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# Résultats de recherche

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## S. Ghazouani - Isoholonomic foliations of moduli spaces of Riemann surfaces

In this talk, I will introduce families of foliations on the moduli space of Riemann surfaces M_{g,n} which we call Veech foliations. These foliations are defined by identifying M_{g,n} to certain moduli spaces of flat structures and were first defined by Bill Veech. I will try to expose their specificities, both of geometric and dynamical nature. If time permits I will try to illustrate how the case g=1 is linked to certain differential equations whose solutions are special functions of distinguished interest. This is joint work with ... Voir la vidéole (1h3m4s)

## Bubeck 5/9 - 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 (48m4s)

## Bubeck 6/9 - 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 (56m22s)

## Bubeck 7/9 - 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 (49m53s)

## Zdeborová - Loss landscape and behaviour of algorithms in the spiked matrix-tensor model

A key question of current interest is: How are properties of optimization and sampling algorithms influenced by the properties of the loss function in noisy high-dimensional non-convex settings? Answering this question for deep neural networks is a landmark goal of many ongoing works. In this talk I will answer this question in unprecedented detail for the spiked matrix-tensor model. Information theoretic limits, and Kac-Rice analysis of the loss landscapes, will be compared to the analytically studied performance of message passing algorithms, of the Langevin dynamics and of the gradient flow. Several rather non-intuitive results will be unveiled and explained. Voir la vidéole (1h1m44s)

## Tropp 5/9 - 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 (1h3m21s)

## C. Araujo - Foliations and birational geometry (Part 3)

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 (59m57s)

## G. Binyamini - Point counting for foliations over number fields

We consider an algebraic $V$ variety and its foliation, both defined over a number field. Given a (compact piece of a) leaf $L$ of the foliation, and a subvariety $W$ of complementary codimension, we give an upper bound for the number of intersections between $L$ and $W$. The bound depends polynomially on the degree of $W$, the logarithmic height of $W$, and the logarithmic distance between $L$ and the locus of points where leafs of the foliation intersect $W$ improperly. Using this theory ... Voir la vidéole (51m21s)