The Painlevé Equations Through The Lens Of Algebra: 120 Years Later

The annual Marden Lecture in Math is presented by Dr. Joel Nagloo, Associate Professor of Mathematics at the University of Illinois, Chicago.

The Painlevé equations are second order ordinary differential equations that come in six families P1 – P6. They were discovered strictly for mathematical considerations, in the early part of the 20th century, by mathematicians Paul Painlevé, Bertrand Gambier and Richard Fuchs. Nevertheless, these equations have arisen in a variety of important physical applications including for example statistical mechanics, random matrix theory, general relativity and fibre optics. In this talk, I will start by giving an overview of the history of the Painlevé equations and describing the classical questions surrounding the transcendental nature of their solutions. I will then explain how, in recent years, considerable progress has been made in understanding these equations algebraically.

Dr. Nagloo holds a bachelor’s degree in math from the University of Mauritius, an MSc in pure mathematics from Imperial College London, and a PhD in mathematics from the University of Leeds in London.

Reception follows in EMS E495.