BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Isabel Vogt (University of Washington) DTSTART:20210402T220000Z DTEND:20210402T230000Z DTSTAMP:20260423T024728Z UID:UCSBsga/17 DESCRIPTION:Title: Brill--Noether theory over the Hurwitz space\nby Isabel Vogt (Univers ity of Washington) as part of UCSB Seminar on Geometry and Arithmetic\n\n\ nAbstract\nLet C be a curve of genus g. A fundamental problem in the theor y of algebraic curves is to understand maps of C to projective space of di mension r of degree d. When the curve C is general\, the moduli space of s uch maps is well-understood by the main theorems of Brill--Noether theory. However\, in nature\, curves C are often encountered already equipped wi th a map to some projective space\, which may force them to be special in moduli. The simplest case is when C is general among curves of fixed gona lity. Despite much study over the past three decades\, a similarly comple te picture has proved elusive in this case. In this talk\, I will discuss joint work with Eric Larson and Hannah Larson that completes such a pictur e\, by proving analogs of all of the main theorems of Brill--Noether theor y in this setting. In the course of our degenerative argument\, we'll exp loit a close relationship with the combinatorics of the affine symmetric g roup.\n LOCATION:https://researchseminars.org/talk/UCSBsga/17/ END:VEVENT END:VCALENDAR