Women in Mathematics Week

Speaker: Lisa Goldberg

Time: 3:05 PM

Room: Love 101

Abstract: I will discuss recent results that identify and correct bias in high-dimensional eigenvectors. These results rely on geometry and concentration of measure in high dimensions, and have potential applications to machine learning, genomics, and signal processing, as well as to problems in portfolio optimization that were introduced in the 1950s by Nobel Laureate Harry Markowitz. My work, developed in collaboration with Alec Kercheval, Alex Shkolnik, and many others, is dedicated to his memory.

Biography: Lisa Goldberg is Professor of the Practice of Economics at UC Berkeley and Managing Director at BlackRock. Her current academic work analyzes spectral properties of high-dimensional data with applications to portfolio construction and artificial intelligence. In industry, she works primarily on personalized quantitative investing, having started at Aperio, which was later acquired by BlackRock. In 2025, BlackRock's Aperio division manages over $120 billion in more than 22,000 separately managed accounts.

Speaker: Eko Hironaka

Lecture Title: Lehmer's Number in Topology, Geometry, and Dynamics

Time: 3:05 PM

Room: Love 101

Abstract: 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..

Biography: 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.