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BEGIN:VEVENT
SUMMARY:Tiago Jardim Da Fonseca (Oxford)
DTSTART;VALUE=DATE-TIME:20200422T150000Z
DTEND;VALUE=DATE-TIME:20200422T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/1
DESCRIPTION:Title: On
Fourier coefficients of Poincaré series\nby Tiago Jardim Da Fonseca (
Oxford) as part of London number theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/LNTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ila Varma (Toronto)
DTSTART;VALUE=DATE-TIME:20200429T150000Z
DTEND;VALUE=DATE-TIME:20200429T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/2
DESCRIPTION:Title: Mal
le's conjecture for octic D4-fields\nby Ila Varma (Toronto) as part of
London number theory seminar\n\n\nAbstract\nWe consider the family of nor
mal octic fields with Galois group $D_4$\, ordered by their discriminants.
In forthcoming joint work with Arul Shankar\, we verify the strong form o
f Malle's conjecture for this family of number fields\, obtaining the orde
r of growth as well as the constant of proportionality. In this talk\, we
will discuss and review the combination of techniques from analytic number
theory and geometry-of-numbers methods used to prove this and related res
ults.\n
LOCATION:https://researchseminars.org/talk/LNTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Lazda (Warwick)
DTSTART;VALUE=DATE-TIME:20200506T150000Z
DTEND;VALUE=DATE-TIME:20200506T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/3
DESCRIPTION:Title: A N
éron-Ogg-Shafarevich criterion for K3 surfaces\nby Chris Lazda (Warwi
ck) as part of London number theory seminar\n\n\nAbstract\nThe naive analo
gue of the Néron–Ogg–Shafarevich criterion fails for K3 surfaces\, th
at is\, there exist K3 surfaces over Henselian\, discretely valued fields
K\, with unramified etale cohomology groups\, but which do not admit good
reduction over K. Assuming potential semi-stable reduction\, I will show h
ow to correct this by proving that a K3 surface has good reduction if and
only if its second cohomology is unramified\, and the associated Galois re
presentation over the residue field coincides with the second cohomology o
f a certain “canonical reduction” of X. This is joint work with B. Chi
arellotto and C. Liedtke.\n
LOCATION:https://researchseminars.org/talk/LNTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chantal David (Concordia)
DTSTART;VALUE=DATE-TIME:20200513T150000Z
DTEND;VALUE=DATE-TIME:20200513T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/4
DESCRIPTION:Title: Non
-vanishing cubic Dirichlet L-functions at s = 1/2\nby Chantal David (C
oncordia) as part of London number theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/LNTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rong Zhou (Imperial)
DTSTART;VALUE=DATE-TIME:20200520T150000Z
DTEND;VALUE=DATE-TIME:20200520T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/5
DESCRIPTION:Title: Ind
ependence of $l$ for Frobenius conjugacy classes attached to abelian varie
ties\nby Rong Zhou (Imperial) as part of London number theory seminar\
n\n\nAbstract\nLet $A$ be an abelian variety over a number field $E\\subse
t \\mathbb{C}$ and let $v$ be a place of good reduction lying over a prime
$p$. For a prime $l\\neq p$\, a theorem of Deligne implies that upon maki
ng a finite extension of $E$\, the Galois representation on the $l$-adic T
ate module factors as $\\rho_l:\\Gamma_E\\rightarrow G_A(\\mathbb{Q}_l)$\,
where $G_A$ is the Mumford-Tate group of $A$. We prove that the conjugacy
class of $\\rho_l(Frob_v)$ is defined over $\\mathbb{Q}$ and independent
of $l$. This is joint work with Mark Kisin.\n
LOCATION:https://researchseminars.org/talk/LNTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Tamiozzo (Imperial)
DTSTART;VALUE=DATE-TIME:20200527T150000Z
DTEND;VALUE=DATE-TIME:20200527T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/6
DESCRIPTION:Title: Blo
ch-Kato special value formulas for Hilbert modular forms\nby Matteo Ta
miozzo (Imperial) as part of London number theory seminar\n\n\nAbstract\nT
he Bloch-Kato conjectures predict a relation between arithmetic invariants
of a motive and special values of the associated $L$-function. We will ou
tline a proof of (the $p$-part of) one inequality in the relevant special
value formula for Hilbert modular forms of parallel weight two\, in analyt
ic rank at most one.\n
LOCATION:https://researchseminars.org/talk/LNTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunqing Tang (Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20200603T150000Z
DTEND;VALUE=DATE-TIME:20200603T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/7
DESCRIPTION:Title: Pic
ard ranks of reductions of K3 surfaces over global fields\nby Yunqing
Tang (Paris-Saclay) as part of London number theory seminar\n\n\nAbstract\
nFor a K3 surface $X$ over a number field with potentially good reduction
everywhere\, we prove that there are infinitely many primes modulo which t
he reduction of $X$ has larger geometric Picard rank than that of the gene
ric fiber $X$. A similar statement still holds true for ordinary K3 surfac
es with potentially good reduction everywhere over global function fields.
In this talk\, I will present the proofs via the (arithmetic) intersectio
n theory on good integral models (and its special fibers) of $\\mathrm{GSp
in}$ Shimura varieties. These results are generalizations of the work of C
harles on exceptional isogenies between reductions of a pair of elliptic c
urves. This talk is based on joint work with Ananth Shankar\, Arul Shankar
\, and Salim Tayou and with Davesh Maulik and Ananth Shankar.\n
LOCATION:https://researchseminars.org/talk/LNTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Dimitrov (Toronto)
DTSTART;VALUE=DATE-TIME:20200612T150000Z
DTEND;VALUE=DATE-TIME:20200612T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/8
DESCRIPTION:Title: p-a
dic Eisenstein series\, arithmetic holonomicity criteria\, and irrationali
ty of the 2-adic $\\zeta(5)$\nby Vesselin Dimitrov (Toronto) as part o
f London number theory seminar\n\n\nAbstract\nIn this exposition of a join
t work in progress with Frank Calegari and Yunqing Tang\, I will explain a
new arithmetic criterion for a formal function to be holonomic\, and how
it revives an approach to the arithmetic nature of special values of L-fun
ctions. The new consequence to be proved in this talk is the irrationality
of the 2-adic version of $\\zeta(5)$ (of Kubota-Leopoldt). But I will als
o draw a parallel to a work of Zudilin\, and try to leave some additional
open ends where the holonomicity theorem could be useful. The ingredients
of the irrationality proof are Calegari's p-adic counterpart of the Apery-
Beukers method\, which is based on the theory of overconvergent p-adic mod
ular forms (IMRN\, 2005) taking its key input from Buzzard's theorem on p-
adic analytic continuation (JAMS\, 2002)\, and a Diophantine approximation
method of Andre enhanced to a power of the modular curve $X_0(2)$. The ov
erall argument\, as we shall discuss\, turns out to bear a surprising affi
nity to a recent solution of the Schinzel-Zassenhaus conjecture on the orb
its of Galois around the unit circle.\n
LOCATION:https://researchseminars.org/talk/LNTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yifeng Liu (Yale)
DTSTART;VALUE=DATE-TIME:20200617T130000Z
DTEND;VALUE=DATE-TIME:20200617T140000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/9
DESCRIPTION:Title: Bei
linson-Bloch conjecture and arithmetic inner product formula\nby Yifen
g Liu (Yale) as part of London number theory seminar\n\n\nAbstract\nIn thi
s talk\, we study the Chow group of the motive associated to a tempered gl
obal $L$-packet $\\pi$ of unitary groups of even rank with respect to a CM
extension\, whose global root number is $-1$. We show that\, under some r
estrictions on the ramification of $\\pi$\, if the central derivative $L'(
1/2\,\\pi)$ is nonvanishing\, then the $\\pi$-nearly isotypic localization
of the Chow group of a certain unitary Shimura variety over its reflex fi
eld does not vanish. This proves part of the Beilinson--Bloch conjecture f
or Chow groups and L-functions (which generalizes the B-SD conjecture). Mo
reover\, assuming the modularity of Kudla's generating functions of specia
l cycles\, we explicitly construct elements in a certain $\\pi$-nearly iso
typic subspace of the Chow group by arithmetic theta lifting\, and compute
their heights in terms of the central derivative $L'(1/2\,\\pi)$ and loca
l doubling zeta integrals. This confirms the conjectural arithmetic inner
product formula proposed by me a decade ago. This is a joint work with Cha
o Li.\n
LOCATION:https://researchseminars.org/talk/LNTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART;VALUE=DATE-TIME:20200708T150000Z
DTEND;VALUE=DATE-TIME:20200708T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/12
DESCRIPTION:Title: Pa
rtial Frobenius structures\, Tate’s conjecture\, and BSD over function f
ields.\nby Jared Weinstein (Boston University) as part of London numbe
r theory seminar\n\n\nAbstract\nTate’s conjecture predicts that Galois-i
nvariant classes in the $l$-adic cohomology of a variety are explained by
algebraic cycles. It is known to imply the conjecture of Birch and Swinne
rton-Dyer (BSD) for elliptic curves over function fields. When the variet
y\, now assumed to be in characteristic p\, admits a “partial Frobenius
structure”\, there is a natural extension of Tate’s conjecture. Ass
uming this conjecture\, we get not only BSD\, but the following result: t
he top exterior power of the Mordell-Weil group of an elliptic curve is sp
anned by a “Drinfeld-Heegner” point. This is a report on work in prog
ress.\n
LOCATION:https://researchseminars.org/talk/LNTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Newton
DTSTART;VALUE=DATE-TIME:20201007T150000Z
DTEND;VALUE=DATE-TIME:20201007T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/13
DESCRIPTION:Title: Ev
aluating the wild Brauer group\nby Rachel Newton as part of London num
ber theory seminar\n\n\nAbstract\nThe local-global approach to the study o
f rational points on varieties over number fields begins by embedding the
set of rational points on a variety X into the set of its adelic points. T
he Brauer-Manin pairing cuts out a subset of the adelic points\, called th
e Brauer-Manin set\, that contains the rational points. If the set of adel
ic points is non-empty but the Brauer-Manin set is empty then we say there
's a Brauer-Manin obstruction to the existence of rational points on X. Co
mputing the Brauer-Manin pairing involves evaluating elements of the Braue
r group of X at local points. If an element of the Brauer group has order
coprime to p\, then its evaluation at a p-adic point factors via reduction
of the point modulo p. For p-torsion elements this is no longer the case:
in order to compute the evaluation map one must know the point to a highe
r p-adic precision. Classifying p-torsion Brauer group elements according
to the precision required to evaluate them at p-adic points gives a filtra
tion which we describe using work of Bloch and Kato. Applications of our w
ork include addressing Swinnerton-Dyer's question about which places can p
lay a role in the Brauer-Manin obstruction. This is joint work with Martin
Bright.\n
LOCATION:https://researchseminars.org/talk/LNTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziyang Gao
DTSTART;VALUE=DATE-TIME:20201014T150000Z
DTEND;VALUE=DATE-TIME:20201014T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/14
DESCRIPTION:Title: Bo
unding the number of rational points on curves\nby Ziyang Gao as part
of London number theory seminar\n\n\nAbstract\nMazur conjectured\, after F
altings’s proof of the Mordell conjecture\, that the number of rational
points on a curve of genus g at least 2 defined over a number field of deg
ree d is bounded in terms of g\, d and the Mordell-Weil rank. In particula
r the height of the curve is not involved. In this talk I will explain how
to prove this conjecture and some generalizations. I will focus on how fu
nctional transcendence and unlikely intersections are applied in the proof
. If time permits\, I will talk about how the dependence on d can be furth
ermore removed if we moreover assume the relative Bogomolov conjecture. Th
is is joint work with Vesselin Dimitrov and Philipp Habegger.\n
LOCATION:https://researchseminars.org/talk/LNTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Kurinczuk (Imperial College London)
DTSTART;VALUE=DATE-TIME:20201028T160000Z
DTEND;VALUE=DATE-TIME:20201028T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/15
DESCRIPTION:Title: Mo
duli of Langlands parameters and LLIF\nby Rob Kurinczuk (Imperial Coll
ege London) as part of London number theory seminar\n\n\nAbstract\nThe con
jectural local Langlands correspondence connects representations of p-adic
groups to certain representations of Galois groups of local fields called
Langlands parameters. In recent joint work with Dat\, Helm\, and Moss\,
we have constructed moduli spaces of Langlands parameters over Z[1/p] and
studied their geometry. We expect this geometry is reflected in the repre
sentation theory of the p-adic group. In particular\, our main conjecture
"local Langlands in families" describes the GIT quotient of the moduli sp
ace of Langlands parameters in terms of the centre of the category of repr
esentations of the p-adic group generalising a theorem of Helm-Moss for GL
(n).\n
LOCATION:https://researchseminars.org/talk/LNTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Lourenço
DTSTART;VALUE=DATE-TIME:20201111T160000Z
DTEND;VALUE=DATE-TIME:20201111T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/16
DESCRIPTION:Title: Th
e Scholze-Weinstein conjecture on local models\nby João Lourenço as
part of London number theory seminar\n\n\nAbstract\nInspired by the theory
of local models of Shimura varieties\, Scholze-Weinstein proposed a conje
cture predicting representability of certain minuscule closed sub-v-sheave
s of their p-adic de Rham affine Grassmannian by a projective flat and geo
metrically reduced normal scheme.\n\nIn my talk\, I'll explain the motivat
ion behind the problem stemming from Shimura varieties\, review the necess
ary technical background and ultimately sketch a proof for pseudo-tame gro
ups without exceptional factors. To achieve this\, I'll determine the Pica
rd group of the Witt vectors affine Grassmannian as conjectured by Bhatt-S
cholze. Time permitting\, I might outline a (very much incomplete) strateg
y for handling exceptional groups.\n
LOCATION:https://researchseminars.org/talk/LNTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annette Huber (Universität Freiburg)
DTSTART;VALUE=DATE-TIME:20201118T160000Z
DTEND;VALUE=DATE-TIME:20201118T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/17
DESCRIPTION:Title: Ex
ponential periods and o-minimality\nby Annette Huber (Universität Fre
iburg) as part of London number theory seminar\n\n\nAbstract\n(joint work
with Johan Commelin and Philipp Habegger)\nRoughly\, period numbers are de
fined by integrals of the form\n$\\int_\\sigma\\omega$ with $\\omega$ and
$\\sigma$ of algebraic nature.\nThis can be made precise in very different
languages: as values of\nthe period pairing between de Rham cohomology an
d singular homology\nof algebraic varieties or motives defined over number
fields\, or more\nnaively as\nvolumes of semi-algebraic sets.\n\nMore rec
ently\, exponential periods have come into focus. Roughly\, they\nare of t
he form $\\int_\\sigma e^{-f}\\omega$ with $\\sigma\,\\omega$ and now\nals
o $f$ of algebraic nature. They appear are periods for the Rham complex\no
f an irregular connection. We want to explain how the "naiv" side of\nthe
story can be formulated in this case.\n
LOCATION:https://researchseminars.org/talk/LNTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Garcia (UCl)
DTSTART;VALUE=DATE-TIME:20201209T160000Z
DTEND;VALUE=DATE-TIME:20201209T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/20
DESCRIPTION:Title: Ei
senstein classes and hyperplane complements\nby Luis Garcia (UCl) as p
art of London number theory seminar\n\n\nAbstract\nIn recent years several
authors (Sczech\, Nori\, Hill\, Charollois-Dasgupta-Greenberg\, Beilinson
-Kings-Levin) have defined and studied certain group cocycles ("Eisenstein
cocycles") in the cohomology of arithmetic groups. I will discuss how the
se constructions can be understood in terms of equivariant cohomology and
characteristic classes. This point of view relates the cocycles to the the
ta correspondence and leads to generalisations relating the homology of ar
ithmetic groups to algebraic objects such as meromorphic differentials on
hyperplane complements. I will discuss these generalisations and an applic
ation to critical values of L-functions. \n\nThe talk is based on joint wo
rk-in-progress with Nicolas Bergeron\, Pierre Charollois and Akshay Venkat
esh.\n
LOCATION:https://researchseminars.org/talk/LNTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Lemos (University College London)
DTSTART;VALUE=DATE-TIME:20201216T160000Z
DTEND;VALUE=DATE-TIME:20201216T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/21
DESCRIPTION:Title: Re
sidual Galois representations of elliptic curves with image in the normali
ser of a non-split Cartan\nby Pedro Lemos (University College London)
as part of London number theory seminar\n\n\nAbstract\nIt is known that if
$p$ is a prime $>37$\, then the image of the residual Galois representati
on $\\bar{\\rho}_{E\,p}: G_{\\mathbb{Q}}\\rightarrow {\\rm GL}_2(\\mathbb{
F}_p)$ attached to an elliptic curve $E/\\mathbb{Q}$ without complex multi
plication is either ${\\rm GL}_2(\\mathbb{F}_p)$\, or is contained in the
normaliser of a non-split Cartan subgroup of ${\\rm GL}_2(\\mathbb{F}_p)$.
I will report on a recent joint work with Samuel Le Fourn where we improv
e this result by showing that if $p>1.4\\times 10^7$\, then $\\bar{\\rho}_
{E\,p}$ is either surjective\, or its image is the normaliser of a non-spl
it Cartan subgroup of ${\\rm GL}_2(\\mathbb{F}_p)$.\n
LOCATION:https://researchseminars.org/talk/LNTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lennart Gehrmann (University of Duisburg-Essen / McGill University
)
DTSTART;VALUE=DATE-TIME:20201021T150000Z
DTEND;VALUE=DATE-TIME:20201021T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/22
DESCRIPTION:Title: L-
invariants\, completed cohomology and big principal series\nby Lennart
Gehrmann (University of Duisburg-Essen / McGill University) as part of Lo
ndon number theory seminar\n\n\nAbstract\nLet $f$ be a newform of weight $
2$ that is Steinberg at $p$. Darmon showed that the Fontaine-Mazur $L$-inv
ariant of the associated local $p$-adic Galois representation can be compu
ted in terms of the cohomology of $p$-arithmetic subgroups of the group $P
GL_2(\\mathbb{Q})$.\nOn the other hand Breuil showed that one can compute
the $f$-isoyptical part of completed cohomology of the modular curve in te
rms of the cohomology of $p$-arithmetic groups.\nIn this talk I will give
generalizations of both results to higher rank reductive groups. This is p
artly joint work with Giovanni Rosso.\n
LOCATION:https://researchseminars.org/talk/LNTS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sally Gilles
DTSTART;VALUE=DATE-TIME:20201104T160000Z
DTEND;VALUE=DATE-TIME:20201104T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/23
DESCRIPTION:Title: Pe
riod morphisms and syntomic cohomology\nby Sally Gilles as part of Lon
don number theory seminar\n\n\nAbstract\nIn 2017\, Colmez and Nizioł prov
ed a comparison theorem between arithmetic p-adic nearby cycles and syntom
ic cohomology sheaves. To prove it\, they gave a local construction using
$(\\varphi\,\\Gamma)$-modules theory which allows to reduce the period iso
morphism to a comparison theorem between Lie algebras. In this talk\, I wi
ll first give the geometric version of this construction before explaining
how to globalize it. This period morphism can be used to describe the é
tale cohomology of rigid analytic spaces. In particular\, we deduce the se
mi-stable conjecture of Fontaine-Jannsen\, which relates the étale cohom
ology of the rigid analytic variety associated to a formal proper semi-sta
ble scheme to its Hyodo-Kato cohomology. This result was also proved by (a
mong others) Tsuji\, via the Fontaine-Messing map\, and by Česnavičius
and Koshikawa\, which generalized the proof of the crystalline conjecture
by Bhatt\, Morrow and Scholze. In the second part of the talk\, I will ex
plain how we can use the previous map to show that the period morphism of
Tsuji and the one of Česnavičius-Koshikawa are the same.\n
LOCATION:https://researchseminars.org/talk/LNTS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Graham (Imperial College London)
DTSTART;VALUE=DATE-TIME:20210113T160000Z
DTEND;VALUE=DATE-TIME:20210113T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/24
DESCRIPTION:Title: An
ticyclotomic Euler systems for conjugate self-dual representations of $GL(
2n)$\nby Andrew Graham (Imperial College London) as part of London num
ber theory seminar\n\n\nAbstract\nAn Euler system is a collection of Galoi
s cohomology classes which satisfy certain compatibility relations under c
orestriction\, and by constructing an Euler system and relating the classe
s to $L$-values\, one can establish instances of the Bloch--Kato conjectur
e. In this talk\, I will describe a construction of an anticyclotomic Eule
r system for a certain class of conjugate self-dual automorphic representa
tions\, which can be seen as a generalisation of the Heegner point constru
ction. The classes arise from special cycles on unitary Shimura varieties
and are closely related to the branching law associated with the spherical
pair $(GL(n) \\times GL(n)\, GL(2n))$. This is joint work with S.W.A. Sha
h.\n
LOCATION:https://researchseminars.org/talk/LNTS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Steiner (ETH Zürich)
DTSTART;VALUE=DATE-TIME:20210120T160000Z
DTEND;VALUE=DATE-TIME:20210120T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/25
DESCRIPTION:Title: Fo
urth moments and sup-norms with the aid of theta functions\nby Raphael
Steiner (ETH Zürich) as part of London number theory seminar\n\n\nAbstra
ct\nIt is a classical problem in harmonic analysis to bound $L^p$-norms of
eigenfunctions of the Laplacian on (compact) Riemannian manifolds in term
s of the eigenvalue. A general sharp result in that direction was given by
Hörmander and Sogge. However\, in an arithmetic setting\, one ought to d
o better. Indeed\, it is a classical result of Iwaniec and Sarnak that exa
ctly that is true for Hecke-Maass forms on arithmetic hyperbolic surfaces.
They achieved their result by considering an amplified second moment of H
ecke eigenforms. Their technique has since been adapted to numerous other
settings. In my talk\, I shall explain how to use Shimizu's theta function
to express a fourth moment of Hecke eigenforms in geometric terms (second
moment of matrix counts). In joint work with Ilya Khayutin and Paul Nelso
n\, we give sharp bounds for said matrix counts and thus a sharp bound on
the fourth moment in the weight and level aspect. As a consequence\, we im
prove upon the best known bounds for the sup-norm in these aspects. In par
ticular\, we prove a stronger than Weyl-type sub-convexity result.\n
LOCATION:https://researchseminars.org/talk/LNTS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lynnelle Ye (Stanford University)
DTSTART;VALUE=DATE-TIME:20210127T160000Z
DTEND;VALUE=DATE-TIME:20210127T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/26
DESCRIPTION:Title: Pr
operness for eigenvarieties\nby Lynnelle Ye (Stanford University) as p
art of London number theory seminar\n\n\nAbstract\nCan a family of finite-
slope modular Hecke eigenforms lying over a punctured disc in weight space
always be extended over the puncture? This was first asked by Coleman and
Mazur in 1998 and settled by Diao and Liu in 2016 using deep\, powerful G
alois-theoretic machinery. We will discuss a new proof which is geometric
and explicit and uses no Galois theory\, and which generalizes in some cas
es to Hilbert modular forms. We adapt an earlier method of Buzzard and Cal
egari based on elementary properties of overconvergent modular forms\, for
which we have to extend the construction of Andreatta-Iovita-Pilloni over
convergent forms farther into the supersingular locus.\n
LOCATION:https://researchseminars.org/talk/LNTS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lassina Dembélé (University of Luxembourg)
DTSTART;VALUE=DATE-TIME:20210203T160000Z
DTEND;VALUE=DATE-TIME:20210203T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/27
DESCRIPTION:Title: Fi
nite flat $p$-group schemes over $\\mathbf{Z}$\nby Lassina Dembélé (
University of Luxembourg) as part of London number theory seminar\n\n\nAbs
tract\nConjecture (Abrashkin-Fontaine): For $p$ prime\, the only simple fi
nite flat group schemes of $p$-power order defined over $\\mathbf{Z}$ are
$\\mathbf{Z}/p\\mathbf{Z}$ and $\\mu_p$.\n\nAbrashkin and Fontaine separat
ely proved that this conjecture is true for $p \\le 17$. In this talk\, we
extend their result to the primes $p \\le 37$ under GRH. (This is joint w
ork with René Schoof.)\n
LOCATION:https://researchseminars.org/talk/LNTS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Esteban Rodriguez Camargo (ENS de Lyon)
DTSTART;VALUE=DATE-TIME:20210210T160000Z
DTEND;VALUE=DATE-TIME:20210210T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/28
DESCRIPTION:Title: Du
al Eichler-Shimura maps for the modular curve\nby Juan Esteban Rodrigu
ez Camargo (ENS de Lyon) as part of London number theory seminar\n\n\nAbst
ract\nAndreatta-Iovita-Stevens have constructed interpolations of the sm
all slope part of the Eichler-Shimura decomposition for the modular curve.
Roughly speaking\, they defined in a geometric way a map from the overcon
vergent modular symbols of weight k\, to the overconvergent modular forms
of weight k+2. Then\, using classicality theorems of Coleman and Ash-Ste
vens\, they achieved a Hodge-Tate decomposition of the small slope part of
overconvergent modular symbols. On the other hand\, in a recent paper of
Boxer-Pilloni\, the authors proved that higher Coleman and Hida theories
exist for the modular curve. The aim of this talk is to construct geometri
cally a map from the higher cohomology of overconvergent modular forms of
weight -k to the modular symbols as above. We shall recover the Hodge-Tat
e decomposition of the small slope part of modular symbols\, with the addi
tion that all the maps involved are defined using the geometry of the modu
lar curve. If time permits\, we will discuss the compatibility of the prev
ious work with duality.\n
LOCATION:https://researchseminars.org/talk/LNTS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Li (Columbia University)
DTSTART;VALUE=DATE-TIME:20210217T160000Z
DTEND;VALUE=DATE-TIME:20210217T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/29
DESCRIPTION:Title: Be
ilinson-Bloch conjecture for unitary Shimura varieties\nby Chao Li (Co
lumbia University) as part of London number theory seminar\n\n\nAbstract\n
For certain automorphic representations $\\pi$ on unitary groups\, we show
that if $L(s\, \\pi)$ vanishes to order one at the center $s=1/2$\, then
the associated $\\pi$-localized Chow group of a unitary Shimura variety is
nontrivial. This proves part of the Beilinson-Bloch conjecture for unitar
y Shimura varieties\, which generalizes the BSD conjecture. Assuming Kudla
's modularity conjecture\, we further prove the arithmetic inner product f
ormula for $L'(1/2\, \\pi)$\, which generalizes the Gross-Zagier formula.
We will motivate these conjectures and discuss some aspects of the proof.
We will also mention recent extensions applicable to certain symmetric pow
er L-functions of elliptic curves. This is joint work with Yifeng Liu.\n
LOCATION:https://researchseminars.org/talk/LNTS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Chan (MIT)
DTSTART;VALUE=DATE-TIME:20210224T160000Z
DTEND;VALUE=DATE-TIME:20210224T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/30
DESCRIPTION:Title: Ge
ometric L-packets of toral supercuspidal representations\nby Charlotte
Chan (MIT) as part of London number theory seminar\n\n\nAbstract\nIn 2001
\, Yu gave an algebraic construction of supercuspidal representations of p
-adic groups (now known to be exhaustive when the residual characteristic
is sufficiently large---Kim\, Fintzen). There has since been a lot of prog
ress towards explicitly constructing the local Langlands correspondence: K
azhdan-Varshavsky and DeBacker-Reeder (depth zero)\, Reeder and DeBacker-S
pice (toral)\, and Kaletha (regular supercuspidals). In this talk\, we pre
sent recent and ongoing work investigating a geometric counterpart to this
story. This is based on joint work with Alexander Ivanov and joint work w
ith Masao Oi.\n
LOCATION:https://researchseminars.org/talk/LNTS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anders Södergren (Chalmers University of Technology)
DTSTART;VALUE=DATE-TIME:20210303T160000Z
DTEND;VALUE=DATE-TIME:20210303T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/31
DESCRIPTION:Title: Cu
bic fields\, low-lying zeros and the L-functions Ratios Conjecture\nby
Anders Södergren (Chalmers University of Technology) as part of London n
umber theory seminar\n\n\nAbstract\nIn this talk I will discuss recent wor
k on the low-lying zeros in the family of $L$-functions attached to non-Ga
lois cubic Dedekind zeta functions. In particular\, I will describe the cl
ose relation between these low-lying zeros and precise counting results fo
r cubic fields with local conditions. The main application of this investi
gation is a conditional omega result for cubic field counting functions. I
will also discuss the $L$-functions Ratios Conjecture associated to this
family of Dedekind zeta functions and the fact that the conjecture in its
standard form does not predict all the terms in the family's one-level den
sity of low-lying zeros. This is joint work with Peter Cho\, Daniel Fioril
li and Yoonbok Lee.\n
LOCATION:https://researchseminars.org/talk/LNTS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Min Lee
DTSTART;VALUE=DATE-TIME:20210310T160000Z
DTEND;VALUE=DATE-TIME:20210310T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/32
DESCRIPTION:Title: Li
nnik problem for Maass-Hecke cusp forms and effective multiplicity one the
orem\nby Min Lee as part of London number theory seminar\n\n\nAbstract
\nThe strong multiplicity one theorem (for GL(2)\, proved by Jacquet and L
anglands) implies that if two Maass-Hecke cuspforms share the same Laplaci
an eigenvalue and the same Hecke eigenvalues for almost all primes then th
e two forms must be equal up to a constant multiple. In this talk we cons
ider the following question\, an analogue of Linnik’s question for Diric
hlet characters: if the two forms are not equal up to a constant multiple\
, how large can the first prime p be\, such that the corresponding Hecke e
igenvalues differ? Alternatively we can also ask: how large is the dimensi
on of the joint eigenspace of the given finite set of Hecke operators and
the Laplace operator? We approach these two questions with two different m
ethods. This is a joint work with Junehyuk Jung.\n
LOCATION:https://researchseminars.org/talk/LNTS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Lecouturier (Yau Mathematical Sciences Center and Tsinghu
a University (Beijing))
DTSTART;VALUE=DATE-TIME:20210317T160000Z
DTEND;VALUE=DATE-TIME:20210317T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/33
DESCRIPTION:Title: On
an analogue of a conjecture of Sharifi for imaginary quadratic fields
\nby Emmanuel Lecouturier (Yau Mathematical Sciences Center and Tsinghua U
niversity (Beijing)) as part of London number theory seminar\n\n\nAbstract
\nWe explore a relation between the cohomology of certain Bianchi 3-folds\
, modulo some Eisenstein ideal\, to the arithmetic of imaginary quadratic
fields.\nFor instance\, in the case of Euclidean imaginary quadratic field
s\, we get a relation between modular symbols and cup-products of elliptic
units.\nThis is similar to conjectures of Sharifi for classical modular c
urves\, relating modular symbols to cup-product of cyclotomic units. \nThi
s is work in progress with Jun Wang.\n
LOCATION:https://researchseminars.org/talk/LNTS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akshay Venkatesh (Institute for Advanced Study)
DTSTART;VALUE=DATE-TIME:20210324T160000Z
DTEND;VALUE=DATE-TIME:20210324T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/34
DESCRIPTION:Title: Ce
ntral L-values up to squares\nby Akshay Venkatesh (Institute for Advan
ced Study) as part of London number theory seminar\n\n\nAbstract\nThis is
a report on joint work -- in progress -- with A. Abdurrahman. \nGiven an
everywhere unramified symplectic Galois representation\nover a function fi
eld\, we propose a conjectural formula for its central L-value\nup to squa
res in the coefficient field\, in terms of a certain cohomological invaria
nt\nof the representation. \n \nI'll describe three types of evidence f
or this conjecture\, coming\nfrom numerical examples\, topology\, and auto
morphic forms. \nThen I will discuss (much more speculatively) what the ra
mified/number field\nanalogue of the formula might be\, and its potential
relationship to a theory\nof "higher epsilon factors."\n
LOCATION:https://researchseminars.org/talk/LNTS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Viehmann
DTSTART;VALUE=DATE-TIME:20210428T150000Z
DTEND;VALUE=DATE-TIME:20210428T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/36
DESCRIPTION:Title: Ne
wton strata on the B$_{dR}$-Grassmannian\nby Eva Viehmann as part of L
ondon number theory seminar\n\n\nAbstract\nRecently\, Fargues and Scholze
laid the foundations for\na geometric Langlands program on the Fargues-Fon
taine curve. One of the\ncentral objects of interest is the stack Bun$_G$
of $G$-bundles on the\ncurve. I will explain how to determine the underlyi
ng topological space\n|Bun$_{G}$| and its relation to the Newton stratific
ation on the\nB$_{dR}$-Grassmannian.\n
LOCATION:https://researchseminars.org/talk/LNTS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitris Koukoulopoulos
DTSTART;VALUE=DATE-TIME:20210505T150000Z
DTEND;VALUE=DATE-TIME:20210505T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/37
DESCRIPTION:Title: An
atomy of integers\, polynomials and permutations\nby Dimitris Koukoulo
poulos as part of London number theory seminar\n\n\nAbstract\nThere is a f
amous analogy between the statistics of the prime factors of a random inte
ger\, of the irreducible factors of a random polynomial over a finite fiel
d\, and of the cycles of a random permutation. This analogy allows us to t
ransfer techniques and intuition from one setup to the other\, and it has
been in the center of a lot of recent activity in probabilistic number the
ory and group theory. I will survey some of this progress\, focusing in pa
rticular on results about the irreducibility of randomly chosen polynomial
s with 0\,1 coefficients (joint with Lior Bary-Soroker and Gady Kozma)\, a
s well as on results about the concentration of divisors of random integer
s and the size of the Hooley Delta function (joint with Ben Green and Kevi
n Ford).\n
LOCATION:https://researchseminars.org/talk/LNTS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jef Laga
DTSTART;VALUE=DATE-TIME:20210512T150000Z
DTEND;VALUE=DATE-TIME:20210512T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/38
DESCRIPTION:Title: Ra
tional points and Selmer groups of genus 3 curves\nby Jef Laga as part
of London number theory seminar\n\n\nAbstract\nManjul Bhargava and Arul S
hankar have determined the average size of the n-Selmer group of the famil
y of all elliptic curves over Q ordered by height\, for n at most 5. They
used this to show that the average rank of elliptic curves is less than on
e. \n\nIn this talk we will consider a family of nonhyperelliptic genus 3
curves\, and bound the average size of the 2-Selmer group of their Jacobia
ns. This implies that a majority of curves in this family have relatively
few rational points. We also consider a family of abelian surfaces which a
re not principally polarized and obtain similar results.\n
LOCATION:https://researchseminars.org/talk/LNTS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Medvedovsky
DTSTART;VALUE=DATE-TIME:20210526T150000Z
DTEND;VALUE=DATE-TIME:20210526T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/39
DESCRIPTION:by Anna Medvedovsky as part of London number theory seminar\n\
nInteractive livestream: https://ucl.zoom.us/j/98667980283\nPassword hint:
Password=$j(\\sqrt{-1})$="cubic inches in a cubic foot"=$12^3$\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/LNTS/39/
URL:https://ucl.zoom.us/j/98667980283
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lillian Pierce
DTSTART;VALUE=DATE-TIME:20210602T150000Z
DTEND;VALUE=DATE-TIME:20210602T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/40
DESCRIPTION:by Lillian Pierce as part of London number theory seminar\n\nI
nteractive livestream: https://ucl.zoom.us/j/98667980283\nPassword hint: P
assword=$j(\\sqrt{-1})$="cubic inches in a cubic foot"=$12^3$\nAbstract: T
BA\n
LOCATION:https://researchseminars.org/talk/LNTS/40/
URL:https://ucl.zoom.us/j/98667980283
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pip Goodman
DTSTART;VALUE=DATE-TIME:20210609T150000Z
DTEND;VALUE=DATE-TIME:20210609T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/41
DESCRIPTION:by Pip Goodman as part of London number theory seminar\n\nInte
ractive livestream: https://ucl.zoom.us/j/98667980283\nPassword hint: Pass
word=$j(\\sqrt{-1})$="cubic inches in a cubic foot"=$12^3$\nAbstract: TBA\
n
LOCATION:https://researchseminars.org/talk/LNTS/41/
URL:https://ucl.zoom.us/j/98667980283
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pär Kurlberg
DTSTART;VALUE=DATE-TIME:20210616T150000Z
DTEND;VALUE=DATE-TIME:20210616T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/42
DESCRIPTION:by Pär Kurlberg as part of London number theory seminar\n\nIn
teractive livestream: https://ucl.zoom.us/j/98667980283\nPassword hint: Pa
ssword=$j(\\sqrt{-1})$="cubic inches in a cubic foot"=$12^3$\nAbstract: TB
A\n
LOCATION:https://researchseminars.org/talk/LNTS/42/
URL:https://ucl.zoom.us/j/98667980283
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sug Woo Shin
DTSTART;VALUE=DATE-TIME:20210623T100000Z
DTEND;VALUE=DATE-TIME:20210623T110000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/43
DESCRIPTION:by Sug Woo Shin as part of London number theory seminar\n\nInt
eractive livestream: https://ucl.zoom.us/j/98667980283\nPassword hint: Pas
sword=$j(\\sqrt{-1})$="cubic inches in a cubic foot"=$12^3$\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/LNTS/43/
URL:https://ucl.zoom.us/j/98667980283
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Young (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20210421T150000Z
DTEND;VALUE=DATE-TIME:20210421T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/44
DESCRIPTION:Title: An
improved spectral large sieve inequality for $\\text{SL}_3(\\mathbb Z)$.<
/a>\nby Matt Young (Texas A&M University) as part of London number theory
seminar\n\n\nAbstract\nI will discuss recent progress on the spectral larg
e sieve problem for $\\text{SL}_3(\\mathbb Z)$. The method of proof uses
duality and its structure reveals unexpected connections to Heath-Brown's
large sieve for cubic characters.\n
LOCATION:https://researchseminars.org/talk/LNTS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lilian Matthiesen
DTSTART;VALUE=DATE-TIME:20210630T150000Z
DTEND;VALUE=DATE-TIME:20210630T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T204556Z
UID:LNTS/45
DESCRIPTION:by Lilian Matthiesen as part of London number theory seminar\n
\nInteractive livestream: https://ucl.zoom.us/j/98667980283\nPassword hint
: Password=$j(\\sqrt{-1})$="cubic inches in a cubic foot"=$12^3$\nAbstract
: TBA\n
LOCATION:https://researchseminars.org/talk/LNTS/45/
URL:https://ucl.zoom.us/j/98667980283
END:VEVENT
END:VCALENDAR