BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Shaun Stevens (University of East Anglia)
DTSTART:20240306T160000Z
DTEND:20240306T170000Z
DTSTAMP:20260418T064723Z
UID:LNTS/123
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/123/">H
 ow many local factors does it take to determine a representation?</a>\nby 
 Shaun Stevens (University of East Anglia) as part of London number theory 
 seminar\n\nLecture held in Medawar G02 Watson.\n\nAbstract\nIn 1993\, Henn
 iart proved that the (then conjectural) Local Langlands Correspondence for
  $\\operatorname{GL}(n$) is determined by gamma-factors of pairs. More pre
 cisely\, he proved a local converse theorem: for $F$ a non-archimedean loc
 al field\, an irreducible (smooth complex) representation $\\pi$ of $\\ope
 ratorname{GL}(n\,F)$ is determined by the collection of gamma-factors of t
 he pairs $(\\pi\,\\tau)$ as $\\tau$ runs through the irreducible represent
 ations of all $\\operatorname{GL}(m\,F)$ with $m < n$. More recently\, Cha
 i (2019) and Jacquet—Liu (2018) showed that one only needs to consider $
 m\\leq n/2$ to determine $\\pi$. This bound on $m$ is best possible\, at l
 east when $n$ is less that the residual characteristic of $F$\, by work of
  Adrian—Liu—Stevens—Tam (2018) and Adrian (2023). \n\n \n\nFor group
 s other than $\\operatorname{GL}(n)$ there are additional complications. I
 ’ll explain what I know is already known about this problem and report o
 n some joint work with Moshe Adrian\, which gives some answers but also le
 aves many questions.\n
LOCATION:https://researchseminars.org/talk/LNTS/123/
END:VEVENT
END:VCALENDAR