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 Gang Tian’s Orsay lecture 28-06-2017

Existence of conic Kaehler-Einstein metrics Joint work with Feng Wang, Zhejiang university. A log-Fano manifold is the date of a compact Kaehler manifold , a divisor with normal crossings such that the line bundle is positive. A metric is a … Continue reading

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Notes of Oana Ivanovici’s Orsay lecture 28-06-2017

Geometry and analysis of waves in manifolds with boundary The wave-front is a subset of the cotangent bundle, whose projection is the singular support. In all dimensions, in Euclidean space, it travels at constant speed along straight lines (Fermat,…, Hormander). … Continue reading

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Notes of Erlend Grong’s Orsay lecture 27-06-2017

Asymptotic expansions of holonomy Joint with Pierre Pansu. 1. Motivation Given a connection on a principal bundle , holonomy along a based loop of is an element of resulting from lifting horizontally to . We look for an expression such … Continue reading

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Notes of Karen Vogtmann’s second Cambridge lecture 23-06-2017

The borders of Outer Space Joint work with Kai-Uwe Bux and Peter Smillie. 1. Duality groups I am interested in Poincare duality. For a group, assume is a smooth -manifold, then Bieri-Eckmann observed that is suffices that acts freely cocompactly … Continue reading

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Notes of Grigori Avramidi’s Cambridge lecture 23-06-2017

Topology of ends of nonpositively curved manifolds Joint work with T. Nguyen Pham. I am interested in complete Riemannian manifolds with curvature in , and finite volume. Example. Product of two hyperbolic surfaces. The end is homeomorphic to , with … Continue reading

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Notes of Christopher Leininger’s Cambridge lecture 23-06-2017

Free-by-cyclic groups and trees Joint work with S. Dowdall and I. Kapovich. The Bieri-Neumann-Strebel invariant is an open subset of , it is the set of such that is surjective on . Here, is the torsion free abelian cover of … Continue reading

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Notes of Kevin Shreve’s Cambridge lecture 23-06-2017

Action dimension and Cohomology Joint work with Giang Le and Mike Davis. 1. Action dimension This is the minimal dimension of contractible manifolds which admit a proper -action. The geometric dimension replaces manifolds with complexes. 1.1. Examples If is of … Continue reading

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