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SUMMARY:The Modularity/Automorphy of Calabi–Yau Varieties of CM type - N
 oriko Yui\, Queens University.
DTSTART:20170531T131500Z
DTEND:20170531T141500Z
UID:TALK72518@talks.cam.ac.uk
CONTACT:Mark Gross
DESCRIPTION:Abstract: We consider Calabi–Yau varieties of dimension d at
  most 3 defined over Q\, and address the\nmodularity/automorphy question o
 f such Calabi–Yau varieties `a la Langlands. When the dimension of the\n
 associated Galois representations are large (for instance\, > 2)\, the pro
 blem poses a serious challenge and is\nout of reach in the general situati
 ons.\nIn this talk\, I will concentrate on Calabi–Yau varieties of CM ty
 pe\, and establish their (motivic) mod-\nularity/automorphy. The presentat
 ion is focused on the two examples:\n• d = 2: K3 surfaces with non-sympl
 ectic automorphisms\, and\n• d = 3: Calabi–Yau threefolds of Borcea–
 Voisin type.\nIf time permits\, we will discuss arithmetic mirror symmetry
  for K3 surfaces.
LOCATION:CMS MR13
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