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Monthly Archives: February 2011
Notes of Urs Lang’s lecture nr 4
1. Cone types This is a tool to get upper bounds on ranks, and therefore dimensions of injective hulls. 1.1. Definition Definition 1 Let be a metric space, and , . Their cone is Lemma … Continue reading
Notes of Stefan Wenger’s lecture nr 1
I am interested in isoperimetric inequalities. The aim is to find relations between the growth of isoperimetric functions and the large scale geometry of the underlying space. I will use tools from geometric measure theory. Today, I will give an … Continue reading
Notes of James Lee’s lecture nr 5
1. Negative type metrics We started studying distorsion of embeddings of finite metric spaces into spaces. We discussed obstructions for a metric space to have small distorsion into spaces. Today, we make steps in the direction of embeddings. Terminology: say … Continue reading
Summary of Stefan Wenger’s course
Here is a summary of Stefan Wenger’s course, starting next Thursday at 10:30 am. Isoperimetric filling problems appear in various areas of mathematics, notably in geometry, geometric group theory, and analysis. The purpose of the present lectures is to discuss … Continue reading
Notes of Urs Lang’s lecture nr 3
1. Polyhedral structure on From now on, we concentrate on metric spaces whose metric is integer valued (a preparation for the case of finitely generated groups). For simplicity, assume that is countable. 1.1. An approximation to … Continue reading
Link to Massimiliano Gubinelli’s notes
Massimiliano Gubinelli has started posting notes of his Université ParisDauphine course on Analysis of Boolean functions on this page.
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Notes of James Lee’s lecture nr 4
1. Embedding finite metric spaces into Hilbert spaces Definition 1 Let be a map between metric spaces. The Lipschitz norm of is and the distorsion of is . The distorsion of is We are interested is quantitative aspects … Continue reading