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

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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

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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

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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

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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

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Link to Massimiliano Gubinelli’s notes

Massimiliano Gubinelli has started posting notes of his Université Paris-Dauphine 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

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