Back to Departmental Colloquium: Spring 2001
Departmental Colloquium
Date: Thursday, Mar 22, 2001
Time: 4:15PM
Location: JWB 335
Eriko Hironaka
Florida State
Title |
Lehmer's problem and pretzel knots |
Abstract |
For a monic integer polynomial f(x) the Mahler measure of f(x) is the product of the roots outside the unit circle. In 1933, Lehmer posed the following problems: Can the Mahler measure for noncyclotomic irreducible monic integer polynomials be bounded away from 1? If yes, is the lower bound given by L(x) = x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1? Despite extensive computer searches, and attempts from a wide range of areas in number theory and geometry, both problems remain open. In this talk I will describe some partial results involving Alexander polynomials of knots and growth rates of Coxeter reflection groups. |
Number Theory
Geometric Group Theory
Topology