BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eric Rains DTSTART:20211019T160000Z DTEND:20211019T170000Z DTSTAMP:20260423T052805Z UID:Freemath/59 DESCRIPTION:Title: The birational geometry of noncommutative surfaces\nby Eric Rains as part of Free Mathematics Seminar\n\n\nAbstract\nIn commutative algebraic geometry\, the theory of smooth projective surfaces is\, of course\, very highly developed\, with a major result being the birational classification of such surfaces. For the noncommutative analogue\, much less is known\, with even the notion of "birational" not being very well understood. In pa rticular\, although several constructions have been known (noncommutative projective planes\, noncommutative ruled surfaces\, and noncommutative blo wups)\, many basic isomorphisms have proved elusive (e.g.\, that blowups i n distinct points commute). I'll discuss a new approach to the problem via derived categories that not only makes it easy to construct the desired i somorphisms but also to prove a number of other results\, in particular th at anything birational to a ruled surface is either ruled or a projective plane\, and the corresponding moduli spaces of simple sheaves are Poisson\ , with smooth symplectic leaves.\n LOCATION:https://researchseminars.org/talk/Freemath/59/ END:VEVENT END:VCALENDAR