Fri, January 18, 2019
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3:00pm [3:30pm] Prof. Dominique Guillot, University of Delaware, USA
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).
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