 
Summary: RESEARCH BLOG 4/15/03: U. OF ARKANSAS SPRING LECTURE SERIES
I went to the U. of Arkansas Spring Lecture Series in Mathematical
Sciences last week. I'll discuss some of the talks that were given (but
see the abstracts at the web site for a more complete picture of what
was discussed).
Casson gave a series of five lectures on the AndrewsCurtis and
PoincarŽe conjectures. There were a lot of wellknown topologists and
geometric group theorists that were at the conference (other than the
speakers), who probably came mainly to hear what Casson had to say.
His first couple of lectures were mainly background material, explaining
the conjectures and their context in mathematics. He discussed refor
mulations of the AndrewsCurtis and PoincarŽe conjectures in terms of
automorphisms of free groups. He also showed various 2generator bal
anced presentations which he had found using a computer program.
He found five AndrewsCurtis equivalence classes of presentations of
the trivial group such that the total length of the relators is 14, and
he doesn't know whether the equivalence classes are AndrewsCurtis
equivalent. The only other group he encountered was the binary octa
hedral group, and when considering length 15 balanced presentations,
he also found the (2, 3, 7) triangle group (or rather, the index 2 sub
