BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Zheglov (Lomonosov State University\, Russia) DTSTART:20260824T150000Z DTEND:20260824T160000Z DTSTAMP:20260825T025048Z UID:ENAAS/205 DESCRIPTION:Title: Theory of normal forms of differential operators and some of its applicati ons\nby Alexander Zheglov (Lomonosov State University\, Russia) as par t of European Non-Associative Algebra Seminar\n\n\nAbstract\nThe theory of normal forms appeared in a series of my works with co‑authors as a conv enient tool for studying quantum integrable systems (in a broad sense) — by this I mean rings of commuting operators of various natures. The norma l forms of differential operators mentioned in the title are operators of a special type in a certain complete non‑commutative ring \\hat{D}_n^{sy m} (not the well‑known ring of formal pseudo‑differential operators!). They are obtained by conjugating the operators under study by an invertib le operator (a generalised Schur operator)\, which is constructed from a c hosen operator in the commutative ring.\n\nIn my talk\, I will give an ove rview of recent results obtained by myself and with co‑authors that foll ow from the theory of normal forms: an alternative classification of commu tative rings of ordinary differential operators and the associated descrip tion of torsion‑free sheaves with zero cohomology on irreducible project ive curves\; a constructive one‑to‑one correspondence between solution s of the string equation and commuting ordinary differential operators\; a nd the resulting proof of the Dixmier conjecture for the first Weyl algebr a.\n LOCATION:https://researchseminars.org/talk/ENAAS/205/ END:VEVENT END:VCALENDAR