|Title||Reflection groups and discrete integrable systems|
|Presenter||Yang Shi (The University of Sydney)|
|Session||Mathematical Physics and Industrial Mathematics|
Discrete integrable systems include many types of well-known equations such as: Hirota’s octahedron equation, the cross-ratio equation, and discrete analogues of the Painlevé equations. One of the big questions in this area is if/how are these systems related to each other. Active investigations in the past decade have led to exciting discoveries and clarifications of this question, henceforth a better understanding of integrable systems as a whole. In this talk we discuss some recent progress concerning the relation between two classes of discrete integrable systems: a list of quadrilateral equations (known as the ABS equations) and Sakai’s classification of 22 types of discrete Painlevé equations. This connection was made possible by exploiting combinatorial/geometrical properties of the Weyl groups.
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