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Nombre de programmes trouvés : 9926
Cours magistraux

le (59m6s)

Tropp 2/9 - 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 ...
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Conférences

le (1h20m33s)

C. Araujo - Foliations and birational geometry (Part 2)

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 ...
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Conférences

le (55m58s)

H. Guenancia - A decomposition theorem for singular spaces with trivial canonical class (Part 1)

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.
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Conférences

le (59m9s)

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 ...
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Cours magistraux

le (1h18s)

Bubeck 3/9 - 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 ...
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Cours magistraux

le (55m13s)

Bubeck 4/9 - 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 ...
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Conférences

le (41m33s)

Massoulié - Planting trees in graphs, and finding them back

In this talk we  consider detection and reconstruction of planted structures in Erdős-Rényi random graphs. For planted line graphs, we establish the following phase diagram. In a low density region where the average degree λ of the initial graph is below some critical value λc, detection and reconstruction go from impossible to easy as the line length K crosses some critical value f(λ)ln(n), where n is the number of nodes in the graph. In the high density region λ>λc, detection goes from impossible to easy as K goes from o(\sqrt{n}) to ω(\sqrt{n}), and reconstruction remains impossible so long as K=o(n). We show similar properties for planted D-ary trees. These results are in contrast with the ...
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