Archives: October 2014

Notes of Alessio Figalli’s lecture

Quantitative stability estimates for the Brunn-Minkowski inequality 1. The stability problem 1.1. Brunn-Minkowski’s inequality Let . Note that , so When does equality hold ? When . This is an easy particular case of the following. Theorem 1 (Brunn-Minkowski) Let … Continue reading

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Pansu’s Lille slides

Slides of Pansu’s 2 lectures on Lp cohomology and large scale conformal maps. lille_15oct14_beamer

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Notes of Romain Tessera’s Lille lecture nr 2

1. Consequence Corollary 1 Let be a real Lie group. Then is hyperbolic iff it acts isometrically and transitively on a negatively curved Riemannian manifold. Let be a -adic Lie group. Then is hyperbolic iff it acts isometrically and transitively … Continue reading

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Notes of François Le Maître’s lecture

Full groups in the locally compact measure preserving setting 1. Orbit equivalence Let be a locally compact secound countable group, a standard probability measure space, on which acts preserving . Let denote the corresponding equivalence relation. 1.1. A general lemma … Continue reading

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Notes of Henrik Petersen’s lecture

Quasiisometries of nilpotent groups Joint work (in progress) with David Kyed. The paper is not fully written, so be careful. 1. Nilpotent groups Let be finitely generated torsion free nilpotent. Mal’cev’s theorem states that there exists a unique connected Lie … Continue reading

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Notes of Damien Gaboriau’s Lille lecture nr 3

Lück’s approximation theorem For residually finite groups, -Betti numbers can be obtained as limits of ordinary Betti numbers. Theorem 1 (Lück) Let be decreasing finte index normal subgroups of . Assume that Assume that acts freely cocompactly on some simplicial … Continue reading

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Notes of Gaboriau’s Lille lecture nr 2

1. Formulae Free products of infinite groups: add up for , add up plus one. Free products with amalgamation: idem ( add up…) provided amalgamated subgroup is amenable. 2. Betti numbers of amenable groups Following Cheeger and Gromov, I show … Continue reading

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