# Colloquium

Organisateur : Nicolas Billerey

## 2019

Erwan Brugallé (Université de Nantes) -- mardi 19 novembre 2019

# A venir

A venir
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Renaud Chorlay (ESPE-Paris) -- mardi 28 mai 2019 à 14h45 -- organisé en partenariat avec le PHIER

# From Problems to Structures: the Cousin Problems and the Emergence of the Sheaf Concept

Historical work on the emergence of sheaf theory has mainly concentrated on the topological origins of sheaf cohomology in the period from 1945 to 1950 and on subsequent developments. However, a shift of emphasis both in time-scale and disciplinary context can help gain new insight into the emergence of the sheaf concept. This paper concentrates on Henri Cartan’s work in the theory of analytic functions of several complex variables and the strikingly different roles it played at two stages of the emergence of sheaf theory: the definition of a new structure and formulation of a new research programme in 1940–1944; the unexpected integration into sheaf cohomology in 1951–1952. In order to bring this two-stage structural transition into perspective, we will concentrate more specifically on a family of problems, the so-called Cousin problems, from Poincaré (1883) to Cartan. This medium-term narrative provides insight into two more general issues in the history of contemporary mathematics. First, we will focus on the use of problems in theory-making. Second, the history of the design of structures in geometrically flavoured contexts—such as for the sheaf and fibre-bundle structures—which will help provide a more comprehensive view of the structuralist moment, a moment whose algebraic component has so far been the main focus for historical work.
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Emmanuel Peyre (Grenoble) -- mardi 5 février 2019 à 14h45 Amphi Hennequin

# Des solutions au hasard, mais pas seulement

Un des développement les plus intéressants en géométrie arithmétique durant ces 30 dernières années vient de l'étude de la distribution asymptotique des solutions entières ou rationnelles d'équations polynomiales en plusieurs variables. Nous commencerons par regarder le cas de la sphère $X^2+Y^2+Z^2=1$ pour expliquer la notion d'équidistribution des solutions, avant de passer à des exemples où les solutions «évidentes» sont beaucoup plus nombreuses que les autres. Nous expliquerons ensuite comment ces distributions peuvent être maintenant mieux comprises à l'aide d'invariants de nature géométrique.
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