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Monthly Archives: May 2017
Notes of Alina Vdovina’s Cambridge lecture 31052017
Expanders, Beauville surfaces and buildings 1. Expanders For a graph, Cheeger’s constant enters in the isoperimetric inequality Example. For a regular tree, . Definition 1 An expander is a sequence of finite bounded degree graphs whose Cheeger constants are bounded … Continue reading
Notes of Viktor Schroeder’s third informal Cambridge lecture 30052017
Moebius structures on boundaries, III Today’s material is taken from Jonas Beyrer’s PhD. Given a space, Bourdon’s formula often takes value 0. Nevertheless, for higher rank symmetric spaces, or for products of spaces, the restriction to the Furstenberg boundary is … Continue reading
Notes of Richard Schwartz’ sixth Cambridge lecture 26052017
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
Notes of Richard Schwartz’ fifth Cambridge lecture 24052017
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
Notes of Viktor Schroeder’s second informal Cambridge lecture 23052017
Moebius structures on boundaries, II 1. Ptolemaic Moebius structures Recall that a Moebius structure is Ptolemaic if crossratios satisfy the Ptolemaic inequality, This means that takes its values in the triangle with vertices at the extra points . Examples Boundaries … Continue reading
Notes of Nicolas Matte Bon’s Cambridge lecture 23052017
Uniformly recurrent subgroups and rigidity of nonfree 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
Notes of Erik Guentner’s Cambridge lecture 23052017
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