BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Stokes (University College London) DTSTART:20210318T230000Z DTEND:20210319T010000Z DTSTAMP:20260423T035715Z UID:WiSe/12 DESCRIPTION:Title: Wh at is an integrable difference equation?\nby Alexander Stokes (Univers ity College London) as part of What is ...? Seminar\n\n\nAbstract\nAn inte resting feature of the field of integrable systems in general is that ther e is no single definition (applicable to all contexts) of what integrabili ty 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 sy stems. \nThis is especially so in the theory of discrete integrable system s\, and in this talk we will present some novel definitions of certain cla sses of integrable difference equations\, emphasising how they are formula ted in parallel with the classical differential case. \nA particularly bea utiful 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 affi ne Weyl groups.\nWe will see definitions of integrability for lattice equa tions\, for second-order equations defining birational mappings of the pla ne\, and a particularly beautiful way of defining discrete analogues of th e Painlevé differential equations.\n LOCATION:https://researchseminars.org/talk/WiSe/12/ END:VEVENT END:VCALENDAR