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SUMMARY:Catherine Hsu (Swarthmore College)
DTSTART:20230601T210000Z
DTEND:20230601T220000Z
DTSTAMP:20260423T022915Z
UID:UCSD_NTS/97
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/97/
 ">Explicit non-Gorenstein R=T via rank bounds</a>\nby Catherine Hsu (Swart
 hmore College) as part of UCSD number theory seminar\n\nLecture held in AP
 M 6402 and online.\n\nAbstract\nIn his seminal work on modular curves and 
 the Eisenstein ideal\, Mazur studied the existence of congruences between 
 certain Eisenstein series and newforms\, proving that Eisenstein ideals as
 sociated to weight 2 cusp forms of prime level are locally principal. In t
 his talk\, we'll explore generalizations of Mazur's result to squarefree l
 evel\, focusing on recent work\, joint with P. Wake and C. Wang-Erickson\,
  about a non-optimal level N that is the product of two distinct primes an
 d where the Galois deformation ring is not expected to be Gorenstein. Firs
 t\, we will outline a Galois-theoretic criterion for the deformation ring 
 to be as small as possible\, and when this criterion is satisfied\, deduce
  an R=T theorem. Then we'll discuss some of the techniques required to com
 putationally verify the criterion.\n\nPre-talk\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/97/
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