BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:David Marcil (Columbia University)
DTSTART:20241022T203000Z
DTEND:20241022T213000Z
DTSTAMP:20260423T125811Z
UID:MITNT/100
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/100/">
 $p$-adic $L$-functions for $P$-ordinary Hida families on unitary groups</a
 >\nby David Marcil (Columbia University) as part of MIT number theory semi
 nar\n\nLecture held in Room 2-449 in the Simons Building (building 2).\n\n
 Abstract\nI will first discuss the notion of automorphic representations o
 n a unitary group that are $P$-ordinary (at $p$)\, where $P$ is some parab
 olic subgroup. In the “ordinary” setting (i.e. when $P$ is minimal)\, 
 such a representation $\\pi$ has a relatively simple structure at $p$\, us
 ing a theorem of Hida. I will describe a generalization of the latter in t
 he more general $P$-ordinary setting using the theory of types. I will use
  this structure theorem to analyze and parametrize a $P$-ordinary Hida fam
 ily $C_\\pi$ associated to $\\pi$.\n\nThen\, I will introduce a $p$-adic f
 amily of Eisenstein series that is “compatible” with $C_\\pi$. Namely\
 , the Fourier coefficients of the former can be interpolated $p$-adically 
 to induce an “Eisenstein measure” and the family can be paired with $C
 _\\pi$\, using an algebraic version of the doubling method\, to $p$-adical
 ly interpolated special values of $L$-functions.\n\nI will conclude by exp
 laining how this Eisenstein measure corresponds to a $p$-adic $L$-function
  for $C_\\pi$ viewed as an element of a $P$-ordinary Hecke algebra.\n\nThe
 se results generalize the ones obtained by Eischen-Harris-Li-Skinner in th
 e ordinary setting and are from the speaker’s thesis.\n
LOCATION:https://researchseminars.org/talk/MITNT/100/
END:VEVENT
END:VCALENDAR