DATE:       May 11 2005 
TIME:       2:00 pm in Weber 202
SPEAKER:    Giorgio Ottaviani (Universita di Firenze)
TITLE:      Hyperdeterminants

ABSTRACT:   We give a short introduction to hyperdeterminants of 
multidimensional matrices (hypermatrices) emphasizing their role in
the existence of solutions of multilinear systems, which is analogous
to the case of usual square matrices. In the case of a 2x2x3
hypermatrix, there is a simple formula for the hyperdeterminant that
has easy generalizations in only a few cases. We will characterize
"diagonal" and "triangular" hypermatrices and we will give an example
of a Vandermonde hypermatrix. We will see how the usual Binet-Cauchy
formula has to be modified. Finally, we will give a sketch of the
existence of canonical forms whose blocks have sizes given by
Fibonacci numbers.