Description
Speaker: Prof. Dominique Guillot, University of Delaware, USA.
Date and time: 18th January, Friday, 3:30 PM.
Venue: Ramanujan Hall.
Title: Totally nonnegative GCD matrices and kernels
Abstract: Let X=(x_1, ... ,x_n) be a vector of distinct positive integers. The n x n
matrix with ij-th entry equal to gcd(x_i,x_j), the greatest common divisor of x_i
and x_j, is called the GCD matrix on X. By a surprising result of Beslin and Ligh
(1989), all GCD matrices are positive definite. In this talk, we will discuss new
characterizations of the GCD matrices satisfying the stronger property of being
totally nonnegative (i.e., all their minors are nonnegative). Joint work with Lucas
Wu (U. Delaware).