Seminar Lecture - March 1
On the Geometry of Discrete Painlevé Equations
Dr. ANTON DZHAMAY
University of Northern Colorado and Courant Institute
Friday March 1st, 2013 at NOON
In this talk we'll explain some ideas behind the geometric approach to the theory of continuous and discrete Painlevé equations. Continuous Painlevé equations were originally defined (in early 1900) as a special class of ordinary second-order nonlinear differential equations that have the property that the only movable singularities of their solutions are poles. These equations, and their discrete analogues, turned out to have many remarkable features, and they are getting more and more important for very diverse applications in mathematics and physics. In 2000, in a truly remarkable paper H.Sakai showed that both continuous and discrete Painlevé equations can be considered in a unified scheme based on the birational algebraic geometry of a special class of algebraic surfaces. In this talk we'll give a gentle introduction to Sakai's geometric approach by showing how it can be used to determine a type of discrete Painlevé equations arising from the theory of isomonodromic deformations, and also how these rather abstract geometric ideas can help us do something as concrete as finding the change of coordinates that would transform a given discrete Painlevé equation into its standard form.
AUDIENCE: This talk is aimed at general audience, some basic knowledge of ODEs, Linear Algebra, and Multivariable Calculus should suffice for understanding of the majority of the talk. Students are welcomed!
Information: Zora Thomova, email@example.com, 792-7397
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