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Monthly Archives: March 2017
Notes of Yves Benoist’s Southampton lecture 29-03-2017
Harmonic quasisometric maps Joint with Dominique Hulin. 1. The result We deal with Hadamard manifolds, i.e. complete simply connected nonpositively curved Riemannian manifolds. Say it is pinched if sectional curvature is between two negative constants. Harmonic maps are critical points … Continue reading
Notes of David Rosenthal’s Southampton lecture 29-03-2017
Regular finite decomposition complexity Joint with Daniel Kasprowski and Andrew Nicas. Theorem 1 If has regular FDC, a finite dimensional classifying space and a global upper bound on the orders of its finite subgroups, the assembly map is a split … Continue reading
Notes of Kang Li’s Southampton lecture 29-03-2017
Structure and -theory of uniform Roe algebras It turns out that uniform Roe algebras are easier to classify than Roe algebras. 1. Uniform Roe algebra of a space See Wright’s talk for the definition: this is the closure (in operator … Continue reading
Notes of Arthur Bartels’ second Southampton lecture 29-03-2017
The Farrell-Jones Conjecture and (coarse) flow spaces, II 1. Coarse flow spaces and N–amenability Let be a collection of subgroups of . Let act on space . Say that is an -set if if translates of are either disjoint or … Continue reading
Notes of Rufus Willett’s first Southampton lecture 28-03-2017
Dynamic asymptotic dimension and applications, I With Guentner and Yu. 1. Motivations 1. Controlled topology. In 1998, Yu showed that if a group has a finite classifying space and finite asymptotic dimension, then Novikov conjecture holds. 2. Structure of -algebras. … Continue reading
Notes of Damian Sawicki’s Southampton lecture 28-03-2017
Warped cones With Piotr Nowak. Theorem 1 Let be a Banach space. Let act by homeos on compact space preserving a probability measure . Assume that has a spectral gap on some . Then does not coarsely embed in , … Continue reading
Notes of Pierre Pansu’s Southampton lecture 28-03-2017
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Notes of Romain Tessera’s Southampton lecture 27-03-2017
Proper -actions and weak amenability for relatively hyperbolic groups 1. Weak amenability Start with the following characterization of amenability. is amenable iff there is a sequence of finitely supported positive definite functions tending to 1 pointwise as tends to . … Continue reading
Notes of Indira Chatterji’s Southampton lecture 27-03-2017
Acylindrical hyperbolicity and -cube complexes Joint with Alexandre Martin. Theorem 1 Let act on a finite dimensional cube complex . Assume action is essential and non-elementary. Assume that there exist two hyperplanes of the common stabilizer is finite. Then is … Continue reading
Notes of Arthur Bartels’ first Southampton lecture 27-03-2017
The Farrell-Jones Conjecture and (coarse) flow spaces, I Today, actions on ERs. Tomorrow, flows. Theorem 1 (Farrell-Jones) closed manifold of non-positive curvature, dimension at least 5. Then is topologically rigid: anay manifold homotopy equivalent to is homeomorphic to (i.e. Borel’s … Continue reading
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