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SUMMARY:Arvind Suresh (U of Arizona)
DTSTART:20220906T210000Z
DTEND:20220906T220000Z
DTSTAMP:20260423T024753Z
UID:UAANTS/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/47/">
 Curves with large rank via the PTE problem</a>\nby Arvind Suresh (U of Ari
 zona) as part of University of Arizona Algebra and Number Theory Seminar\n
 \nLecture held in ENR2 S395.\n\nAbstract\nIt is an open question whether t
 he rank of a curve X/Q (i.e. the Mordell--Weil rank of the group of ration
 al points of the Jacobian J/Q) is bounded in terms of the genus g of X. Sh
 ioda extended a construction of Mestre to produce infinite families of g>1
  curves over Q with rank at least 4g+7. \nIn this talk\, I will present a 
 refinement of the Mestre--Shioda construction which leads to some interest
 ing families of curves over Q (and over cyclotomic fields) with rank large
 r than 4g+7. These families are parametrized by certain highly symmetric r
 ational varieties associated to the Prouhet--Tarry--Escott (PTE) problem\,
  a classical problem in number theory.\n
LOCATION:https://researchseminars.org/talk/UAANTS/47/
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