### Graduate Student Seminar, 4:45pm November 10, 2003

#### Speaker:

Wesley Calvert
#### Title:

The Structure of Abelian Groups
#### Abstract:

Most of us know that any finitely generated Abelian group is a direct sum
of cyclic groups (finite or infinite). When I first saw this theorem, I
asked, "What about the rest?" This is not meaningless abstraction: some
of our favorite groups do not have this form (the additive group of
rationals, for instance).

It turns out that a great deal is known about the structure of Abelian
groups in general. Every Abelian group splits into a torsion part and a
torsion-free part. The torsion part is completely understood. The
torsion-free part can be a good deal more complicated, and it is in the
more exotic corners of torsion-free Abelian group theory that we find the
few remaining open problems in the classification of Abelian Groups -- and
some truly remarkable techniques.

This talk will outline the classification of Abelian groups to the extent
that it is known. I will also tell about recent progress on the last
frontier, where the tools used include both computable model theory and
ergodic theory.

To volunteer to give a talk, or for any other questions regarding this schedule, contact Wesley Calvert