BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Mikhailov (University of Leeds) DTSTART:20260916T162000Z DTEND:20260916T180000Z DTSTAMP:20260914T075735Z UID:GDEq/157 DESCRIPTION:Title: F inite dimensional reductions of integrable differential-difference equatio ns\nby Alexander Mikhailov (University of Leeds) as part of Geometry o f differential equations seminar\n\nLecture held in room 303 of the Indepe ndent University of Moscow.\n\nAbstract\nIntegrable partial differential e quations\, such as the Korteweg-de Vries (KdV) equation\, admit infinite h ierarchies of commuting higher symmetries. Their symmetry reductions give rise to integrable finite-dimensional dynamical systems that are solvable in terms of Abelian functions. This observation underlies the finite-gap i ntegration method for the KdV equation\, introduced by S.P. Novikov and su bsequently extended to a wide class of integrable systems. In this paper\, we introduce a new and more general class of reductions for integrable di fferential-difference equations\, leading to integrable finite-dimensional systems in both commutative and noncommutative settings. The reduction co nstraints define integrable maps that enable solutions of the reduced syst ems to be extended to solutions of the corresponding differential-differen ce equations. The construction is illustrated using the Volterra and Toda hierarchies.\n LOCATION:https://researchseminars.org/talk/GDEq/157/ END:VEVENT END:VCALENDAR