BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Georgy Sharygin DTSTART:20221221T162000Z DTEND:20221221T180000Z DTSTAMP:20260423T010006Z UID:GDEq/76 DESCRIPTION:Title: Ch opping integrals of the full symmetric Toda system\, a new approach\nb y Georgy Sharygin as part of Geometry of differential equations seminar\n\ nLecture held in room 303 of the Independent University of Moscow.\n\nAbst ract\nIn my talk I will try to answer the questions that has been causing my anxiety for a rather long time: where do the additional integrals of th e full symmetric Toda system come from\, why they are rational and what do es all this have to do with "chopping". Even if we can use the AKS method there remains the question\, why do the initial functions actually commute (and whether it is possible to find other with the same property). The kn own answers were concerned either with rather hard straightforward computa tions\, or with the properties of a Gaudin system\; they look pretty compl icated. In my talk I will show how one can obtain these integrals with the help of some simple differential operators (in the manner of the argument shift method). Besides this\, we will discuss some other possible integra ls as well as the method to solve the corresponding flows by QR decomposit ion.\n\nThe talk is based on a common work with Yu. Chernyakov and D. Tala laev.\n LOCATION:https://researchseminars.org/talk/GDEq/76/ END:VEVENT END:VCALENDAR