APRG Seminar

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).


Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 05 Dec 2019