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# Résultats de recherche

**4167**

le (1h6m50s)

## A. Belotto da Silva - Singular foliations in sub-Riemannian geometry and the Strong Sard Conjecture

Given a totally nonholonomic distribution of rank two $\Delta$ on a three-dimensional manifold $M$, it is natural to investigate the size of the set of points $\mathcal{X}^x$ that can be reached by singular horizontal paths starting from a same point $x \in M$. In this setting, the Sard conjecture states that $\mathcal{X}^x$ should be a subset of the so-called Martinet surface of 2-dimensional Hausdorff measure zero. I will present a reformulation of the conjecture in terms of the behavior of a (real) singular ... Voir la vidéole (54m38s)

## S. Druel - A decomposition theorem for singular spaces with trivial canonical class (Part 5)

The Beauville-Bogomolov decomposition theorem asserts that any compact Kähler manifold with numerically trivial canonical bundle admits an étale cover that decomposes into a product of a torus, an irreducible, simply-connected Calabi-Yau, and holomorphic symplectic manifolds. With the development of the minimal model program, it became clear that singularities arise as an inevitable part of higher dimensional life. We will present recent works in which a singular version of the decomposition theorem is established. Voir la vidéole (49m24s)

## Bubeck 8/9 - Some geometric aspects of randomized online decision making

This course is concerned with some of the canonical non-stochastic models of online decision making. These models have their origin in works from the 1950's and 1960's, and went through a resurgence in the mid-2000's due to many applications in the internet economy. This course focuses on a set of challenging conjectures around these models from the 1980's and 1990's. We present a unified approach based on a combination of convex optimization techniques together with powerful probabilistic tools, which will allow us to derive state of the art results in online learning, bandit optimization, as well as some classical online computing ... Voir la vidéole (57m3s)

## Bubeck 9/9 - Some geometric aspects of randomized online decision making

This course is concerned with some of the canonical non-stochastic models of online decision making. These models have their origin in works from the 1950's and 1960's, and went through a resurgence in the mid-2000's due to many applications in the internet economy. This course focuses on a set of challenging conjectures around these models from the 1980's and 1990's. We present a unified approach based on a combination of convex optimization techniques together with powerful probabilistic tools, which will allow us to derive state of the art results in online learning, bandit optimization, as well as some classical online computing ... Voir la vidéole (54m25s)

## Carpentier - Introduction to some problems of composite and minimax hypothesis testing

A fundamental question in statistics is: how well can we fulfil a given aim given the data that one possesses? Answering this question sheds light on the possibilities, but also on the fundamental limitations, of statistical methods and algorithms. In this talk, we will consider some examples of this question and its answers in the hypothesis testing setting. We will consider the Gaussian model in (high) dimension p where the data are of the form X = \theta + \sigma \epsilon, where \epsilon is a standard Gaussian vector with identity covariance matrix. An important hypothesis testing question consists in deciding whether \theta belongs to ... Voir la vidéole (56m12s)

## Tropp 6/9 - Random matrix theory and computational linear algebra

This course treats some contemporary algorithms from computational linear algebra that involve random matrices. Rather than surveying the entire field, we focus on a few algorithms that are both simple and practically useful. We begin with an introduction to matrix concentration inequalities, which are a powerful tool for analyzing structured random matrices. We use these ideas to study matrix approximations constructed via randomized sampling, such as the random features method. As a more sophisticated application, we present a complete treatment of a recent algorithm for solving graph Laplacian linear systems in near-linear time. Some references : 1. Tropp, "An introduction to ... Voir la vidéole (0s)

## Tropp 7/9 - Random matrix theory and computational linear algebra

This course treats some contemporary algorithms from computational linear algebra that involve random matrices. Rather than surveying the entire field, we focus on a few algorithms that are both simple and practically useful. We begin with an introduction to matrix concentration inequalities, which are a powerful tool for analyzing structured random matrices. We use these ideas to study matrix approximations constructed via randomized sampling, such as the random features method. As a more sophisticated application, we present a complete treatment of a recent algorithm for solving graph Laplacian linear systems in near-linear time. Some references : 1. Tropp, "An introduction to ... Voir la vidéole (1h20m38s)

## C. Araujo - Foliations and birational geometry (Part 4)

In the last few decades, much progress has been made in birational algebraic geometry. The general viewpoint is that complex projective manifolds should be classified according to the behavior of their canonical class. As a result of the minimal model program (MMP), every complex projective manifold can be built up from 3 classes of (possibly singular) projective varieties, namely, varieties $X$ for which $K_X$ satisfies $K_X0$. Projective manifolds $X$ whose anti-canonical class $-K_X$ is ample are called Fano manifolds. Techniques ... Voir la vidéole (57m38s)