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X-WR-CALNAME:Algebra Seminar
X-WR-TIMEZONE:America/Chicago
X-WR-CALDESC:Algebra Seminar — (SCEN) Science Engineering Building\, Faye
 tteville. Via thenwatoday.com.
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UID:algebra-seminar-2026-11-06@thenwatoday.com
DTSTAMP:20261103T172316Z
DTSTART;TZID=America/Chicago:20261106T125500
DTEND;TZID=America/Chicago:20261106T145500
SUMMARY:Algebra Seminar
LOCATION:(SCEN) Science Engineering Building\, Fayetteville
DESCRIPTION:Speaker: Jaclyn Lang (Temple University)\n\nTitle: Quantifying 
 level-raising congruences between modular forms via modular representation
  theory\n\n \n\nAbstract: Level-raising congruences between modular forms 
 have played an important role in many modern advances in number theory\, p
 erhaps most famously in Fermat’s Last theorem. Starting from a modular f
 orm 𝑓 of level 𝑁\, one asks whether\, for a prime 𝑝 not dividing 
 𝑁\, there is another (new)form 𝑔 of level 𝑁𝑝 such that 𝑓 an
 d 𝑔 are congruent modulo another prime ℓ. Work on this problem began 
 with Ribet and was answered decisively by Diamond and Taylor. Roughly spea
 king\, such a 𝑔 exists whenever there is no local obstruction to its ex
 istence. These results only apply when 𝑓 is “non-Eisenstein modulo 
 ℓ”\; the Eisenstein case is more subtle and is still not entirely unde
 rstood. In this talk we explain how the mod-ℓ representation theory of P
 GL₂(𝔽ₚ) can be used to give information about how many such forms 
 𝑔 exist. Our methods are agnostic about whether 𝑓 is Eisenstein modu
 lo ℓ and gives new information in both the Eisenstein and non-Eisenstein
  settings. This is joint work with Robert Pollack and Preston Wake.\n\n \n
 \n \n\nIn the evening after the talk\, seminar participants are welcome to
  come to dinner with the speaker. Please email me (bergdall@uark.edu) if y
 ou'd like to come\, or else just talk with me at the seminar. Other detail
 s about the algebra seminar can be found at https://math-colloquium.uark.e
 du/algebra-research-seminar/.
URL:https://thenwatoday.com/events/algebra-seminar-2026-11-06
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