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 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 Sebastien Bubeck’s course 13-03-2018

Bandit regret optimization Blackboard course. Slides available on the PGMO website. Video available in a few weeks. 1. Introduction to regret analysis 1.1. Framework At each time step , the player selects an action at random, according to a distribution … Continue reading

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Notes of Journee francilienne d’accueil des post-doctorants en mathematiques

Journee francilienne d’accueil des post-doctorants en mathematiques 1. Eleonora di Nezza: Special metrics in Kähler geometry I work in Kähler geometry. It has to do with complex manifolds. Let us start with the uniformization theorem. It implies that compact Riemann … Continue reading

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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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