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Cours magistraux

le (1h2m21s)

## F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part1)

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of Bruinier-Yang and Buinier-Kudla-Yang which provide explicit formulas for the arithmetic intersection of such divisors and the CM points. We will show that they imply an averaged version of a conjecture of Colmez. Finally we will present the main ingredients in the proof of the conjectures. The lectures are base on joint works with E. Goren, ...
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Cours magistraux

le (1h30m57s)

## F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part2)

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of Bruinier-Yang and Buinier-Kudla-Yang which provide explicit formulas for the arithmetic intersection of such divisors and the CM points. We will show that they imply an averaged version of a conjecture of Colmez. Finally we will present the main ingredients in the proof of the conjectures. The lectures are base on joint works with E. Goren, ...
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Cours magistraux

le (1h1m34s)

## F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part3)

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of Bruinier-Yang and Buinier-Kudla-Yang which provide explicit formulas for the arithmetic intersection of such divisors and the CM points. We will show that they imply an averaged version of a conjecture of Colmez. Finally we will present the main ingredients in the proof of the conjectures. The lectures are base on joint works with E. Goren, ...
Voir la vidéo
Cours magistraux

le (1h33m12s)

## F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part4)

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of Bruinier-Yang and Buinier-Kudla-Yang which provide explicit formulas for the arithmetic intersection of such divisors and the CM points. We will show that they imply an averaged version of a conjecture of Colmez. Finally we will present the main ingredients in the proof of the conjectures. The lectures are base on joint works with E. Goren, B. Howard ...
Voir la vidéo
Cours magistraux

le (54m53s)

## F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part5)

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of Bruinier-Yang and Buinier-Kudla-Yang which provide explicit formulas for the arithmetic intersection of such divisors and the CM points. We will show that they imply an averaged version of a conjecture of Colmez. Finally we will present the main ingredients in the proof of the conjectures. The lectures are base on joint works with E. Goren, B. Howard ...
Voir la vidéo
Cours magistraux

le (1h33m49s)

## R. Dujardin - Some problems of arithmetic origin in complex dynamics and geometry (part1)

Some themes inspired from number theory have been playing an important role in holomorphic and algebraic dynamics (iteration of rational mappings) in the past ten years. In these lectures I would like to present a few recent results in this direction. This should include: the dynamical Manin-Mumford problem, in particular in the case of product rational maps (P(x),Q(y)) (after Ghioca, Nguyen, and Ye) the “unlikely intersection” problem (after Baker and DeMarco, and also Favre and ...
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Cours magistraux

le (1h31m1s)

## R. Dujardin - Some problems of arithmetic origin in complex dynamics and geometry (part2)

Some themes inspired from number theory have been playing an important role in holomorphic and algebraic dynamics (iteration of rational mappings) in the past ten years. In these lectures I would like to present a few recent results in this direction. This should include: the dynamical Manin-Mumford problem, in particular in the case of product rational maps (P(x),Q(y)) (after Ghioca, Nguyen, and Ye) the “unlikely intersection” problem (after Baker and DeMarco, and also Favre and ...
Voir la vidéo
Cours magistraux

le (1h32m37s)

## R. Dujardin - Some problems of arithmetic origin in complex dynamics and geometry (part3)

Some themes inspired from number theory have been playing an important role in holomorphic and algebraic dynamics (iteration of rational mappings) in the past ten years. In these lectures I would like to present a few recent results in this direction. This should include: the dynamical Manin-Mumford problem, in particular in the case of product rational maps (P(x),Q(y)) (after Ghioca, Nguyen, and Ye) the “unlikely intersection” problem (after Baker and DeMarco, and also Favre and ...
Voir la vidéo
Cours magistraux

le (1h31m6s)

## G. Freixas i Montplet - Automorphic forms and arithmetic intersections (part 2)

In these lectures I will focus on the Riemann-Roch theorem in Arakelov geometry, in the specific context of some simple Shimura varieties. For suitable data, the cohomological part of the theorem affords an interpretation in terms of both holomorphic and non-holomorphic modular forms. The formula relates these to arithmetic intersection numbers, that can sometimes be evaluated through variants of the first Kroenecker limit formula. I will first explain these facts, and then show how the Jacquet-Langlands correspondence allows to relate arithmetic intersection numbers for ...
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