2024-2025 Women in Mathematics Lecture
Colloquium
Women in Mathematics Lecture
Abstract
Title: Lehmer's number in Topology, Geometry and Dynamics
A Salem number is an algebraic integer s with the property that all roots of its minimal polynomial P(x) besides s and 1/s have complex norm equal to one (i.e. lie on the unit circle). In 1933, after extensive computer search, Lehmer asked whether the larger real root of P(x) = x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1 (roughly 1.17625) is the smallest Salem number. The problem is still open. Lehmer's query has led to an on-going study of deep relations between number theory, and the study of the topology, geometry and dynamical properties of a variety of mathematical objects. In this talk we will discuss some results in these directions that have come to light in recent decades involving knot theory, hyperbolic geometry, Coxeter theory, and the dynamics of rational maps.
Eko Hironaka is a mathematician whose research spans geometric topology, complex dynamics, and number theory. Her work explores the interplay between geometry and algebra, with a focus on the distribution of Salem and Pisot numbers and the dynamics of rational surface automorphisms. Hironaka has demonstrated excellence not only as a researcher but also in various professional environments for mathematicians. She is currently an Emeritus Professor at Florida State University and has spent the last ten years contributing her expertise as a consultant for math publications at the American Mathematical Society (AMS) and at the National Science Foundation (NSF). Beyond her research, Hironaka is dedicated to mentoring and promoting diversity in mathematics through organizing events and seminars that foster inclusivity and support the growth of the mathematical community.
Convergence & Conversation: A Dinner for Junior Math Faculty | Thursday, March 27
The Sum of Us: A Lunch for Aspiring Mathematicians | Friday, March 28, 11 a.m. to 1 p.m. | SSB Room 203
Lecture | Friday, March 28 | 3:05-3:55 p.m.