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UID:news1935@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20251129T092410
DTSTART;TZID=Europe/Zurich:20251204T141500
SUMMARY:Number Theory Seminar: Jerson Caro (Boston University)
DESCRIPTION:Title: Counting and Finding Rational Points on Surfaces\\r\\nAb
 stract: A celebrated result of Coleman gives an explicit version of Chabau
 ty's theorem\, bounding the number of rational points on curves over numbe
 r fields via the study of zeros of p-adic analytic functions. While many d
 evelopments have extended and refined this result\, obtaining analogous ex
 plicit bounds for higher-dimensional subvarieties of abelian varieties rem
 ains a major challenge.\\r\\nIn this talk\, I will sketch the proof of suc
 h an explicit bound for surfaces contained in abelian varieties — a step
  toward a higher-dimensional Chabauty–Coleman method. This is joint work
  with Héctor Pastén.I will also describe an application of this method t
 o a computational problem: determining an upper bound for the number of un
 expected quadratic points on hyperelliptic curves of genus 3 defined over 
 Q. I will illustrate the method through an explicit example where this set
  can be computed. This is joint work with Jennifer Balakrishnan.
X-ALT-DESC:<h2>Title: Counting and Finding Rational Points on Surfaces</h2>
 \n<p>Abstract: A celebrated result of Coleman gives an explicit version of
  Chabauty's theorem\, bounding the number of rational points on curves ove
 r number fields via the study of zeros of p-adic analytic functions. While
  many developments have extended and refined this result\, obtaining analo
 gous explicit bounds for higher-dimensional subvarieties of abelian variet
 ies remains a major challenge.</p>\n<p><br />In this talk\, I will sketch 
 the proof of such an explicit bound for surfaces contained in abelian vari
 eties — a step toward a higher-dimensional Chabauty–Coleman method. Th
 is is joint work with Héctor Pastén.<br />I will also describe an applic
 ation of this method to a computational problem: determining an upper boun
 d for the number of unexpected quadratic points on hyperelliptic curves of
  genus 3 defined over Q. I will illustrate the method through an explicit 
 example where this set can be computed. This is joint work with Jennifer B
 alakrishnan.</p>
DTEND;TZID=Europe/Zurich:20251204T151500
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