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Category Archives: seminar
Notes of Leonid Polterovich’ Orsay lecture 03042018
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 13062017
Strong property (T), subexponential growth of derivatives and invariant metrics Theorem 1 (BrownFisherHurtado) 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
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 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
Notes of David Kyed’s Cambridge lecture 18052017
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
Notes of Nina Friedrich’s Cambridge lecture 17052017
Homological stability of moduli spaces of highdimensional 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
Notes of Viktor Schroeder’s first informal Cambridge lecture 16052017
Moebius structures on boundaries, I This is an informal series of 3 lectures. I start with boundaries of hyperbolic groups. I will continue with Furstenberg boundaries of higher rank symmetric spaces (joint work with my student Beyrer). 1. Moebius structures … Continue reading