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BEGIN:VEVENT
SUMMARY:Michele Fornea (Columbia)
DTSTART:20200918T143000Z
DTEND:20200918T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/2
DESCRIPTION:Title: Points on elliptic curves via p-adic integration\nby Michele Forn
ea (Columbia) as part of Columbia Automorphic Forms and Arithmetic Seminar
\n\n\nAbstract\nThe work of Bertolini\, Darmon and their schools has shown
that p-adic multiplicative integrals can be successfully employed to stud
y the global arithmetic of elliptic curves. Notably\, Guitart\, Masdeu and
Sengun have recently constructed and numerically computed Stark-Heegner p
oints in great generality. Their results strongly support the expectation
that Stark-Heegner points completely control the Mordell-Weil group of ell
iptic curves of rank 1.\n\nIn our talk\, we will report on work in progres
s about a conjectural construction of global points on modular elliptic cu
rves\, generalizing the p-adic construction of Heegner points via Cerednik
-Drinfeld uniformization. Inspired by Nekovar and Scholl's plectic conject
ures\, we expect the non-triviality of these plectic Heegner points to con
trol the Morderll-Weil group of higher rank elliptic curves. We provide so
me evidence for our conjectures by showing that higher derivatives of anti
cyclotomic p-adic L-functions compute plectic Heegner points.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Gaitsgory (Harvard)
DTSTART:20200925T143000Z
DTEND:20200925T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/3
DESCRIPTION:Title: The stack of local systems with restricted variation and the passage
from geometric to classical Langlands theory\nby Dennis Gaitsgory (Har
vard) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAb
stract\nThe goal of this talk is two explain to closely related phenomena:
the existence of the categorical geometric Langlands theory for l-adic sh
eaves and the link between geometric to classical Langlands via the operat
ion of categorical trace. A key ingredient is played by a new geometric ob
ject: the stack of local systems with restricted variation.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hector Pasten (PUC Chile)
DTSTART:20201002T143000Z
DTEND:20201002T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/4
DESCRIPTION:Title: A Chabauty-Coleman estimate for surfaces in abelian threefolds\nb
y Hector Pasten (PUC Chile) as part of Columbia Automorphic Forms and Arit
hmetic Seminar\n\n\nAbstract\nColeman's explicit version of Chabauty's the
orem gives a remarkable upper bound for the number of rational points in h
yperbolic curves over number fields\, under a certain rank condition. This
result is obtained by p-adic methods. Despite considerable efforts in thi
s topic\, higher dimensional extensions of such a bound have remained elus
ive. In this talk I will sketch the proof for hyperbolic surfaces containe
d in abelian threefolds\, which provides the first case beyond the scope o
f curves. This is joint work with Jerson Caro.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Wang (MIT)
DTSTART:20201009T143000Z
DTEND:20201009T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/5
DESCRIPTION:Title: Local L-values and geometric harmonic analysis on spherical varieties
\nby Jonathan Wang (MIT) as part of Columbia Automorphic Forms and Ari
thmetic Seminar\n\n\nAbstract\nAlmost a decade ago\, Sakellaridis conjectu
red a vast generalization of the Rankin-Selberg method to produce integral
representations of L-functions using affine spherical varieties. The conj
ecture is still very much unknown\, but generalized Ichino-Ikeda formulas
of Sakellaridis-Venkatesh relate the global problem to certain problems in
local harmonic analysis. I will explain how we can use techniques from ge
ometric Langlands to compute integrals which give special values of unrami
fied local L-functions over a local function field\, for a large class of
spherical varieties. This is joint work with Yiannis Sakellaridis. Our res
ults give new integral representations of L-functions (in a right half pla
ne) over global function fields when the integral "unfolds".\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Boxer (ENS de Lyon)
DTSTART:20201016T143000Z
DTEND:20201016T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/6
DESCRIPTION:Title: Higher Coleman Theory\nby George Boxer (ENS de Lyon) as part of C
olumbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nWe introdu
ce a higher coherent cohomological analog of overconvergent modular forms
on Shimura varieties and explain how to compute the finite slope part of t
he coherent cohomology of Shimura varieties in terms of them. We also dis
cuss how they vary p-adically. This is joint work with Vincent Pilloni.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Zerbes (UCL)
DTSTART:20201023T143000Z
DTEND:20201023T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/7
DESCRIPTION:Title: The Bloch—Kato conjecture for GSp(4)\nby Sarah Zerbes (UCL) as
part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nI
n my talk\, I will sketch a proof of new cases of the Bloch—Kato conject
ure for the spin Galois representation attached to genus 2 Siegel modular
forms. More precisely\, I will show that if the L-function is non-vanishin
g at some critical value\, then the corresponding Selmer group is zero\, a
ssuming a number of technical hypotheses. I will also mention work in prog
ress on extending this result to Siegel modular forms of parallel weight 2
\, with potential applications to the Birch—Swinnerton-Dyer conjecture f
or abelian surfaces. This is joint work with David Loeffler.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Loeffler (Warwick)
DTSTART:20201030T143000Z
DTEND:20201030T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/8
DESCRIPTION:Title: P-adic interpolation of Gross--Prasad periods and diagonal cycles
\nby David Loeffler (Warwick) as part of Columbia Automorphic Forms and Ar
ithmetic Seminar\n\n\nAbstract\nThe Gross--Prasad conjecture for orthogona
l groups relates special values of L-functions for SO(n) x SO(n+1) to peri
od integrals of automorphic forms. This conjecture is known for n = 3\, in
which case the group SO(3) x SO(4) is essentially GL2 x GL2 x GL2\; and t
he study of these GL2 triple product periods\, and in particular their var
iation in p-adic families\, has had important arithmetic applications\, su
ch as the work of Darmon and Rotger on the equivariant BSD conjecture for
elliptic curves.\n\nI'll report on work in progress with Sarah Zerbes stud
ying these periods in the n = 4 case\, where the group concerned is isogen
ous to GSp4 x GL2 x GL2. I'll explain a construction of p-adic L-functions
interpolating the Gross--Prasad periods in Hida families\, and an 'explic
it reciprocity law' relating these p-adic L-functions to diagonal cycle cl
asses in etale cohomology. These constructions are closely analogous to th
e Euler system for GSp(4) described in Sarah's talk\, but with cusp forms
in place of the GL2 Eisenstein series.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Yun Hsu (UCLA)
DTSTART:20201106T153000Z
DTEND:20201106T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/9
DESCRIPTION:Title: Construction of Euler systems for GSp4×GL2\nby Chi-Yun Hsu (UCLA
) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstra
ct\nFollowing a strategy similar to the work of Loeffler-Skinner-Zerbes\,
we construct Euler systems for Galois representations coming from automorp
hic representations of GSp4×GL2. We will explain how the tame norm relati
ons follow from a local calculation in smooth representation theory\, in w
hich the integral formula of L-functions\, due to Novodvorsky in our case\
, plays an important role. This is a joint work with Zhaorong Jin and Ryot
aro Sakamoto.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuanqing Cai (Kyoto)
DTSTART:20201113T153000Z
DTEND:20201113T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/10
DESCRIPTION:Title: Certain representations with unique models\nby Yuanqing Cai (Kyo
to) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbst
ract\nThe uniqueness of Whittaker models is an important ingredient in the
study of certain Langlands L-functions. However\, this property fails for
groups such as GL(n\,D)\, where D is a central division algebra over a lo
cal field. \n\nIn this talk\, we discuss a family of irreducible represent
ations of GL(n\,D) that admit unique models. We also discuss some related
local and global questions.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takuya Yamauchi (Tohoku)
DTSTART:20201120T153000Z
DTEND:20201120T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/11
DESCRIPTION:Title: Automorphy of mod 2 Galois representations associated to the quintic
Dwork family and reciprocity of some quintic trinomials\nby Takuya Ya
mauchi (Tohoku) as part of Columbia Automorphic Forms and Arithmetic Semin
ar\n\n\nAbstract\nIn this talk\, I will explain my recent work with Tsuzuk
i Nobuo on computing\nmod $2$ Galois representations $\\overline{\\rho}_{\
\psi\,2}:G_K:={\\rm Gal}(\\overline{K}/K)\\longrightarrow {\\rm GSp}_4(\\F
_2)$\nassociated to the mirror motives of rank 4 with pure weight 3 coming
from the\nDwork quintic family\n$$X^5_0+X^5_1+X^5_2+X^5_3+X^5_4-5\\psi X_
0X_1X_2X_3X_4=0\,\\ \\psi\\in K$$\ndefined over a number field $K$ under t
he irreducibility condition of the quintic trinomial\n$f_\\psi(x)=4x^5-5\\
psi x^4+1$.\nIn the course of the computation\, we observe that the image
of such a mod $2$ representation is governed by reciprocity of\n$f_\\psi(x
)$ whose decomposition field is generically of type\n5-th symmetric group
$S_5$.\nWhen K=F is totally real field\, we apply the modularity of\n2-dim
ensional\, totally odd Artin representations of ${\\rm Gal}(\\overline{F}/
F)$ due to Shu Sasaki\nto obtain automorphy of $\\overline{\\rho}_{\\psi\,
2}$ after a suitable (at most) quadratic base extension.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugen Hellmann (Münster)
DTSTART:20201204T153000Z
DTEND:20201204T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/12
DESCRIPTION:Title: Towards automorphy lifting for semi-stable Galois representations\nby Eugen Hellmann (Münster) as part of Columbia Automorphic Forms and
Arithmetic Seminar\n\n\nAbstract\nAutomorphy lifting theorems aim to show
that a p-adic global Galois representation that is unramified almost every
where and de Rham at places dividing p is associated to an automorphic rep
resentation\, provided its reduction modulo p is. In the past years there
has been a lot of progress in the case of polarizable representations that
are crystalline at p. In the semi-stable case much less is known (beyond
the ordinary case and the 2-dimensional case).\n\nI will explain recent pr
ogress on classicality theorems for p-adic automorphic forms whose associa
ted Galois representation is semi-stable at places dividing p. In the cont
ext of automorphy lifting problems\, these results can be used to deduce t
he semi-stable case from the crystalline case.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhilin Luo (Minnesota)
DTSTART:20201211T153000Z
DTEND:20201211T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/13
DESCRIPTION:Title: A local trace formula for the local Gan-Gross-Prasad conjecture for
special orthogonal groups\nby Zhilin Luo (Minnesota) as part of Columb
ia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nThe local Gan-G
ross-Prasad conjecture studies the restriction and branching problems for
representations of classical and metaplectic groups. In this talk\, I will
talk about my proof for the tempered part of the local Gan-Gross-Prasad c
onjecture (multiplicity one in Vogan packets) for special orthogonal group
s over any local fields of characteristic zero\, which combines the work o
f Waldspurger (for the tempered part of the conjecture for special orthogo
nal groups over $p$-adic fields) and Beuzart-Plessis (for the tempered par
t of the conjecture for unitary groups over real field) in a non-trivial w
ay. In the proof\, an indispensable result which is also of independent in
terest is a formula expressing the regular nilpotent germs of quasi-split
reductive Lie algebras over any local fields of characteristic zero via en
doscopic invariants\, which was previously proved by Shelstad over $p$-adi
c fields. We also relate the formula with the Kostant's sections.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amadou Bah (IHES)
DTSTART:20201218T153000Z
DTEND:20201218T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/14
DESCRIPTION:Title: Variation of the Swan conductor of an $\\mathbb{F}_{\\ell}$-sheaf on
a rigid disc\nby Amadou Bah (IHES) as part of Columbia Automorphic Fo
rms and Arithmetic Seminar\n\n\nAbstract\nLet $K$ be a complete discrete v
aluation field of residue characteristic $p>0$ and $\\ell\\neq p$ a prime
number. To a finite dimensional $\\mathbb{F}_{\\ell}$-representation $M$ o
f the absolute Galois group $G_K$\, the ramification theory of Abbes and S
aito attaches a Swan conductor ${\\rm sw}(M)$ and a characteristic cycle $
{\\rm CC}(M)$. Let $D$ be the rigid unit disc over $K$ and $\\mathcal{F}$
a lisse sheaf of $\\mathbb{F}_{\\ell}$-modules on $D$. For $t\\in \\mathbb
{Q}_{\\geq 0}$\, the normalized integral model $\\mathcal{D}^{(t)}$ of the
subdisc $D^{(t)}$ of radius $t$ is defined over some finite extension of
$K$. The restriction $\\mathcal{F}_{\\lvert D^{(t)}}$ defines\, at the gen
eric point $\\mathfrak{p}^{(t)}$ of the special fiber of $\\mathcal{D}^{(t
)}$\, a Galois representation $M_t$ over a complete discrete valuation fie
ld\, thus yielding a Swan conductor ${\\rm sw}(M_t)$ and a characteristic
cycle ${\\rm CC}(M_t)$. The goal of the talk is to explain how we connect
earlier works\, of Lütkebohmert on a discriminant function attached to a
cover of $D$\, and of Kato on the ramification of valuation rings of heigh
t $2$\, and prove that the function $t\\mapsto {\\rm sw}(M_t)$ is continuo
us and piecewise linear with finitely many slopes which are all integers\,
and that its right derivative is $t\\mapsto -{\\rm ord}_{\\mathfrak{p}^{(
t)}}({\\rm CC}(M_t)) + \\dim_{\\mathbb{F}_{\\ell}}(M_t/M_t^{(0)})$\, where
${\\rm ord}_{\\mathfrak{p}^{(t)}}$ is a normalized discrete valuation at
$\\mathfrak{p}^{(t)}$ extended to differentials and $M_t^{(0)}$ is the tam
e part of $M_t$.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Nelson (ETH Zurich)
DTSTART:20210129T153000Z
DTEND:20210129T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/15
DESCRIPTION:Title: The orbit method\, microlocal analysis and applications to L-functio
ns\nby Paul Nelson (ETH Zurich) as part of Columbia Automorphic Forms
and Arithmetic Seminar\n\n\nAbstract\nI will describe how the orbit method
can be developed in a quantitative form\, along the lines of microlocal a
nalysis\, and applied to local problems in representation theory and globa
l problems concerning automorphic forms. The local applications include a
symptotic expansions of relative characters. The global applications incl
ude moment estimates and subconvex bounds for L-functions. These results
are the subject of two papers\, the first joint with Akshay Venkatesh:\n\n
https://arxiv.org/abs/1805.07750\nhttps://arxiv.org/abs/2012.02187\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shizhang Li (Michigan)
DTSTART:20210205T153000Z
DTEND:20210205T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/16
DESCRIPTION:Title: On the boundary case of Breuil--Caruso's theory\nby Shizhang Li
(Michigan) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\
n\nAbstract\nIn the talk I shall report on recent joint work with Tong Liu
on integral p-adic Hodge theory. Using newly developed cohomology theory
we extend a result of Caruso\, stating roughly that\, in nice situations\,
certain natural structure on the crystalline cohomology of a variety is a
Breuil module related to its étale cohomology.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yingkun Li (TU Darmstadt)
DTSTART:20210212T153000Z
DTEND:20210212T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/17
DESCRIPTION:Title: Integrality of regularized Petersson inner product\nby Yingkun L
i (TU Darmstadt) as part of Columbia Automorphic Forms and Arithmetic Semi
nar\n\n\nAbstract\nPetersson inner products of classical cusp forms contai
n\nimportant arithmetic information\, such as congruences of modular forms
.\nWhen the cusp forms are replaced by meromorphic modular form\, the\nPet
ersson inner product can still be defined and calculated after suitable\nr
egularization. It turns out these regularized inner product also carry\nin
teresting arithmetic information\, such as special values of derivatives\n
of L-function. In this talk\, we will recall some of these results\, and\n
discuss a joint work with Markus Schwagenscheidt from ETH\, where we\nobta
ined an integrality result of such regularized inner products\ninvolving u
nary theta functions.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashay Burungale (Caltech)
DTSTART:20210226T160000Z
DTEND:20210226T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/18
DESCRIPTION:Title: An even parity instance of the Goldfeld conjecture\nby Ashay Bur
ungale (Caltech) as part of Columbia Automorphic Forms and Arithmetic Semi
nar\n\n\nAbstract\nIn 1979 D. Goldfeld conjectured: 50% of the quadratic t
wists of an elliptic curve over the rationals have analytic rank zero. We
present the first instance - the congruent number elliptic curves (joint w
ith Y. Tian).\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiwei Yun (MIT)
DTSTART:20210312T153000Z
DTEND:20210312T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/19
DESCRIPTION:Title: Towards a higher arithmetic Siegel-Weil formula for unitary groups\nby Zhiwei Yun (MIT) as part of Columbia Automorphic Forms and Arithmet
ic Seminar\n\n\nAbstract\nThe classical Siegel-Weil formula relates an int
egral of a theta function along one classical group H to special values of
the Siegel-Eisenstein series on another classical group G. Kudla proposed
an arithmetic analogue of it that relates a generating series of algebrai
c cycles on the Shimura variety for H to the first derivative of the Siege
l-Eisenstein series for G\, which has become a very active program. We pro
pose to go further in the function field case\, relating a generating seri
es of algebraic cycles on the moduli of H-Shtukas with multiple legs to hi
gher derivatives of the Siegel-Eisenstein series for G\, when H and G are
unitary groups. We prove such a formula for nonsingular Fourier coefficien
ts\, relating their higher derivatives to degrees of zero cycles on the mo
duli of unitary Shtukas. The proof ultimately relies on an argument from S
pringer theory. This is joint work with Tony Feng and Wei Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cong Xue (CNRS/IMJ-PRG)
DTSTART:20210319T143000Z
DTEND:20210319T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/20
DESCRIPTION:Title: Cohomology sheaves of stacks of shtukas\nby Cong Xue (CNRS/IMJ-P
RG) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbst
ract\nThe stacks of shtukas play an important role in the Langlands corres
pondence for function fields. In this talk\, we will recall the definition
of cohomology sheaves of stacks of shtukas and review the partial Frobeni
us morphisms and Drinfeld's lemma. Then we will talk about the smoothness
property of the cohomology sheaves and some applications.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Zhang (NUS)
DTSTART:20210326T143000Z
DTEND:20210326T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/21
DESCRIPTION:Title: Twisted Automorphic Descent and Gan-Gross-Prasad Conjecture\nby
Lei Zhang (NUS) as part of Columbia Automorphic Forms and Arithmetic Semin
ar\n\n\nAbstract\nIn this talk\, we will discuss the theory of twisted aut
omorphic descents\, which is an extension of the automorphic descent of Gi
nzburg-Rallis-Soudry.\nOne of our goals is to construct cuspidate automorp
hic modules in the generic global Arthur packets by using Fourier coeffici
ents of automorphic representations.\nMoreover\, we will discuss our appro
ach for one direction of Gan-Gross-Prasad Conjecture for the Bessel-Fourie
r models and some connections between Fourier coefficients and spherical v
arieties.\nThis is a joint work with Dihua Jiang.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Litt (Georgia)
DTSTART:20210409T143000Z
DTEND:20210409T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/23
DESCRIPTION:Title: Single-valued Hodge\, p-adic^2\, and tropical integration\nby Da
niel Litt (Georgia) as part of Columbia Automorphic Forms and Arithmetic S
eminar\n\n\nAbstract\nI'll discuss 4 different types of single-valued inte
gration on algebraic varieties -- one in the complex setting\, one in the
tropical setting\, and two in the p-adic setting\, and the relationships b
etween them. In particular\, I'll explain how to compute Vologodsky's "sin
gle-valued" iterated integrals on curves of bad reduction in terms of Berk
ovich integrals\, and how to give a single-valued integration theory on co
mplex varieties. Time permitting\, I'll explain some potential arithmetic
applications. This is a report on joint work in progress with Sasha Shmako
v (in the complex setting) and Eric Katz (in the p-adic setting).\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Zhang (Columbia)
DTSTART:20210917T143000Z
DTEND:20210917T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/24
DESCRIPTION:Title: Modular Gelfand pairs and multiplicity-free triples\nby Robin Zh
ang (Columbia) as part of Columbia Automorphic Forms and Arithmetic Semina
r\n\n\nAbstract\nThe classical theory of Gelfand pairs and its generalizat
ions over the complex numbers has many applications to number theory and a
utomorphic forms\, such as the uniqueness of Whittaker models and the non-
vanishing of the central value of a triple product L-function. With an eye
towards similar applications in the modular setting\, this talk presents
an extension of the classical theory to representations of finite groups o
ver algebraically closed fields whose characteristics possibly divide the
orders of the groups.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linus Hamann (Princeton)
DTSTART:20211001T143000Z
DTEND:20211001T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/25
DESCRIPTION:Title: Compatibility of the Fargues-Scholze and Gan-Takeda Local Langlands<
/a>\nby Linus Hamann (Princeton) as part of Columbia Automorphic Forms and
Arithmetic Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Lawrence (UCLA)
DTSTART:20211008T143000Z
DTEND:20211008T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/26
DESCRIPTION:Title: Sparsity of Integral Points on Moduli Spaces of Varieties\nby Br
ian Lawrence (UCLA) as part of Columbia Automorphic Forms and Arithmetic S
eminar\n\n\nAbstract\nInteresting moduli spaces don't have many integral p
oints. More precisely\, if $X$ is a variety over a number field\, admitti
ng a variation of Hodge structure whose associate period map is injective\
, then the number of $S$-integral points on $X$ of height at most $H$ grow
s more slowly than $H^{\\epsilon}$\, for any positive $\\epsilon$. This i
s a sort of weak generalization of the Shafarevich conjecture\; it is a co
nsequence of a point-counting theorem of Broberg\, and the largeness of th
e fundamental group of $X$. Joint with Ellenberg and Venkatesh.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Disegni (BGU)
DTSTART:20211015T143000Z
DTEND:20211015T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/27
DESCRIPTION:Title: Euler systems for conjugate-symplectic motives\nby Daniel Disegn
i (BGU) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\n
Abstract\nKolyvagin's original Euler system (1990)\, based on Heegner poin
ts\, complemented the height formula of Gross and Zagier to prove a key ca
se of the Birch and Swinnerton-Dyer conjecture. I will introduce some new
Euler systems. They are of a species theorized by Jetchev--Nekovar--Skinne
r\, and pertain to those representations of the Galois group of a CM field
that are automorphic\, carry a conjugate-symplectic form\, and have the s
implest Hodge--Tate type. \n\nThe construction is based on Kudla's special
cycles on unitary Shimura varieties\, under an assumption of modularity f
or their generating series. Together with a recent height formula by Li--L
iu and the forthcoming theory of JNS\, this reduces some cases of the Beil
inson--Bloch--Kato conjecture to the injectivity of Abel--Jacobi maps.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunqing Tang (Princeton)
DTSTART:20211022T143000Z
DTEND:20211022T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/28
DESCRIPTION:Title: The unbounded denominators conjecture\nby Yunqing Tang (Princeto
n) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstr
act\n(Joint work with Frank Calegari and Vesselin Dimitrov.) The unbounded
denominators conjecture\, first raised by Atkin and Swinnerton-Dyer\, ass
erts that a modular form for a finite index subgroup of SL_2(Z) whose Four
ier coefficients have bounded denominators must be a modular form for some
congruence subgroup. In this talk\, we will give a sketch of the proof of
this conjecture based on a new arithmetic algebraization theorem.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Mantovan (Caltech)
DTSTART:20211029T170000Z
DTEND:20211029T183000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/29
DESCRIPTION:Title: Infinitely many primes of basic reduction\nby Elena Mantovan (Ca
ltech) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nA
bstract\nIn 1987\, Elkies proved that an elliptic curve defined over the f
ield of rational numbers has infinitely many primes of supersingular reduc
tion. I will discuss a generalization of this result to the case of specia
l cyclic covers of the projective line ramified at 4 points. This talk is
based on joint work in progress with Wanlin Li\, Rachel Pries and Yunqing
Tang.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ming-Lun Hsieh (Academia Sinica)
DTSTART:20211105T143000Z
DTEND:20211105T160000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/30
DESCRIPTION:Title: On the first derivatives of the cyclotomic Katz p-adic L-functions f
or CM fields\nby Ming-Lun Hsieh (Academia Sinica) as part of Columbia
Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nBuyukboduk and Sak
amoto in 2019 proposed a precise conjectural formula relating the leading
coefficient at the trivial zero s=0 of the cyclotomic Katz p-adic L-functi
ons associated with ray class characters of a CM field K to suitable L-inv
ariants/regulators of K. They were able to prove this formula in most case
s when K is an imaginary quadratic field thanks to the existence of the Eu
ler system of elliptic units/Rubin-Stark elements. In this talk\, we will
present a formula relating the first derivative of the cyclotomic Katz p-a
dic L-functions for general CM fields attached to ring class characters to
the product of the L-invariant and the value of the improved Katz p-adic
L-function at s=0. In particular\, when the trivial zero occurs at s=0\, w
e prove that the Katz p-adic L-function has a simple zero at s=0 if certai
n L-invariant is non-vanishing. Our method uses the congruence of Hilbert
CM forms and does reply on the existence of the conjectural Rubin-Stark el
ements. This is a joint work with Adel Betina.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yujie Xu (Harvard)
DTSTART:20211112T153000Z
DTEND:20211112T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/31
DESCRIPTION:Title: On normalization in the integral models of Shimura varieties of Hodg
e type\nby Yujie Xu (Harvard) as part of Columbia Automorphic Forms an
d Arithmetic Seminar\n\n\nAbstract\nShimura varieties are moduli spaces of
abelian varieties with extra structures. Over the decades\, various mathe
maticians (e.g. Rapoport\, Kottwitz\, etc.) have constructed integral mode
ls of Shimura varieties. In this talk\, I will discuss some motivic aspect
s of integral models of Hodge type constructed by Kisin (resp. Kisin-Pappa
s). I will talk about recent work on removing the normalization step in th
e construction of such integral models\, which gives closed embeddings of
Hodge type integral models into Siegel integral models under some assumpti
on. I will explain how this question is related to the Grothendieck Standa
rd Conjecture D for abelian varieties\, and sketch a proof of this type of
questions if time permits. I will also mention an application to toroidal
compactifications of Hodge type integral models.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Fox (Oregon)
DTSTART:20211119T153000Z
DTEND:20211119T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/32
DESCRIPTION:Title: Supersingular Loci of Unitary (2\,m-2) Shimura Varieties\nby Mar
ia Fox (Oregon) as part of Columbia Automorphic Forms and Arithmetic Semin
ar\n\n\nAbstract\nThe supersingular locus of a Unitary (2\,m-2) Shimura va
riety parametrizes supersingular abelian varieties of dimension m\, with a
n action of a quadratic imaginary field meeting the "signature (2\,m-2)" c
ondition. In some cases\, for example when m=3 or m=4\, every irreducible
component of the supersingular locus is isomorphic to a Deligne-Lusztig va
riety\, and the intersection combinatorics are governed by a Bruhat-Tits b
uilding. We'll consider these cases for motivation\, and then see how the
structure of the supersingular locus becomes very different for m>4. (The
new result in this talk is joint with Naoki Imai.)\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Lei (Laval)
DTSTART:20211203T153000Z
DTEND:20211203T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/33
DESCRIPTION:Title: Iwasawa theory over imaginary quadratic fields for inert primes\
nby Antonio Lei (Laval) as part of Columbia Automorphic Forms and Arithmet
ic Seminar\n\n\nAbstract\nLet $p$ be a fixed odd prime and $K$ an imaginar
y quadratic field where $p$ is inert. Let $f$ be an elliptic modular form
with good ordinary reduction at $p$. We discuss how the cyclotomic Iwasawa
theory of the Rankin-Selberg product of $f$ and a $p$-non-ordinary CM for
m allows us to study the Iwasawa theory of $f$ over the $\\mathbf{Z}_p^2$-
extension of $K$. We make use of the plus and minus theory of Kobayashi an
d Pollack as well as Euler systems built out of Beilinson--Flach elements.
This is joint work with Kazim Buyukboduk.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaul Zemel (Einstein Institute of Mathematics)
DTSTART:20211210T153000Z
DTEND:20211210T170000Z
DTSTAMP:20260404T110823Z
UID:CAFAS/34
DESCRIPTION:Title: Special cycles on toroidal compactifications of orthogonal Shimura v
arieties\nby Shaul Zemel (Einstein Institute of Mathematics) as part o
f Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nWe dete
rmine the behavior of automorphic Green functions along the boundary compo
nents of toroidal compactifications of orthogonal Shimura varieties. We us
e this analysis to define boundary components of special divisors and prov
e that the generating series of the resulting special divisors on a toroid
al compactification is modular. This is joint work with Jan Bruinier.\n
LOCATION:https://stable.researchseminars.org/talk/CAFAS/34/
END:VEVENT
END:VCALENDAR