Title: Totally nonnegative GCD matrices and kernels
Speaker: Dominique Guillot (University of Delaware, Newark, USA)
Date: 16 January 2019
Time: 3 pm
Venue: LH-1, Mathematics Department
Let $X=(x_1, … ,x_n)$ be a vector of distinct positive integers.
The $n \times n$ matrix with $(i,j)$ 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).