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SUMMARY:Jun Su (University of Cambridge)
DTSTART:20201013T133000Z
DTEND:20201013T143000Z
DTSTAMP:20260404T111326Z
UID:CamNT/1
DESCRIPTION:Title: Automorphy of Hecke modules from geometry\nby Jun Su (University
of Cambridge) as part of Cambridge Number Theory Seminar\n\n\nAbstract\nCo
homology of locally symmetric spaces/varieties and their compactifications
make fundamental bridges between Galois and automorphic representations.
While these cohomology groups have natural Hecke actions and connection to
function spaces\, 1. if these Hecke modules are built up by automorphic r
epresentations (automorphy) and 2. which automorphic representations appea
r are both non-trivial questions in general. In this talk we’ll plug var
ious interesting cohomology groups into these questions\, while our main e
xamples will be a. cohomology of automorphic local systems over locally sy
mmetric spaces and b. automorphic vector bundles on locally symmetric vari
eties\, whose automorphy are proved in 1995 and 2018 respectively.\n
LOCATION:https://stable.researchseminars.org/talk/CamNT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashwin Iyengar (King's College London)
DTSTART:20201027T143000Z
DTEND:20201027T153000Z
DTSTAMP:20260404T111326Z
UID:CamNT/5
DESCRIPTION:Title: Families of p-adic L-functions\nby Ashwin Iyengar (King's College
London) as part of Cambridge Number Theory Seminar\n\n\nAbstract\nI will
discuss a formulation of a two-variable Iwasawa main conjecture over the n
ormalization of the N-new components of the extended eigencurve of tame le
vel N\, building on previous work of David Hansen\, and will discuss some
ideas about how to prove such a statement.\n
LOCATION:https://stable.researchseminars.org/talk/CamNT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanneke Wiersema (King's College London)
DTSTART:20201110T143000Z
DTEND:20201110T153000Z
DTSTAMP:20260404T111326Z
UID:CamNT/6
DESCRIPTION:Title: Minimal weights of mod p Galois representations\nby Hanneke Wiers
ema (King's College London) as part of Cambridge Number Theory Seminar\n\n
\nAbstract\nThe strong form of Serre's conjecture states that every two-di
mensional continuous\, odd\, irreducible mod p representation of the absol
ute Galois group of $\\mathbb{Q}$ arises from a modular form of a specific
minimal weight\, level and character. In this talk we use modular represe
ntation theory to prove the minimal weight is equal to a notion of minimal
weight inspired by work of Buzzard\, Diamond and Jarvis. Moreover\, using
the Breuil-Mézard conjecture we give a third interpretation of this mini
mal weight as the smallest k>1 such that the representation has a crystall
ine lift of Hodge-Tate type $(0\, k-1)$. Finally\, we will report on work
in progress where we study similar questions in the more general setting o
f mod $p$ Galois representations over a totally real field.\n
LOCATION:https://stable.researchseminars.org/talk/CamNT/6/
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SUMMARY:Andrew Graham (Imperial College London)
DTSTART:20201124T143000Z
DTEND:20201124T153000Z
DTSTAMP:20260404T111326Z
UID:CamNT/7
DESCRIPTION:Title: Anticyclotomic Euler systems for conjugate self-dual representations
of $GL(2n)$\nby Andrew Graham (Imperial College London) as part of Cam
bridge Number Theory Seminar\n\n\nAbstract\nAn Euler system is a collectio
n of Galois cohomology classes which satisfy certain compatibility relatio
ns under corestriction\, and by constructing an Euler system and relating
the classes to L-values\, one can establish instances of the Bloch--Kato c
onjecture. In this talk\, I will describe a construction of an anticycloto
mic Euler system for a certain class of conjugate self-dual automorphic re
presentations\, which can be seen as a generalisation of the Heegner point
construction. The classes arise from special cycles on unitary Shimura va
rieties and are closely related to the branching law associated with the s
pherical pair $(GL(n)\\times GL(n)\, GL(2n))$. This is joint work with S.W
.A. Shah.\n
LOCATION:https://stable.researchseminars.org/talk/CamNT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Boxer (ENS de Lyon)
DTSTART:20210126T143000Z
DTEND:20210126T153000Z
DTSTAMP:20260404T111326Z
UID:CamNT/8
DESCRIPTION:Title: Higher Coleman Theory\nby George Boxer (ENS de Lyon) as part of C
ambridge Number Theory Seminar\n\n\nAbstract\nThe goal of Higher Coleman T
heory is to introduce higher coherent cohomological analogs of overconverg
ent modular forms on Shimura varieties and to explain how they relate to c
lassical automorphic forms. We also discuss how they vary in p-adic famili
es. This is joint work with Vincent Pilloni.\n
LOCATION:https://stable.researchseminars.org/talk/CamNT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lassina Dembélé (University of Luxembourg)
DTSTART:20210209T143000Z
DTEND:20210209T153000Z
DTSTAMP:20260404T111326Z
UID:CamNT/9
DESCRIPTION:Title: Semistable abelian varieties with good reduction outside 73\nby L
assina Dembélé (University of Luxembourg) as part of Cambridge Number Th
eory Seminar\n\n\nAbstract\nIn this talk\, we describe all simple semistab
le abelian varieties over $\\mathbf{Q}$\, with good reduction outside $73$
\, up to isogeny. Our classification depends on GRH.\n
LOCATION:https://stable.researchseminars.org/talk/CamNT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Trias (University of East Anglia)
DTSTART:20210223T143000Z
DTEND:20210223T153000Z
DTSTAMP:20260404T111326Z
UID:CamNT/10
DESCRIPTION:Title: Towards an integral local theta correspondence: universal Weil modul
e and first conjectures\nby Justin Trias (University of East Anglia) a
s part of Cambridge Number Theory Seminar\n\n\nAbstract\nThe theta corresp
ondence is an important and somewhat mysterious tool in number theory\, wi
th arithmetic applications ranging from special values of L-functions\, ep
silon factors\, to the local Langlands correspondence. The local variant o
f the theta correspondence is described as a bijection between prescribed
sets of irreducible smooth complex representations of groups $G_1$ and $G_
2$\, where $(G_1\,G_2)$ is a reductive dual pair in a symplectic p-adic gr
oup. The basic setup in the theory (Stone-von Neumann theorem\, the metapl
ectic group and the Weil representation) can be extended beyond complex re
presentations to representations with coefficients in any algebraically cl
osed field R as long as the characteristic of R does not divide p. However
\, the correspondence defined in this way may no longer be a bijection dep
ending on the characteristic of R compared to the pro-orders of the pair $
(G_1\,G_2)$. In the recent years\, there has been a growing interest in st
udying representations with coefficients in as general a ring as possible.
In this talk\, I will explain how the basic setup makes sense over an A-a
lgebra B\, where A is the ring obtained from the integers by inverting p a
nd adding enough p-power roots of unity. Eventually\, I will discuss some
conjectures towards an integral local theta correspondence. In particular\
, one expects that the failure of this correspondence for fields having ba
d characteristic does appear in terms of some torsion submodule in integra
l isotypic families of the Weil representation with coefficients in B.\n
LOCATION:https://stable.researchseminars.org/talk/CamNT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edna Jones (Rutgers University)
DTSTART:20210309T143000Z
DTEND:20210309T153000Z
DTSTAMP:20260404T111326Z
UID:CamNT/11
DESCRIPTION:Title: An Asymptotic Local-Global Principle for Integral Kleinian Sphere Pa
ckings\nby Edna Jones (Rutgers University) as part of Cambridge Number
Theory Seminar\n\n\nAbstract\nWe will discuss an asymptotic local-global
principle for certain integral Kleinian sphere packings. Examples of Klein
ian sphere packings include Apollonian circle packings and Soddy sphere pa
ckings. Sometimes each sphere in a Kleinian sphere packing has a bend (1/r
adius) that is an integer. When all the bends are integral\, which integer
s appear as bends? For certain Kleinian sphere packings\, we expect that e
very sufficiently large integer locally represented everywhere as a bend o
f the packing is a bend of the packing. We will discuss ongoing work towar
ds proving this for certain Kleinian sphere packings. This work uses the c
ircle method\, quadratic forms\, and spectral theory.\n
LOCATION:https://stable.researchseminars.org/talk/CamNT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xuhua He (Chinese University of Hong Kong)
DTSTART:20210504T133000Z
DTEND:20210504T143000Z
DTSTAMP:20260404T111326Z
UID:CamNT/12
DESCRIPTION:Title: Affine Deligne-Lusztig varieties and Generalized affine Springer fib
ers\nby Xuhua He (Chinese University of Hong Kong) as part of Cambridg
e Number Theory Seminar\n\n\nAbstract\nThe notion of affine Springer fiber
was introduced by Kazhdan and Lusztig in 1988. It plays a crucial role in
the geometric representation theory and the Langlands program. The genera
lized affine Springer fibers were first studied by Kottwitz and Viehmann f
or the hyperspecial level structure in 2012 and by Lusztig for arbitrary p
arahoric level structure in 2015. Many geometric properties for the hypers
pecial level structure were further studied by Bouthier and Chi.\n\nIn thi
s talk\, I will propose a new approach to study the generalized affine Spr
inger fibers. The key observation is that the affine Deligne-Lusztig varie
ties\, in some sense\, may be regarded as the ``shadow'' of generalized af
fine Springer fibers. I will also explain some ingredients used to deduce
some geometric properties (nonemptiness\, dimension\, irreducible componen
ts) of generalized affine Springer fibers from the properties of the affin
e Deligne-Lusztig varieties. This talk is based a work in progress.\n
LOCATION:https://stable.researchseminars.org/talk/CamNT/12/
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