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## Past meetings

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## Title: Random walks on hyperbolic groups (part II)

## Date, time and place: February 20, 2020; 18:10-21:00; R 405

## Speaker: Pierre Mathieu (I2M, Universite d'Aix-Marseille)

## Slides: [pdf]

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## Title: Random walks on hyperbolic groups (part I)

## Date, time and place: February 13, 2020; 18:10-21:00; R 208

## Speaker: Pierre Mathieu (I2M, Universite d'Aix-Marseille)

## Abstract: In the first part of the talk, we will present some classical results about random walks on hyperbolic groups. In the second part, some more recent developments will be discussed.

## Slides: [pdf]

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## Title: Quantization and k-means in metric spaces

## Date, time and place: February 6, 2020; 18:10-19:30; R 308

## Speaker: Q. Paris

## Abstract: We discuss the k-means problem in Euclidean spaces and discuss some possible extentions and open problems in the context of metric spaces.

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## Title: Informal meeting

## Date, time and place: January 30, 2020; 18:10-19:30; R 308

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## Title: Sequential prediction in metric spaces

## Date, time and place: December 12, 2019; 18:10-19:30; N 508

## Speaker: Q. Paris

## Abstract: This talk studies the problem of sequential prediction in a metric space. The first part of the talk will present classical results in the euclidean setting, including the performance of the Exponential Weighted Average (EWA) predictor as well as the EXP4.P algorithm, an extension in the context of partial feedback (bandit problem). The second part of the talk will present preliminary results concerning the adaptation of these algorithms in metric spaces.

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## Title: Article presentations

## Date, time and place: December 5, 2019; 18:10-19:30; N 506

## Speaker: L. Beaudou and Q. Paris

## Abstract: We will present very briefly a few papers selected from the list provided in the 'Resources' page. The goal is for the participants to choose one in order to present it in the near future.

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## Title: And graphs came in ...

## Date, time and place: November 28, 2019; 18:10-19:30; N 508

## Speaker: L. Beaudou

## Abstract: We shall speak of graphs and their curvatures

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## Title: Geometry of the space of probability measures

## Date, time and place: November 21, 2019; 18:10-19:30; N 508

## Speaker: Q. Paris

## Abstract: In the first part of this meeting we will briefly discuss the geometry of the space of probability measures in connection with the theory of optimal transport. We'll show in particular that it is geodesic and will present its curvature properties. In a second part, we will define the notion of coarse Ricci curvature introduced by Yann Ollivier and show how optimal transport can be used to define curvature bounds in discrete metric spaces.

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## Title: On the curvature of metric spaces

## Date, time and place: November 14, 2019; 18:10-19:30; N 507

## Speaker: Q. Paris

## Abstract: The goal of this talk is to give an overview of several definitions of curvature of a metric space as well as some understanding of their implications. We will start by a (visual) description of natural notions of curvature arising from differential geometry (gaussian, sectional and Ricci curvature). Then we'll discuss the notion of geodesic metric spaces and curvature bounds in the sense of Alexandrov (a synthetic analog of sectional curvature) as well as generalisations of Ricci curvature to non smooth settings. Finally, we will present some alternative notions of curvature that make sense for discrete metric spaces (mainly graphs) as well as some open problems.

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## Title: Presentation of the G2PS research group

## Date, time and place: November 7, 2019; 18:10-19:30; R404

## Speakers: Q. Paris and L. Beaudou

## Abstract: We will present the research group, its objectives and a series of example problems that may serve as an initial motivation for our meetings.