BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Linus Hamann (Princeton University)
DTSTART:20230404T203000Z
DTEND:20230404T213000Z
DTSTAMP:20260423T125323Z
UID:MITNT/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/68/">G
 eometric Eisenstein series and the Fargues-Fontaine curve</a>\nby Linus Ha
 mann (Princeton University) as part of MIT number theory seminar\n\nLectur
 e held in Room 2-449 in the Simons Building (building 2).\n\nAbstract\nGiv
 en a connected reductive group $G$ and a Levi subgroup $M$\,\nBraverman-Ga
 itsgory and Laumon constructed geometric Eisenstein\nfunctors which take H
 ecke eigensheaves on the moduli stack $\\operatorname{Bun}_{M}$ of\n$M$-bu
 ndles on a smooth projective curve to eigensheaves on the moduli stack\n$\
 \operatorname{Bun}_{G}$ of\n$G$-bundles. Recently\, Fargues and Scholze co
 nstructed a general\ncandidate for the local Langlands correspondence by d
 oing geometric\nLanglands on the Fargues-Fontaine curve. In this talk\, we
  explain recent work\non carrying the theory of geometric Eisenstein serie
 s over to the\nFargues-Scholze setting. In particular\, we explain how\, g
 iven the\neigensheaf $S_{\\chi}$ on $\\operatorname{Bun}_{T}$ attached to 
 a smooth character $\\chi$ of\nthe maximal torus $T$\, one can construct a
 n eigensheaf on $\\operatorname{Bun}_{G}$ under\na certain genericity hypo
 thesis on $\\chi$\, by applying a geometric\nEisenstein functor to $S_{\\c
 hi}$. Assuming the Fargues-Scholze\ncorrespondence satisfies certain expec
 ted properties\, we fully\ndescribe the stalks of this eigensheaf in terms
  of normalized\nparabolic inductions of the generic $\\chi$. This eigenshe
 af has\nseveral useful applications to the study of the cohomology of\nloc
 al and global Shimura varieties\, and time permitting we will\nexplain suc
 h applications.\n
LOCATION:https://researchseminars.org/talk/MITNT/68/
END:VEVENT
END:VCALENDAR