Cours/Séminaire
Notice
Langue :
Anglais
Crédits
Jérémy MAGNIEN (Réalisation), Jean-Benoît Bost (Intervention)
Conditions d'utilisation
CC BY-NC-ND 4.0
DOI : 10.60527/hhqn-tf43
Citer cette ressource :
Jean-Benoît Bost. I_Fourier. (2017, 13 juin). J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part2) , in 2017. [Vidéo]. Canal-U. https://doi.org/10.60527/hhqn-tf43. (Consultée le 17 juillet 2024)

# J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part2)

Réalisation : 13 juin 2017 - Mise en ligne : 7 mars 2018
• document 1 document 2 document 3
• niveau 1 niveau 2 niveau 3
Descriptif

In the classical analogy between number fields and function fields, an Euclidean lattice (E,∥.∥) may be seen as the counterpart of a vector bundle V on a smooth projective curve C over some field k. Then the arithmetic counterpart of the dimension h0(C,V)=dimkΓ(C,V) of the space of sections of V is the non-negative real number h0θ(E,∥.∥):=log∑v∈Ee−π∥v∥2.

In these lectures, I will firstly discuss diverse properties of the invariant h0θ and of its extensions to certain infinite dimensional generalizations of Euclidean lattices. Then I will present applications of this formalism to transcendence theory and to algebraization theorems in Diophantine geometry.

Intervention
Thème
Documentation

## Dans la même collection

• Conférence
01:00:14

### X. Yuan - On the arithmetic degree of Shimura curves

Yuan
Xinyi

The goal of this talk is to introduce a Gross--Zagier type formula, which relates the arithmetic self-intersection number of the Hodge bundle of a quaternionic Shimura curve over a totally real

• Conférence
01:03:00

### Y. Tang - Exceptional splitting of reductions of abelian surfaces with real multiplication

Tang
Yunqing

Chavdarov and Zywina showed that after passing to a suitable field extension, every abelian surface A with real multiplication over some number field has geometrically simple reduction modulo p

• Conférence
01:01:13

### A. von Pippich - An analytic class number type formula for PSL2(Z)

Pippich
Anna-Maria von

For any Fuchsian subgroup Γ⊂PSL2(R) of the first kind, Selberg introduced the Selberg zeta function in analogy to the Riemann zeta function using the lengths of simple closed geodesics on Γ∖H

• Cours/Séminaire
01:02:26

### Z. Huang - Diophantine approximation and local distribution of rational points

Huang
Zhizhong

We show how to use the recent work of D. McKinnon and M. Roth on generalizations of Diophantine approximation to algebraic varieties to formulate a local version of the Batyrev-Manin principle on

• Cours/Séminaire
01:24:42

### C. Soulé - Arithmetic Intersection (Part4)

Soulé
Christophe

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic

• Cours/Séminaire
01:31:49

### C. Soulé - Arithmetic Intersection (Part1)

Soulé
Christophe

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic

• Cours/Séminaire
01:26:12

### C. Soulé - Arithmetic Intersection (Part3)

Soulé
Christophe

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic

• Cours/Séminaire
01:29:58

### P. Salberger - Quantitative aspects of rational points on algebraic varieties (part4)

Salberger
Per

Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour

• Cours/Séminaire
01:10:08

### C. Soulé - Arithmetic Intersection (Part2)

Soulé
Christophe

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic

• Cours/Séminaire
01:00:09

### D. Loughran - Sieving rational points on algebraic varieties

Loughran
Daniel

Sieves are an important tool in analytic number theory. In a typical sieve problem, one is given a list of p-adic conditions for all primes p, and the challenge is to count the number of integers

• Cours/Séminaire
01:03:57

### P. Salberger - Quantitative aspects of rational points on algebraic varieties (part2)

Salberger
Per

Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour

• Cours/Séminaire
00:55:56

### E. Peyre - Slopes and distribution of points (part3)

Peyre
Emmanuel

The distribution of rational points of bounded height on algebraic varieties is far from uniform. Indeed the points tend to accumulate on thin subsets which are images of non-trivial finite

## Avec les mêmes intervenants et intervenantes

• Conférence
01:31:26

### J.-B. Bost - Techniques d’algébrisation en géométrie analytique, formelle, et diophantienne II (Par…

Bost
Jean-Benoît

Dans ce cours, nous nous proposons d’expliquer comment des théorèmes d’algébrisation classiques, concernant des variétés ou des faisceux cohérents analytiques, possèdent des avatars en géométrie

• Conférence
01:05:38

### J.-B. Bost - Techniques d’algébrisation en géométrie analytique, formelle, et diophantienne II (Par…

Bost
Jean-Benoît

Dans ce cours, nous nous proposons d’expliquer comment des théorèmes d’algébrisation classiques, concernant des variétés ou des faisceux cohérents analytiques, possèdent des avatars en géométrie

• Conférence
01:07:42

### J.-B. Bost - Techniques d’algébrisation en géométrie analytique, formelle, et diophantienne II (Par…

Bost
Jean-Benoît

Dans ce cours, nous nous proposons d’expliquer comment des théorèmes d’algébrisation classiques, concernant des variétés ou des faisceux cohérents analytiques, possèdent des avatars en géométrie

• Conférence
01:23:19

### J.-B. Bost - Techniques d’algébrisation en géométrie analytique, formelle, et diophantienne II (Par…

Bost
Jean-Benoît

Dans ce cours, nous nous proposons d’expliquer comment des théorèmes d’algébrisation classiques, concernant des variétés ou des faisceux cohérents analytiques, possèdent des avatars en géométrie

• Cours/Séminaire
01:31:04

### J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part1)

Bost
Jean-Benoît

In the classical analogy between number fields and function fields, an Euclidean lattice (E,∥.∥) may be seen as the counterpart of a vector bundle V on a smooth projective curve C over some field

## Sur le même thème

• Conférence
01:06:10

### "Le mathématicien Petre (Pierre) Sergescu, historien des sciences, personnalité du XXe siècle"

Herléa
Alexandre

Alexandre HERLEA est membre de la section « Sciences, histoire des sciences et des techniques et archéologie industrielle » du CTHS. Professeur émérite des universités, membre effectif de l'Académie

• Cours/Séminaire
00:49:00

### Webinaire sur la rédaction des PGD

Louvet
Violaine

Rédaction des Plans de Gestion de Données (PGD) sous l’angle des besoins de la communauté mathématique.

• Conférence
00:33:54

### Alexandre Booms : « Usage de matériel pédagogique adapté en géométrie : une transposition à interro…

« Usage de matériel pédagogique adapté en géométrie : une transposition à interroger ». Alexandre Booms, doctorant (Université de Reims Champagne-Ardenne - Cérep UR 4692)

• Conférence
01:15:11

### M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem

Lesourd
Martin

The study of positive scalar curvature on noncompact manifolds has seen significant progress in the last few years. A major role has been played by Gromov's results and conjectures, and in

• Conférence
01:01:02

### J. Fine - Knots, minimal surfaces and J-holomorphic curves

Fine
Joël

I will describe work in progress, parts of which are joint with Marcelo Alves. Let L be a knot or link in the 3-sphere. I will explain how one can count minimal surfaces in hyperbolic 4-space

• Conférence
00:28:18

### J. Wang - Topological rigidity and positive scalar curvature

Wang
Jian

In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with

• Conférence
00:54:15

### R. Perales - Recent Intrinsic Flat Convergence Theorems

Perales
Raquel

Théorèmes récents de convergence plane intrinsèque

• Conférence
01:02:13

### D. Semola - Boundary regularity and stability under lower Ricci bounds

Semola
Daniele

The theory of non smooth spaces with lower Ricci Curvature bounds has undergone huge developments in the last thirty years. On the one hand the impetus came from Gromov’s precompactness theorem

• Conférence
01:00:08

### D. Stern - Harmonic map methods in spectral geometry

Stern
Daniel

Over the last fifty years, the problem of finding sharp upper bounds for area-normalized Laplacian eigenvalues on closed surfaces has attracted the attention of many geometers, due in part to

• Conférence
01:00:08

### P. Burkhardt - Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow

Burkhardt-Guim
Paula

We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C0 metrics. We show the following: that our definitions are stable under greater-than-second

• Conférence
01:13:18

### R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions

Bamler
Richard H.

We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow.

• Conférence
01:03:34

### C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions

Li
Chao

In this talk, I will discuss some recent developments on the topology of closed manifolds admitting Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC