[Binghamton Geometry/Topology Seminar] (no subject)

[Ross Geoghegan]

                   BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

!!!!!!!!!!!!!!!     NOTE:  TWO SEMINARS ON UNUSUAL DAYS    !!!!!!!!!!!!!!!

1. Date: Monday May 8, 2006 (NOTE UNUSUAL DAY)	

   Time:  3.30 pm  (NOTE UNUSUAL TIME)

   Place: Library North 2205 followed by coffee/tea in the Anderson
          Reading Room.

   Speaker: Daniel Biss (U of Chicago)

   Title:   Annihilators in Cayley-Dickson algebras


ABSTRACT:
The Cayley-Dickson algebras form a sequence of R-algebras beginning with
the real numbers, the complex numbers, the quaternions, and the octonions. 
We rarely hear about the subsequent members of this sequence, since they
not only lack associativity but also have zero-divisors (as the Hopf
invariant 1 theorem demands).  These zero-divisors, however, can be viewed 
not as a pathology but rather as an opportunity; the zero-divisors in the
16-dimensional Cayley-Dickson algebra give rise to the Lie group G_2, and
in the larger algebras they seem to be even more interesting.  We'll 
describe joint results with Dan Christensen, Dan Dugger and Dan Isaksen
about the geometry of these spaces of zero-divisors.
________________________________________

2. Date: Wed. May 10, 2006 (NOTE UNUSUAL DAY)

   Time:  3.30 (NOTE UNUSUAL TIME)

   Place: Library North 2205 followed by coffee/tea in the Anderson
       Reading Room.

   Speaker:  Ivonne Ortiz (Miami University of Ohio)

   Title: Lower algebraic $K$-theory of hyperbolic 3-simplex reflection
          groups".


ABSTRACT: A hyperbolic 3-simplex reflection group is a Coxeter
group arising as a lattice in $O^+(3,1)$, with fundamental domain a
geodesic simple in $\mathbb H^3$ (possibly with some ideal vertices).
The classification of these groups is known, and there are exactly
9 cocompact examples, and 23 non-cocompact examples.  We provide
a complete computation of the lower algebraic $K$-theory of the
integral group ring of all the hyperbolic 3-simplex reflection
groups. This is joint work with Jean F. Lafont (Ohio State University).
_________________________________________

For a third (student) seminar by Nigar Tuncer on Thursday May 11, see
separate internal announcement.