Florent Baudier: Metric geometry of stable metric spaces and applications

Data: quinta-feira, 14 e 21 de agosto de 2014, às 10h30

Sala: 144-B

Palestrante: Florent Baudier: Texas A&M e Université Paris 6

Título: Metric geometry of stable metric spaces and applications

Resumo: The metric geometry of stable metric spaces shall be discussed in a two-part talk.

The first part is intended to be rather elementary and accessible to anyone with a basic background in functional analysis. After introducing some important classes of embeddings and spaces, we will motivate the investigation of metric embeddings by touching upon a few applications. The Lipschitz geometry of locally finite metric spaces will then be described.

In the second part, we shall put the emphasis on coarse embeddings and their applications in geometric group theory. For instance, we will discuss the compression theory for the class of proper metric spaces and for the classical Lebesgue sequence spaces. Finally, we will explain some aspects of the metric geometry of stable metric spaces.

Throughout the two talks we will sketch several proofs, in order to get the audience acquainted with some of the classical and fundamental ideas (probabilistic techniques, Ramsey techniques...) whose embedding theory is made of.

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