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April 28 @ 3:30 pm - 4:30 pm Free
Dr. Joel (Ronnie) Nagloo
|The Painlevé equations through the lens of algebra: 120 years later
|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.