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SUMMARY:James Newton (Oxford)
DTSTART:20240221T160000Z
DTEND:20240221T170000Z
DTSTAMP:20260418T064722Z
UID:LNTS/121
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/121/">B
 ase change for modular forms</a>\nby James Newton (Oxford) as part of Lond
 on number theory seminar\n\nLecture held in Executive Suite 103\, Engineer
 ing Front Building.\n\nAbstract\nI'll talk about the base change lifting f
 rom holomorphic modular forms to Hilbert modular forms for totally real fi
 elds F. A new proof of the existence of this base change lifting is contai
 ned in joint work with Laurent Clozel and Jack Thorne. \n\nThe base change
  lifting is a simple example of Langlands functoriality\, corresponding on
  the Galois side to restriction to the absolute Galois group of F. When F 
 is a solvable extension of Q\, its existence was proved by Langlands using
  the twisted trace formula (earlier work by Doi and Naganuma covered the c
 ase where F is quadratic). Dieulefait used modularity lifting theorems and
  a delicate construction of chains of congruences between modular forms to
  prove the existence of the base change lifting without a solvability assu
 mption. Our new proof replaces (at least some of) this chain of congruence
 s with a `p-adic analytic continuation of functoriality' step\, adapted fr
 om my work with Thorne on symmetric power functoriality.\n
LOCATION:https://researchseminars.org/talk/LNTS/121/
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