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SUMMARY:David Urbanik (IAS)
DTSTART:20260512T203000Z
DTEND:20260512T213000Z
DTSTAMP:20260526T085421Z
UID:MITNT/138
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/138/">
 Galois Orbit Bounds for Surface Degenerations</a>\nby David Urbanik (IAS) 
 as part of MIT number theory seminar\n\nLecture held in Room 2-449 in the 
 Simons Building (building 2).\n\nAbstract\nGiven a family g : X -> S of sm
 ooth projective algebraic varieties over a number field K\, one often want
 s to constrain the points s in S where the fibre X_s acquires "extra" alge
 braic structure. A basic sort of constraint which is important in unlikely
  intersection theory is that of a Galois-orbit lower bound: an inequality 
 h(s) <= poly([K(s) : K])\, where h is some logarithmic Weil height and K(s
 ) is the field of definition of s. Recent work has focused on how to use G
 -functions constructed from degenerations of g to produce such inequalitie
 s. We describe some new results in the case where g is a one-parameter deg
 eneration of surfaces\, and the central role played by rigid and "adelic" 
 geometry. This leads to new cases of the Zilber-Pink conjecture for 1-para
 meter families of K3 surfaces.\n
LOCATION:https://researchseminars.org/talk/MITNT/138/
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