Author Archives: metric2011

About metric2011

metric2011 is a program of Centre Emile Borel, an activity of Institut Henri Poincaré, 11 rue Pierre et Marie Curie, 75005 Paris, France. See http://www.math.ens.fr/metric2011/

Notes of Richard Schwartz’ sixth Cambridge lecture 26-05-2017

PETs, pseudogroup actions, and renormalisation Started by group theorist B.H. Neumann in 1959. Outer billiard around a convex polygon composes 180 degrees rotation through vertices. Theorem 1 For a kite (a quadrilateral with one axial symmetry), there exist unbounded orbits … Continue reading

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Notes of Richard Schwartz’ fifth Cambridge lecture 24-05-2017

The pentagram map and discrete integrable systems Joint work with Valentin Ovsienko and Serge Tabachnikov Start with a convex polygon. Draw diagonals between vertices at distance 2, they form a smaller polygon inside. Call this the pentagram map, although the … Continue reading

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Notes of Viktor Schroeder’s second informal Cambridge lecture 23-05-2017

Moebius structures on boundaries, II 1. Ptolemaic Moebius structures Recall that a Moebius structure is Ptolemaic if cross-ratios satisfy the Ptolemaic inequality, This means that takes its values in the triangle with vertices at the extra points . Examples Boundaries … Continue reading

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Notes of Nicolas Matte Bon’s Cambridge lecture 23-05-2017

Uniformly recurrent subgroups and rigidity of non-free minimal actions Joint work with A. Le Boudec and T. Tsankov. 1. The Chabauty space of a group Let be a locally compact group. The Chabauty space of is the set of subgroups … Continue reading

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Notes of Erik Guentner’s Cambridge lecture 23-05-2017

Affine actions, cohomology and hyperbolicity When can a group act properly on a Hilbert space or an space? I start from scratch. 1. Affine actions a discrete group, a Banach space. We are interested in actions of on where each … Continue reading

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Notes of David Kyed’s Cambridge lecture 18-05-2017

-Betti numbers of universal quantum groups Joint with Pichon, Arndt, Vaes,… I spoke on the same subject in the same room in 2006. I think my understading has improved. 1. Infinite discrete groups Let act on vectorspace . There are … Continue reading

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Notes of Nina Friedrich’s Cambridge lecture 17-05-2017

Homological stability of moduli spaces of high-dimensional manifolds 1. Manifolds Say a sequence manifolds and maps satisfies homological stability if induced maps on homomology groups become eventually isomorphisms. How does one prove such a property? We are interested in the … Continue reading

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