The 2024 PME conference is pleased to host Julie Rana as invited speaker.
Dr. Julie Rana is an associate professor of mathematics at Lawrence University. She holds a BS from Marlboro College, and an MA and PhD from the University of Massachusetts, Amherst. After earning her PhD, Dr. Rana held postdoctoral appointments at Marlboro College and the University of Minnesota. Her research is in algebraic geometry, a field of mathematics rooted in the algebra and geometry of polynomials. She has co-organized conferences for women and gender-expansive individuals in algebraic geometry, and in her teaching and professional life is committed to creating spaces where all feel welcome and valued.
Dr. Rana loves mathematical stories that are illuminated by beautiful pictures, and especially stories that lead to joyful and noisy mathematical conversations. In her free time, she hikes, runs, swims, reads, sings, travels, and spends time with her family.
Friday Evening Talk
The Humble (univariate, complex) Polynomial
In this talk, we focus in on univariate, polynomials i.e. polynomials in one variable. We take a deep dive into the relationship between the (complex) roots of a univariate polynomial and the roots of its derivative. Our study gives rise to beautiful pictures, a compelling conjecture (with recent progress by Fields Medalist Terence Tao), and intriguing connections to high school geometry.
Saturday Morning Talk
Classifying trivariate polynomials OR How does an algebraic geometer think about surfaces?
Take a polynomial in three variables say (x2+y2+z2-1) and set it equal to zero. In three-space, the object you get is an algebraic surface, a two-dimensional shape defined, locally, by polynomial equations. Algebraic geometers study algebraic surfaces using an equivalence relation known as birationality. In this talk, we explore the concept of birationality, beginning with a rough classification of algebraic surfaces defined by trivariate polynomials. Our tour begins with classical facts about planes, quadric surfaces, and cubic surfaces, and brings us up to the cutting edge of mathematical research.
