DiMaI - Dipartimento di Matematica e Informatica "Ulisse Dini"

Luke Oeding (Universita' di Firenze)
terra' un seminario Venerdi' 13 Novembre alle 11.30, presso la sala conferenza Tricerri, dal titolo:

"The variety of principal minors of symmetric matrices."

Abstract:
A principal minor of a matrix is the determinant of a submatrix
centered about the main diagonal. A basic linear algebra question asks
to what extent is it possible to prescribe the principal minors of a
matrix. Holtz and Sturmfels studied the algebraic variety of principal
minors of symmetric matrices. The equations of this variety tell when
it is possible for a given vector of length 2^n to be the principal
minors of a symmetric n by n matrix. Holtz and Sturmfels found these
equations in the cases n=3,4 and discovered an interesting connection
to Cayley's hyperdeterminant. They conjectured that the
hyperdeterminantal module generates the equations of the variety.

I will describe the applications that motivate the original question.
Then I will give several examples indicating some of the beautiful
symmetry and geometry of this variety. Finally I will sketch a proof