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SUMMARY:John Bergdall (Bryn Mawr College)
DTSTART:20220318T143000Z
DTEND:20220318T153000Z
DTSTAMP:20260423T053016Z
UID:ANTULaval/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTULaval/9/
 ">Recent investigations of L-invariants of modular forms.</a>\nby John Ber
 gdall (Bryn Mawr College) as part of Algebra and Number Theory Seminars at
  Université Laval\n\n\nAbstract\nIn this talk I will explain new research
  on L-invariants of modular forms\, including ongoing joint work with Robe
 rt Pollack. L-invariants\, which are p-adic invariants of modular forms\, 
 were discovered in the 1980's\, by Mazur\, Tate\, and Teitelbaum\, who wer
 e formulating a p-adic analogue of Birch and Swinnerton-Dyer's conjecture 
 on elliptic curves. In the decades since\, L-invariants have shown up in a
  ton of places: p-adic L-series for higher weight modular forms or higher 
 rank automorphic forms\, the Banach space representation theory of GL(2\,Q
 p)\, p-adic families of modular forms\, Coleman integration on the p-adic 
 upper half-plane\, and Fontaine's p-adic Hodge theory for Galois represent
 ations. In this talk I will focus on recent numerical and statistical inve
 stigations of these L-invariants\, which touch on at least four of the the
 ories just mentioned. I will try to put everything into the overall contex
 t of practical questions in the theory of automorphic forms and Galois rep
 resentations\, keeping everything as concrete as possible\, and explain wh
 at the future holds.\n
LOCATION:https://researchseminars.org/talk/ANTULaval/9/
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