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DTEND;TZID=Europe/Copenhagen:20190528T164500
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DTSTAMP:20190825T032635Z
DESCRIPTION: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
URL;VALUE=URI:http://recherche.math.univ-bpclermont.fr/evenements/colloquium.php
SUMMARY:From Problems to Structures: the Cousin Problems and the Emergence of the Sheaf Concept
DTSTART;TZID=Europe/Copenhagen:20190528T144500
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