**ODTÜ-BÝLKENT
ALGEBRAIC**** GEOMETRY SEM****I****NAR**

**“Cayley hyperdeterminants”**

by

**Alexander
Klyachko**

** **

** **

**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.

** **

** **

**Date:** 16
December, 2005 Friday

**Time:** 15:40

**Place:** Bilkent, Mathematics Seminar Room
SA-141

**Tea and cookies will be served
before the talk.**