TIME & PLACE: 4:05 pm, Wednesday Oct 30, at the IFT seminar room

TITLE: "Finite symmetry"

ABSTRACT:

Symmetry is a fundamental tool in our understanding of the world, and group theory is the abstract study of symmetry. Each finite group can be thought of as a possible finite symmetry configuration. We will discuss efforts that have been made to understand two basic problems. First, what are the possible finite groups? Second, given a finite group in what ways can one represent it as symmetries of mathematical objects?

An important partial answer to the first question is the Classification Theorem of Finite Simple Groups, the theorem whose proof is the longest in all of mathematics. Research on the second question has likewise produced important results. Progress has been made in understanding how given finite groups are automorphisms of fields, of vectors spaces, of sets, and many other structures. A group can sometimes predict the existence of an interesting structure having it as symmetry group.

We will discuss briefly some of these results. The talk will be geared to a general scientific audience.
More details on these topics will be discussed at various events this year during the UF Mathematics Department Special Year of Algebra 2002 - 2003.