Total Positivity and its Applications

  • Date: 10/04/2007

Shaun Fallat (University of Regina)


University of Calgary


A matrix is called totally positive (resp. totally nonnegative)if all
of its minors are positive (resp. nonnegative). This important class of
matrices grew out of three separate applications: Vibrating systems,
interpolation, and statistics. Since the pioneering work of
Gantmacher/Krein, Schoenberg, and Karlin, the subject of total
positivity has evolved into a prominent discipline in mathematics, and
it continues to arise in numerous applications including: Weighted
planar networks (ballot numbers); computer aided geometric design
(shape preserving transformations); probability (moment matrices); and
geometry (McMullen correspondence).

I intend to survey a number of current applications involving this
class (including some mentioned above), and if time permits I will
highlight some recent accomplishments connecting the eigenvalues of
totally nonnegative matrices to the roots of certain biorthogonal

Other Information: 

PIMS Distinguished Lecture 2007