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SUMMARY:A. Raghuram (Fordham University)
DTSTART;VALUE=DATE-TIME:20230127T153000Z
DTEND;VALUE=DATE-TIME:20230127T170000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071922Z
UID:AutoFoArith/1
DESCRIPTION:Title: Special values of Rankin-Selberg L-functions over a totally imaginary
field\nby A. Raghuram (Fordham University) as part of Columbia - Autom
orphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics Hal
l.\n\nAbstract\nI will talk about my recent rationality results on the rat
ios of critical values for Rankin-Selberg L-functions for GL(n) x GL(m) ov
er a totally imaginary base field. In contrast to a totally real base fiel
d\, when the base field is totally imaginary\, some delicate signatures en
ter the reciprocity laws for these special values. These signatures depend
on whether or not the totally imaginary base field contains a CM subfield
. This is a generalization of my work with Günter Harder on rank-one Eise
nstein cohomology for GL(N)\, where N = n + m. The rationality result come
s from interpreting Langlands's constant term theorem in terms of an arith
metically defined intertwining operator between Hecke summands in the coho
mology of the Borel-Serre boundary of a locally symmetric space for GL(N).
The signatures arise from Galois action on certain local systems that int
ervene in boundary cohomology.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/1/
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SUMMARY:J. Weinstein (Boston University)
DTSTART;VALUE=DATE-TIME:20230203T153000Z
DTEND;VALUE=DATE-TIME:20230203T170000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071922Z
UID:AutoFoArith/2
DESCRIPTION:Title: Higher Modularity of Elliptic Curves\nby J. Weinstein (Boston Univ
ersity) as part of Columbia - Automorphic Forms and Arithmetic Seminar\n\n
Lecture held in 520 Mathematics Hall.\n\nAbstract\nElliptic curves E over
the rational numbers are modular: this means there is a nonconstant map fr
om a modular curve to E. When instead the coefficients of E belong to a fu
nction field\, it still makes sense to talk about the modularity of E (and
this is known)\, but one can also extend the idea further and ask whether
E is 'r-modular' for r=2\,3.... To define this generalization\, the modul
ar curve gets replaced with Drinfeld's concept of a 'shtuka space'. The r-
modularity of E is predicted by Tate's conjecture. In joint work with Adam
Logan\, we give some classes of elliptic curves E which are 2- and 3-modu
lar.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/2/
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SUMMARY:J. E. Rodríguez Camargo (Max Planck (Bonn))
DTSTART;VALUE=DATE-TIME:20230210T153000Z
DTEND;VALUE=DATE-TIME:20230210T170000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071922Z
UID:AutoFoArith/3
DESCRIPTION:Title: Solid locally analytic representations\, D-modules and applications to
p-adic automorphic forms\nby J. E. Rodríguez Camargo (Max Planck (Bo
nn)) as part of Columbia - Automorphic Forms and Arithmetic Seminar\n\nLec
ture held in 520 Mathematics Hall.\n\nAbstract\nIn this talk I will presen
t a project in progress with Joaquín Rodrigues Jacinto concerning the stu
dy of locally analytic\nrepresentations of p-adic Lie groups and its relat
ion with p-adic D-modules of rigid spaces à la Ardakov. I will sketch\nho
w both theories are essentially two different looks of the same kind of ob
jects and how they can be interpreted in\nterms of sheaves in suitable sta
cks on analytic rings. If time permits I will mention two possible applica
tions in the\ncohomology of Shimura varieties.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/3/
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BEGIN:VEVENT
SUMMARY:Robert Cass (University of Michigan)
DTSTART;VALUE=DATE-TIME:20230217T153000Z
DTEND;VALUE=DATE-TIME:20230217T170000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071922Z
UID:AutoFoArith/4
DESCRIPTION:by Robert Cass (University of Michigan) as part of Columbia -
Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematic
s Hall.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/4/
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BEGIN:VEVENT
SUMMARY:Yujie Xu (MIT)
DTSTART;VALUE=DATE-TIME:20230224T153000Z
DTEND;VALUE=DATE-TIME:20230224T170000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071922Z
UID:AutoFoArith/5
DESCRIPTION:by Yujie Xu (MIT) as part of Columbia - Automorphic Forms and
Arithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/5/
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