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The ancient Greek word "geometry" is, with its etymological meaning
of "measurement of the earth", one of the oldest of mathematics. The
discovery of non-euclidean geometries in the 19th century dramatically
increased the scope of geometry. This scope was further extended in the
20th century by dividing geometry into branches differing in their
objects of study and their methods: topology, differential geometry,
Riemannian geometry, symplectic geometry, complex geometry, algebraic
geometry, ...
Grothendieck is known primarily for having re-founded algebraic
geometry on entirely new bases. But he himself considered himself to be
a general mathematician, not a specialist. So one may wonder whether
the word "geometry", which he used very often without ever defining it,
has for him a precise meaning that goes beyond algebraic geometry, and
whether certain notions he introduced or to which he gave a central role
are likely to apply to everything that one might imagine to be called
geometric.
The aim of the presentation will be to propose elements of an
answer to this question.
To get more information about the colloquium, join to the following google group:
https://groups.google.com/g/ipm-math-colloquium
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