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BEGIN:VEVENT
SUMMARY:David Zureick-Brown (Emory University)
DTSTART:20200620T150000Z
DTEND:20200620T155000Z
DTSTAMP:20260414T205609Z
UID:CNTD2020/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CNTD2020/1/"
 >Sporadic points on modular curves</a>\nby David Zureick-Brown (Emory Univ
 ersity) as part of Chicago Number Theory Day 2020\n\n\nAbstract\nI'll surv
 ey various results about "sporadic" (or "unexpected") points on modular cu
 rves\, and then focus on recent joint work with Derickx\, Etropolski\, van
  Hoeij\, and Morrow about torsion on elliptic curves over cubic number fie
 lds.\n
LOCATION:https://researchseminars.org/talk/CNTD2020/1/
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BEGIN:VEVENT
SUMMARY:Jennifer Balakrishnan (Boston University)
DTSTART:20200620T180000Z
DTEND:20200620T185000Z
DTSTAMP:20260414T205609Z
UID:CNTD2020/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CNTD2020/2/"
 >Quadratic Chabauty over number fields</a>\nby Jennifer Balakrishnan (Bost
 on University) as part of Chicago Number Theory Day 2020\n\n\nAbstract\nWe
  describe the extent to which p-adic height pairings can allow us to deter
 mine the set of integral or rational points on curves\, in the spirit of K
 im's nonabelian Chabauty program. In particular\, we discuss what aspects 
 of the quadratic Chabauty method can be made practical for certain hyperel
 liptic curves over number fields. This is joint work with Amnon Besser\, F
 rancesca Bianchi\, and Steffen Mueller.\n
LOCATION:https://researchseminars.org/talk/CNTD2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Voight (John Voight)
DTSTART:20200620T190000Z
DTEND:20200620T195000Z
DTSTAMP:20260414T205609Z
UID:CNTD2020/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CNTD2020/3/"
 >Archimedean aspects of the Cohen-Lenstra heuristics</a>\nby John Voight (
 John Voight) as part of Chicago Number Theory Day 2020\n\n\nAbstract\nLike
  rational points on elliptic curves\, units in number rings are gems of ar
 ithmetic.  Refined questions about units remain difficult to answer\, ofte
 n embedded within difficult questions about class groups.  For example: ho
 w often in a number ring is it that all totally positive units are squares
 ? \n\nAbsent theorems\, we may still try to predict the answer to these qu
 estions.  In this talk\, we present heuristics (and some theorems!) for si
 gnatures of unit groups\, inspired by the Cohen-Lenstra heuristics\, formu
 lating precise conjectures and providing evidence for them.  A key role is
  played by a lustrous structure of number rings we call the 2-Selmer signa
 ture map.  This structure clarifies the provenance of reflection theorems\
 , like those due to Leopoldt\, Armitage-Frohlich\, and Gras. \n\nThis is j
 oint work with David S. Dummit and Richard Foote and with Ben Breen\, Noam
  Elkies\, and Ila Varma.\n
LOCATION:https://researchseminars.org/talk/CNTD2020/3/
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