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Rings of Low Rank |

The aim of this Stieltjesweek is
to provide an introduction to the classification theory of rings of low rank,
and to prepare the audience for the workshop The week will consist of
lectures in the morning by three lecturers: Karim Belabas ( The lectures of Jürgen Klüners address the
following type of problem: for a given positive integer The focus of Manjul Bhargava's lectures is
Gauss composition of binary quadratic forms. Appropriate higher dimensional
generalizations of Gauss composition form the key to the recent breakthrough
that the following week will be devoted to. Karim Belabas
lectures on cubic rings. Classical work of The lectures are aimed at
Master's and PhD students in all areas of algebraic number theory, arithmetic
geometry, and computational number theory. Familiarity with the basic theorems
from algebraic number theory and the fundamental techniques of commutative
algebra will be assumed. Knowledge of Dirichlet
series, Tauberian theorems, class field theory, and
the Cohen-Lenstra heuristics is helpful but not
essential. A recent survey that addresses several topics to be covered during
the first week is: K. Belabas, Paramétrisation
de structures algébriques et
densité de discriminants (d'après M. Bhargava), Séminaire Bourbaki 56
(2003.2004), no. 935 [Back] |