Mikami HIRASAWA

Title:
On the Distribution of Zeros of Alexander Polynomials of links

Abstract:
In this talk, we concentrate on the zeros, rather than the
coefficients, of Alexander polynomials of knots and links.
One may plot the zeros of Alexander polynomials to find interesting phenomena.
We say that a link is bi-stable if the zeros of its Alexander polynomial are
either real or complex of modulus one.
We study such links via interlacing property of the real zeros.
Two or more polynomials are said to be interlaced if their real zeros are interlaced.
From an interlaced pair of polynomials we can make another interlaced pair.
We modify Alexander polynomials so that it is bi-stable if and only if
the modified polynomial has only real zeros.
As an application of the interlacing property, we show that some arborescent links
have bi-stable Alexander polynomials.

This is a joint work with K. Murasugi (University of Toronto).