What is an integrable difference equation?

Alexander Stokes (University College London)

18-Mar-2021, 23:00-01:00 (3 years ago)

Abstract: An interesting feature of the field of integrable systems in general is that there is no single definition (applicable to all contexts) of what integrability is, but “you know it when you see it”, so much work in this area relates to defining or describing integrability in different classes of systems. This is especially so in the theory of discrete integrable systems, and in this talk we will present some novel definitions of certain classes of integrable difference equations, emphasising how they are formulated in parallel with the classical differential case. A particularly beautiful feature of the discrete case is that integrability can be described in terms of a wide range of concepts, varying from analytic measures of entropy to the geometry of complex algebraic surfaces associated with affine Weyl groups. We will see definitions of integrability for lattice equations, for second-order equations defining birational mappings of the plane, and a particularly beautiful way of defining discrete analogues of the Painlevé differential equations.

algebraic geometrycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: learners


What is ...? Seminar

Series comments: The ``What is ... ? Seminar'' (WiSe) is a weekly Zoom mathematics seminar. The goal is to explain interesting things to each other in a casual manner. The name is inspired by the What is ...? column of the Notices of the American Mathematical Society. See the website for more details. If you want to receive the zoom link for the talks please fill out the form linked on the website or contact Anna at a.puskas@uq.edu.au.

Organizers: Anna Puskas*, Valentin Buciumas*
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