BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alain Yger (Université Bordeaux) DTSTART:20211117T200000Z DTEND:20211117T210000Z DTSTAMP:20260423T021754Z UID:ags/12 DESCRIPTION:Title: Rev isiting syzygies\, hence division or interpolation problems\, in terms of residue and principal value currents\nby Alain Yger (Université Borde aux) as part of Analysis and Geometry Seminar\n\n\nAbstract\nA joint paper I wrote together with M. Passare and August Tsikh in 2000 (ideas there co ming from my unfortunately last joint paper with Carlos Berenstein in 19 98) inspired since then the construction of what reveals to be a very powe rful method to attack interpolation or division problems in Cn or Pn(C) (a lso on Stein manifolds) by solving them through explicit closed formulae. The beautiful idea which was introduced by Mats Andersson since 2004 consi sts in the following: attach to any generically exact complex of hermitian bundles over a complex analytic space both a Principal Value current and a residue current\, the last one precisely encoding the lack of exactness of the complex of holomorphic bundles one started with. Time has now come\ , despite the technicity inherent to such construction\, to popularize suc h tool facing general questions such as Hilbert’s nullstellensatz\, the surprising (and curiously not so-well known) Brian ̧con-Skoda theorem (ev en in the polynomial setting)\, Euler-Ehrenpreis- Palamodov Fundamental Pr inciple\, or spectral synthesis problem in (ad hoc) weighted algebras of e ntire functions. I will try to explain this in general terms\, avoiding as far as I can technicity by cheating a little\, and will illustrate with f ew concrete examples the novelty and efficiency of such approach.\n LOCATION:https://researchseminars.org/talk/ags/12/ END:VEVENT END:VCALENDAR