Abstract: In the middle of
the 19-th century, when the theory of determinants was firmly established, Cayley wrote a series of papers with different generalizations
of the determinant onto multidimensional matrices (=tensors). He gave them a
common name "hyperdeterminant". One of this hyperdeterminants fell into focus
in 1994, when Gelfand, Kapranov, and Zelevinsky wrote a book about its
numerous applications in algebraic geometry. This hyperdeterminant is
nonzero only for matrices of format (a+1,b+1,c+1), where a,b,c satisfy
triangle inequalities. Cayley himself raised the question about formats of
multidimensional matrices for which there exists a nonzero hyperdeterminant.
In the talk I'll give an answer to this question together with explicit
construction of the hyperdeterminant when it exists.
Place: Bilkent, Mathematics Seminar Room SA-141
Tea and cookies will be served before the talk.