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Discrete Integrable Systems

Course Type: 
PhD Course
Academic Year: 
20 h
This course aims to introduce students to the topic of discrete integrable systems. The main focus will be on an important class of discrete integrable systems known as discrete Painlevé equations.  These are systems of ordinary difference equations that evolve on curves and satisfy special properties characterising their integrability.   Both discrete and continuous Painlevé equations can be understood by the geometry of their spaces of initial conditions which are described by configurations of eight points in complex projective space.  Besides their interest in integrable systems and mathematical physics, they are known to arise in various different contexts including statistical mechanics, random matrices, discrete differential geometry, cluster algebras, and quantum physics and string theory.
The first few lectures will introduce key concepts and ideas for discrete integrable systems. In the remaining lectures we will introduce Sakai's geometric approach to the discrete Painlevé equations by working through examples.  There are no prerequisites for this course.
Next Lectures: 
Friday, December 10, 2021 - 14:30 to 16:30

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