BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Seoyoung Kim (University of Göttingen)
DTSTART:20241023T150000Z
DTEND:20241023T160000Z
DTSTAMP:20260418T065656Z
UID:LNTS/140
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/140/">C
 ertain families of K3 surfaces and their modularity</a>\nby Seoyoung Kim (
 University of Göttingen) as part of London number theory seminar\n\nLectu
 re held in Huxley 140\, Imperial College.\n\nAbstract\nWe start with a dou
 ble sextic family of K3 surfaces with four parameters with Picard number $
 16$. Then by geometric reduction (top-to-bottom) processes\, we obtain thr
 ee\, two and one parameter families of K3 surfaces of Picard number $17\, 
 18$ and $19$ respectively. All these families turn out to be of hypergeome
 tric type in the sense that their Picard--Fuchs differential equations are
  given by hypergeometric or Heun functions. We will study the geometry of 
 two parameter families in detail.\n\nWe will then prove\, after suitable s
 pecializations of  parameters\, these K3 surfaces will have CM (complex mu
 ltiplication)\, and will become modular in the sense that the Galois repre
 sentations of dimensions $\\leq 6$ associated to the transcendental lattic
 es are all induced from $1$-dimensional representations. Thus\, these K3 s
 urfaces will be determined by modular forms of various weights. This is do
 ne starting with one-parameter family establishing the modularity at speci
 al fibers\, and then applying arithmetic induction (bottom-to-top) process
 es to multi-parameter families. This is a joint work with A. Clingher\, A.
  Malmendier\, and N. Yui.\n
LOCATION:https://researchseminars.org/talk/LNTS/140/
END:VEVENT
END:VCALENDAR