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SUMMARY:Nicole Looper (Brown University)
DTSTART:20250923T200000Z
DTEND:20250923T210000Z
DTSTAMP:20260422T173622Z
UID:FCNTS/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FCNTS/6/">Ul
 trafilters and uniformity theorems</a>\nby Nicole Looper (Brown University
 ) as part of Five College Number Theory Seminar\n\nLecture held in Seeley 
 Mudd 207 @Amherst College.\n\nAbstract\nUltrafilters formalize a generaliz
 ed notion of convergence based on a prescribed idea of "largeness" for sub
 sets of the natural numbers\, and underlie constructions like ultraproduct
 s. In the study of moduli spaces\, they provide a clean way to encode dege
 nerations and to establish uniformity results that are difficult to obtain
  using ordinary limits. This talk will discuss applications of ultrafilter
 s to uniformity theorems in dynamics and arithmetic geometry. After introd
 ucing local results that arise from this approach\, I will sketch some of 
 the arithmetic consequences\, including uniform bounds on rational torsion
  points on abelian varieties. This is joint work with Jit Wu Yap.\n
LOCATION:https://researchseminars.org/talk/FCNTS/6/
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