Category Archives: seminar

Notes of Leonid Polterovich’ Orsay lecture 03-04-2018

Persistence modules and barcodes in symplectic geometry and spectral geometry 1. Hamiltonian diffeomorphisms Arnold:“Symplectic topology has the same relation to ordinary topology as Hamiltonian systems have to general dynamical systems”. Already surfaces are difficult examples. Hofer’s length on Hamiltonian diffeomorphism … Continue reading

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Notes of David Fisher’s Cambridge seminar lecture 13-06-2017

Strong property (T), subexponential growth of derivatives and invariant metrics Theorem 1 (Brown-Fisher-Hurtado) Let be a cocompact lattice of acting smoothly on a compact manifold of dimension . Then action factors through a finite group. Definition 2 Say a smooth … Continue reading

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Notes of Alina Vdovina’s Cambridge lecture 31-05-2017

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

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Notes of Viktor Schroeder’s third informal Cambridge lecture 30-05-2017

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

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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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