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BEGIN:VEVENT
SUMMARY:A. Raghuram (Fordham University)
DTSTART:20230127T153000Z
DTEND:20230127T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/1
DESCRIPTION:Title: Special values of Rankin-Selberg L-functions over a totally ima
ginary field\nby A. Raghuram (Fordham University) as part of Columbia
- Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathemat
ics Hall.\n\nAbstract\nI will talk about my recent rationality results on
the ratios of critical values for Rankin-Selberg L-functions for GL(n) x G
L(m) over a totally imaginary base field. In contrast to a totally real ba
se field\, when the base field is totally imaginary\, some delicate signat
ures enter the reciprocity laws for these special values. These signatures
depend on whether or not the totally imaginary base field contains a CM s
ubfield. This is a generalization of my work with Günter Harder on rank-o
ne Eisenstein cohomology for GL(N)\, where N = n + m. The rationality resu
lt comes from interpreting Langlands's constant term theorem in terms of a
n arithmetically defined intertwining operator between Hecke summands in t
he cohomology of the Borel-Serre boundary of a locally symmetric space for
GL(N). The signatures arise from Galois action on certain local systems t
hat intervene in boundary cohomology.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Weinstein (Boston University)
DTSTART:20230203T153000Z
DTEND:20230203T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/2
DESCRIPTION:Title: Higher Modularity of Elliptic Curves\nby J. Weinstein (Bost
on University) as part of Columbia - Automorphic Forms and Arithmetic Semi
nar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nElliptic curves
E over the rational numbers are modular: this means there is a nonconstant
map from a modular curve to E. When instead the coefficients of E belong
to a function 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\, th
e modular 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 wi
th Adam Logan\, we give some classes of elliptic curves E which are 2- and
3-modular.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. E. Rodríguez Camargo (Max Planck (Bonn))
DTSTART:20230210T153000Z
DTEND:20230210T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/3
DESCRIPTION:Title: Solid locally analytic representations\, D-modules and applicat
ions to p-adic automorphic forms\nby J. E. Rodríguez Camargo (Max Pla
nck (Bonn)) as part of Columbia - Automorphic Forms and Arithmetic Seminar
\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nIn this talk I will
present a project in progress with Joaquín Rodrigues Jacinto concerning
the study of locally analytic\nrepresentations of p-adic Lie groups and it
s relation with p-adic D-modules of rigid spaces à la Ardakov. I will ske
tch\nhow both theories are essentially two different looks of the same kin
d of objects and how they can be interpreted in\nterms of sheaves in suita
ble stacks on analytic rings. If time permits I will mention two possible
applications in the\ncohomology of Shimura varieties.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Cass (University of Michigan)
DTSTART:20230217T153000Z
DTEND:20230217T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/4
DESCRIPTION:Title: Geometrization of the mod p Satake transform\nby Robert Cas
s (University of Michigan) as part of Columbia - Automorphic Forms and Ari
thmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nThe
classical Satake isomorphism relates the spherical Hecke algebra of a redu
ctive group $G$ over a local field $F$ to representations of the Langlands
dual group. \nWhen $F$ is of mixed characteristic $(0\,p)$ and the Hecke
algebra has characteristic prime to p\, the Satake isomorphism has been ge
ometrized by X. Zhu\, J. Yu\, Fargues-Scholze\, and Richarz-Scholbach usin
g techniques from p-adic geometry. \n\nIn this talk\, we consider the case
where the Hecke algebra has characteristic $p$. I will speak on my recent
joint work with Yujie Xu\, where we geometrize and obtain explicit formul
as for the mod p Satake isomorphism of Herzig and Henniart-Vignéras using
mod p étale sheaves on Witt vector affine flag varieties.\nOur methods i
nvolve the constant term functors inspired from the geometric Langlands pr
ogram\, especially the geometry of certain generalized Mirković-Vilonen c
ycles. The situation is quite different from l-adic sheaves ($l \\neq p$)
because only three of the six functors preserve constructible sheaves.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yujie Xu (MIT)
DTSTART:20230224T153000Z
DTEND:20230224T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/5
DESCRIPTION:Title: Hecke algebras for p-adic groups and the explicit Local Langlan
ds Correspondence for $G_2$\nby Yujie Xu (MIT) as part of Columbia - A
utomorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics
Hall.\n\nAbstract\nI will talk about my recent joint work with Aubert whe
re we prove the Local Langlands Conjecture for $G_2$ (explicitly). This us
es our earlier results on Hecke algebras attached to Bernstein components
of reductive $p$-adic groups\, as well as an expected property on cuspidal
support\, along with a list of characterizing properties. In particular\,
we obtain "mixed" L-packets containing F-singular supercuspidals and non-
supercuspidals.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier (McGill)
DTSTART:20230303T153000Z
DTEND:20230303T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/6
DESCRIPTION:Title: Counting non-tempered automorphic forms using endoscopy\nby
Mathilde Gerbelli-Gauthier (McGill) as part of Columbia - Automorphic For
ms and Arithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbst
ract\nHow many automorphic representations of level n have a specified loc
al factor at the infinite places? When this local factor is a discrete ser
ies representation\, this questions is asymptotically well-understood as n
grows. Non-tempered local factors\, on the other hand\, violate the Raman
ujan conjecture and should be very rare. We use the endoscopic classificat
ion for representations to quantify this rarity in the case of cohomologic
al representations of unitary groups\, and discuss some applications to th
e growth of cohomology of Shimura varieties.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Patrikis (Ohio State University)
DTSTART:20230310T153000Z
DTEND:20230310T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/7
DESCRIPTION:Title: Compatibility of canonical l-adic local systems on some Shimura
varieties of non-abelian type\nby Stefan Patrikis (Ohio State Univers
ity) as part of Columbia - Automorphic Forms and Arithmetic Seminar\n\nLec
ture held in 520 Mathematics Hall.\n\nAbstract\nLet $(G\, X)$ be a Shimura
datum\, and let $K$ be a compact open subgroup of $G(\\mathbb{A}_f)$. One
hopes that under mild assumptions on $G$ and $K$\, the points of the Shim
ura variety $Sh_K(G\, X)$ form a family of motives\; in abelian type this
is well-understood\, but in non-abelian type it is completely mysterious.
I will discuss joint work with Christian Klevdal showing that for non-abel
ian type Shimura varieties the points (over number fields\, say) at least
yield compatible systems of l-adic representations (to be precise\, after
projection to the adjoint group of G). These should be the l-adic realizat
ions of the conjectural motives.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasho Kaletha (University of Michigan)
DTSTART:20230324T143000Z
DTEND:20230324T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/8
DESCRIPTION:Title: Covers of reductive groups and functoriality\nby Tasho Kale
tha (University of Michigan) as part of Columbia - Automorphic Forms and A
rithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nTo
a connected reductive group $G$ over a local field $F$ we\ndefine a compa
ct topological group $\\tilde\\pi_1(G)$ and an extension\n$G(F)_\\infty$ o
f $G(F)$ by $\\tilde\\pi_1(G)$. From any character $x$ of\n$\\tilde\\pi_1(
G)$ of order n we obtain an n-fold cover $G(F)_x$ of the\ntopological grou
p $G(F)$. We also define an L-group for $G(F)_x$\, which is a\nusually non
-split extension of the Galois group by the dual group of $G$\,\nand deduc
e from the linear case a refined local Langlands correspondence\nbetween g
enuine representations of $G(F)_x$ and L-parameters valued in\nthis L-grou
p.\n\nThis construction is motivated by Langlands functoriality. We show t
hat\na subgroup of the L-group of $G$ of a certain kind naturally lead to
a\nsmaller quasi-split group $H$ and a double cover of $H(F)$. Genuine\nre
presentations of this double cover are expected to be in functorial\nrelat
ionship with representations of $G(F)$. We will present two concrete\nappl
ications of this\, one that gives a characterization of the local\nLanglan
ds correspondence for supercuspidal L-parameters when p is\nsufficiently l
arge\, and one to the theory of endoscopy.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregorio Baldi (IHES)
DTSTART:20230331T143000Z
DTEND:20230331T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/9
DESCRIPTION:Title: The Hodge locus\nby Gregorio Baldi (IHES) as part of Columb
ia - Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathe
matics Hall.\n\nAbstract\nI will report on a joint work with Klingler and
Ullmo. Given a polarizable variation of Hodge structures on a smooth compl
ex quasi-projective variety S (e.g. the one associated to a family of pure
motives over S)\, Cattani\, Deligne and Kaplan proved that its Hodge locu
s (the locus of closed points of S where exceptional Hodge tensors appear)
is a *countable* union of closed algebraic subvarieties of S. In this tal
k I will discuss when this Hodge locus is actually algebraic.\n\nThe first
part of the talk will introduce the Hodge theoretic formalism and highlig
ht differences and similarities with the world of Shimura varieties. If ti
me permits I will present some applications of such a viewpoint to either
the Lawrence-Venkatesh method or to the existence of genus four curves of
"Mumford's type".\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yihang Zhu (University of Maryland)
DTSTART:20230407T143000Z
DTEND:20230407T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/10
DESCRIPTION:Title: Zeta Functions of Shimura Varieties\nby Yihang Zhu (Univer
sity of Maryland) as part of Columbia - Automorphic Forms and Arithmetic S
eminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nI will first
recall the general expectations of Shimura\, Langlands\, and Kottwtiz on t
he shape of the zeta function of a Shimura variety\, or more generally its
étale cohomology. I will then report on some recent progress which parti
ally fulfills these expectations\, for Shimura varieties of unitary groups
and special orthogonal groups. Finally\, I will give a preview of some fo
reseeable developments in the near future.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haruzo Hida (UCLA)
DTSTART:20230414T143000Z
DTEND:20230414T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/11
DESCRIPTION:Title: Adjoint L-value formula and Tate conjecture\nby Haruzo Hid
a (UCLA) as part of Columbia - Automorphic Forms and Arithmetic Seminar\n\
nLecture held in 520 Mathematics Hall.\n\nAbstract\nFor a Hecke eigenform
$f$\, we state an adjoint L-value formula relative to each quaternion alg
ebra $D$ over $\\mathbb{Q}$ with discriminant $\\partial$ and reduce
d norm $N$.\nA key to prove the formula is the theta correspondence for t
he quadratic $\\mathbb{Q}$-space $(D\,N)$. Under the $R=\\mathbb{T}$-the
orem\, the $p$-part of the Bloch-Kato conjecture is known\; so\, the formu
la is\nan adjoint Selmer class number formula. We also describe how to re
late the formula to a consequence of the Tate conjecture for quaternionic
Shimura varieties.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Groechenig (University of Toronto)
DTSTART:20230421T143000Z
DTEND:20230421T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/12
DESCRIPTION:Title: p-adic points of stacks and applications\nby Michael Groec
henig (University of Toronto) as part of Columbia - Automorphic Forms and
Arithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nT
he first half of this talk will be devoted to describing the structural pr
operties of the set of local field valued points of a certain class of alg
ebraic stacks. I will then describe two applications in the second half\,
one joint with Wyss and Ziegler\, and the other one with Esnault. The firs
t application relates the p-adic volume of certain moduli spaces to BPS in
variants and the second application is an elementary proof of the existenc
e of a Fontaine-Laffaille structure for rigid flat connections.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Sangiovanni Vincentelli (Princeton University)
DTSTART:20230908T143000Z
DTEND:20230908T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/13
DESCRIPTION:Title: A Unified Framework for the Construction of Euler Systems\
nby Marco Sangiovanni Vincentelli (Princeton University) as part of Columb
ia - Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathe
matics Hall.\n\nAbstract\nEuler Systems (ESs) are collections of Galois co
homology classes that verify some co-restriction compatibilities. The key
feature of ESs is that they provide a way to bound Selmer groups\, thanks
to the machinery developed by Rubin\, inspired by earlier work of Thaine\,
Kolyvagin\, and Kato. In this talk\, I will present joint work with C. Sk
inner\, in which we develop a new method for constructing Euler Systems an
d apply it to build an ES for the Galois representation attached to the sy
mmetric square of an elliptic modular form. I will stress how this method
gives a unifying approach to constructing ESs\, in that it can be successf
ully applied to retrieve most classical ESs (the cyclotomic units ES\, the
elliptic units ES\, Kato's ES\, Lei-Loeffler-Zerbes ES for the Rankin-Sel
berg convolution of two elliptic modular forms...).\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tongmu He (Institute for Advanced Study)
DTSTART:20230915T143000Z
DTEND:20230915T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/14
DESCRIPTION:Title: Sen Operators and Lie Algebras arising from Galois Representat
ions over p-adic Varieties\nby Tongmu He (Institute for Advanced Study
) as part of Columbia - Automorphic Forms and Arithmetic Seminar\n\nLectur
e held in 520 Mathematics Hall.\n\nAbstract\nAny finite-dimensional $p$-ad
ic representation of the absolute Galois group of a $p$-adic local field w
ith imperfect residue field is characterized by its arithmetic and geometr
ic Sen operators defined by Sen and Brinon. We generalize their constructi
on to the fundamental group of a $p$-adic affine variety with a semi-stabl
e chart\, and prove that the module of Sen operators is canonically define
d\, independently of the choice of the chart. When the representation come
s from a $\\mathbb{Q}_p$-representation of the fundamental group\, we rela
te the infinitesimal action of inertia subgroups with Sen operators\, whic
h is a generalization of a result of Sen and Ohkubo. These Sen operators c
an be extended continuously to certain infinite-dimensional representation
s. As an application\, we prove that the geometric Sen operators annihilat
e locally analytic vectors\, generalizing a result of Pan.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Preston Wake (Michigan State University)
DTSTART:20230922T143000Z
DTEND:20230922T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/15
DESCRIPTION:Title: Rational torsion in modular Jacobians\nby Preston Wake (Mi
chigan State University) as part of Columbia - Automorphic Forms and Arith
metic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nFor a
prime number $N$\, Ogg's conjecture states that the torsion in the Jacobia
n of the modular curve $X_0(N)$ is generated by the cusps. Mazur proved Og
g's conjecture as one of the main theorems in his "Eisenstein ideal" paper
. I'll talk about a generalization of Ogg's conjecture for squarefree $N$
and a proof using the Eisenstein ideal. This is joint work with Ken Ribet.
\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Kramer-Miller (Lehigh University)
DTSTART:20230929T143000Z
DTEND:20230929T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/16
DESCRIPTION:Title: Geometric Iwasawa theory and p-adic families of motives over f
unction fields\nby Joe Kramer-Miller (Lehigh University) as part of Co
lumbia - Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 M
athematics Hall.\n\nAbstract\nGeometric Iwasawa theory studies the behavio
r of p-adic towers of curves. Classically\, the focus has been on the p-pa
rt of class groups\, mirroring Iwasawa theory for number fields. However\,
there are many interesting features of Iwasawa theory for curves that hav
e no number field analogy. The p-part of the class group is only a small p
art of the p-divisible group\, a much more intricate object with no number
field analogy. In this talk I will survey various results and conjectures
about the behavior of p-divisible groups along towers of curves. I will a
lso discuss what geometric Iwasawa theory for motives should look like and
explain new results in this direction.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daxin Xu (Morningside Center of Mathematics)
DTSTART:20231006T143000Z
DTEND:20231006T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/17
DESCRIPTION:Title: $p$-adic non-abelian Hodge theory over curves via moduli stack
s\nby Daxin Xu (Morningside Center of Mathematics) as part of Columbia
- Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathema
tics Hall.\n\nAbstract\nThe $p$-adic Simpson correspondence aims to establ
ish an equivalence between generalized representations and Higgs bundles o
ver a p-adic variety. In this talk\, we will explain how to upgrade such a
n equivalence to a twisted isomorphism of moduli stacks in the curve case.
This is based on a joint work in progress with Heuer.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Howe (University of Utah)
DTSTART:20231013T143000Z
DTEND:20231013T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/18
DESCRIPTION:Title: Differential topology for diamonds\nby Sean Howe (Universi
ty of Utah) as part of Columbia - Automorphic Forms and Arithmetic Seminar
\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nScholze's category
of diamonds gives a robust framework for p-adic geometry that bridges the
gap between Tate's classical theory of rigid analytic varieties and the mo
dern theory of perfectoid spaces. This flexibility is crucial\, for exampl
e\, if one wants to study Hodge-Tate period maps or other natural period m
aps that arise in the study of p-adic cohomology. However\, this flexibili
ty also comes at a price: many diamonds that appear naturally\, including
perfectoid spaces\, are of a fundamentally topological rather than analyti
c nature. This topological nature eliminates some basic tools that we migh
t expect to have available to us based on our experience in complex analyt
ic geometry: for example\, the existence of approximate p-power roots in a
perfectoid algebra guarantees that it will admit no continuous derivation
s and thus no tangent space via the classical Kahler theory\, and because
of this one cannot naively differentiate Hodge-Tate period maps. In this
talk\, we will explain why many diamonds are nonetheless secretly equipped
with the extra data of a Tangent Space. An important motivating example c
omes from the Fargues-Scholze Jacobian Criterion\, but we will go well bey
ond this case. In particular\, we construct Tangent Spaces for p-adic Lie
torsors over rigid analytic varieties and differentiate the Hodge-Tate per
iod map in the de Rham case. The key tools in the construction and computa
tions are the theory of coherent sheaves on the Fargues-Fontaine curve and
its relation to the theory of Banach-Colmez spaces due to le Bras\, the g
eometric Sen theory of Pan and Camargo\, and the p-adic Simpson/Riemann-Hi
lbert correspondence of Liu and Zhu. Motivated by the success of the Fargu
es-Scholze criterion\, it is natural to ask: after these Tangent Spaces an
d derivatives are constructed\, what can they tell us about the topologica
l properties of diamonds and morphisms between them? We will address this
by formulating two general conjectures in the spirit of a "differential to
pology for diamonds" and then conclude by exploring some examples.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziquan Yang (University of Wisconsin\, Madison)
DTSTART:20231020T143000Z
DTEND:20231020T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/19
DESCRIPTION:Title: A new case of BSD conjecture and deformation of line bundles\nby Ziquan Yang (University of Wisconsin\, Madison) as part of Columbia
- Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathema
tics Hall.\n\nAbstract\nI will talk about two results. The first is a new
case of the BSD conjecture\, contained in a joint work with Hamacher and Z
hao. Namely\, we prove the conjecture for elliptic curves of height 1 over
a global function field of genus 1 under a mild assumption. This is obtai
ned by specializing a more general theorem on the Tate conjecture. The key
geometric idea is an application of rigidity properties of the variations
of Hodge structures to study deformation of line bundles in positive and
mixed characteristic. Then I will talk about a generalization of such defo
rmation results recently obtained with Urbanik. Namely\, we show that for
a sufficiently big arithmetic family of smooth projective varieties\, ther
e is an open dense subscheme of the base over which all line bundles in po
sitive characteristics can be obtained by specializing those in characteri
stic 0.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Gros (Université de Rennes 1)
DTSTART:20231027T143000Z
DTEND:20231027T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/20
DESCRIPTION:Title: Functoriality of the p-adic Simpson correspondence by proper d
irect image\nby Michel Gros (Université de Rennes 1) as part of Colum
bia - Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Math
ematics Hall.\n\nAbstract\nFaltings has initiated in 2005 a p-adic analogu
e of the (complex) Simpson's correspondence whose construction has been ta
ken up by different\nauthors\, according to several approaches. After a pr
esentation of the one Ahmed Abbes and I have developed\, I will explain ho
w we establish the\nfunctoriality of the p-adic Simpson correspondence by
proper direct image\, which leads to a generalization of the relative Hodg
e-Tate spectral sequence.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsao-Hsien Chen (University of Minnesota\, Twin Cities)
DTSTART:20231103T143000Z
DTEND:20231103T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/21
DESCRIPTION:Title: On a vanishing conjecture appearing in the Braverman-Kazhdan p
rogram\nby Tsao-Hsien Chen (University of Minnesota\, Twin Cities) as
part of Columbia - Automorphic Forms and Arithmetic Seminar\n\nLecture hel
d in 520 Mathematics Hall.\n\nAbstract\nMotivated by the Langlands functor
iality conjecture and the work of Godement-Jacquet on automorphic L-functi
ons\, Braverman and Kazhdan introduced a non-linear version of the Fourie
r-Deligne transform on reductive groups over finite fields and they conje
cture that this new type of non-linear Fourier-transform satisfies several
remarkable properties similar to the linear case. It was shown that their
conjecture follows from a certain vanishing conjecture (a generalization
of the well-known acyclicity of Artin-Schreier sheaf on affine line to red
uctive groups). I will give an introduction to the work of Braverman and K
azhdan on non-linear version Fourier transforms and explain a proof of the
ir vanishing conjecture. Time permitting I will also discuss applications
to stable Bernstein center conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xinwen Zhu (Stanford University)
DTSTART:20231110T153000Z
DTEND:20231110T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/22
DESCRIPTION:Title: The unipotent categorical local Langlands correspondence\n
by Xinwen Zhu (Stanford University) as part of Columbia - Automorphic Form
s and Arithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstr
act\nI will discuss a conjectural categorical form of the local Langlands
correspondence for p-adic groups and establish the unipotent part of such
correspondence (for characteristic zero coefficient field).\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deepam Patel (Purdue University)
DTSTART:20231201T153000Z
DTEND:20231201T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/24
DESCRIPTION:Title: Motivic Properties of Generalized Alexander Modules\nby De
epam Patel (Purdue University) as part of Columbia - Automorphic Forms and
Arithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\n
This will be a survey of some joint work with Madhav Nori on the theory of
Gamma Motives. Classical Alexander modules are examples\, and we will exp
lain the analogs of the classical monodromy theorem and period isomorphism
s in this context. If time permits\, we will discuss some motivation comin
g from Beilinson's conjectures on special values of L-functions.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Xu (University of California\, Los Angeles)
DTSTART:20231208T153000Z
DTEND:20231208T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/25
DESCRIPTION:Title: Combinatorial Eisenstein cocycles\nby Peter Xu (University
of California\, Los Angeles) as part of Columbia - Automorphic Forms and
Arithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nW
e explain how one can define special cocycles for arithmetic groups via ex
plicit maps of complexes parameterizing linear algebraic data\, in a frame
work simultaneously generalizing work of Bergeron-Charollois-Garcia and Sh
arifi-Venkatesh. We explain some representation-theoretic aspects of these
cocycles\, and point towards some ongoing and future arithmetic applicati
ons.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (McGill University)
DTSTART:20240119T153000Z
DTEND:20240119T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/26
DESCRIPTION:Title: Kudla-Millson lift of toric cycles and diagonal restriction of
Hilbert modular forms\nby Romain Branchereau (McGill University) as p
art of Columbia - Automorphic Forms and Arithmetic Seminar\n\nLecture held
in 520 Mathematics Hall.\n\nAbstract\nLet $Y$ be a locally symmetric spac
e associated to an even dimensional rational quadratic space $(V\,Q)$ of s
ignature $(p\,q)$. The Kudla-Millson lift is a lift from the $q$-th homolo
gy of $Y$ to modular forms of weight $\\frac{p+q}{2}$.\n\nA natural way of
constructing a homology class is by embedding an algebraic torus in the o
rthogonal group of $V$. I will discuss the Kudla-Millson lift of such cycl
es\, and in particular show that it is the diagonal restriction of a Hilbe
rt modular form. In low rank\, one can recover a result of Darmon-Pozzi-Vo
nk and a trace identity due to Darmon-Harris-Rotger-Venkatesh.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyu Zhang (Stanford University)
DTSTART:20240126T153000Z
DTEND:20240126T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/27
DESCRIPTION:Title: Asai motives\, Asai L-functions and twisted arithmetic fundame
ntal lemmas\nby Zhiyu Zhang (Stanford University) as part of Columbia
- Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathemat
ics Hall.\n\nAbstract\nAsai L-functions for GLn are related to arithmetic
of Asai motives. The twisted Gan-Gross-Prasad (GGP) conjecture opens a way
of studying (a twist of) central Asai L-values via descents and period in
tegrals. Firstly\, I will prove new cases of twisted GGP conjecture (joint
work with Weixiao Lu and Danielle Wang)\, based on the relative trace for
mula approach in the thesis work of Wang. Secondly\, I will formulate an a
rithmetic twisted GGP conjecture on central derivatives. As a key ingredie
nt\, I will formulate and prove a twisted arithmetic fundamental lemma. Fo
r the proof\, I will introduce new special cycles and Rapoport-Zink spaces
related to mirabolic and parabolic groups.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Kountouridis (University of Chicago)
DTSTART:20240202T153000Z
DTEND:20240202T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/28
DESCRIPTION:Title: Monodromy of simple singularities and mixed-characteristic deg
enerations\nby Jason Kountouridis (University of Chicago) as part of C
olumbia - Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520
Mathematics Hall.\n\nAbstract\nGiven a smooth proper surface $X$ over a $p
$-adic field\, we study the monodromy action on its $\\ell$-adic cohomolog
y when $X$ degenerates to a surface in characteristic $p$ with simple sing
ularities\, otherwise known as rational double points. This class of singu
larities is a generalization of ordinary double points and has natural inc
arnations in arithmetic geometry and in Lie theory. We will use a mixed-ch
aracteristic version of the Grothendieck-Brieskorn resolution to investiga
te reduction properties of models of $X$\, and we will describe the associ
ated local monodromy via certain Springer representations attached to an a
ppropriate nearby cycles sheaf. Time permitting\, we may see some applicat
ions on derived equivalences of K3 surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Bellovin (University of Glasgow)
DTSTART:20240209T153000Z
DTEND:20240209T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/29
DESCRIPTION:Title: Modularity of trianguline Galois representations\nby Rebec
ca Bellovin (University of Glasgow) as part of Columbia - Automorphic Form
s and Arithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstr
act\nThe Fontaine-Mazur conjecture (proved by Kisin and Emerton) says that
(under certain technical hypotheses) a Galois representation $\\rho:\\mat
hrm{Gal}_{\\mathbb{Q}}\\rightarrow \\mathrm{GL}_{2}(\\overline{\\mathbb{Q}
}_{p})$ is modular if it is unramified outside finitely many places and de
Rham at $p$. I will talk about what this means\, and I will discuss an an
alogous modularity result for Galois representations $\\rho:\\mathrm{Gal}_
{\\mathbb{Q}}\\rightarrow \\mathrm{GL}_{2}(L)$ when $L$ is instead a non-a
rchimedean local field of characteristic $p$.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shizhang Li (Morningside Center of Mathematics)
DTSTART:20240216T153000Z
DTEND:20240216T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/30
DESCRIPTION:Title: General relative Poincare duality in nonarchimedean geometry\nby Shizhang Li (Morningside Center of Mathematics) as part of Columbia
- Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathema
tics Hall.\n\nAbstract\nIn this talk we'll explain a strategy to deduce ge
neral relative Poincare duality in p-adic geometry (previously conjectured
by Bhatt--Hansen) in a diagramatic manner\, whose special cases were pre
viously obtained respectively by Lan--Liu--Zhu\, Gabber--Zavyalov\, Mann.
This is a joint work in preparation with Emanuel Reinecke and Bogdan Zavya
lov.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Sage (University at Buffalo)
DTSTART:20240223T153000Z
DTEND:20240223T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/31
DESCRIPTION:Title: Meromorphic connections on the projective line with specified
local behavior\nby Daniel Sage (University at Buffalo) as part of Colu
mbia - Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mat
hematics Hall.\n\nAbstract\nA fundamental problem in the theory of meromor
phic connections on $\\mathbb{P}^1$ is to understand the space of such sys
tems with given local behavior. Here\, the local behavior of a connection
at a singular point means the "formal type" there--the isomorphism class o
f the induced formal connection. Given a collection of singular points and
corresponding formal types\, there are several natural questions one migh
t ask:\n\n1) Does there exist a connection with these formal types?\n\n2)
If such a connection exists\, is it unique up to isomorphism?\n\n3) Can on
e construct an explicit moduli space of such connections?\n\nClassically\,
these questions were studied under the assumption that all singularities
are regular singular (i.e. simple poles). For example\, in 2003\, Crawley-
Boevey solved the Deligne-Simpson problem for Fuchsian connections (a vari
ant of question 1) by reinterpreting the problem in terms of quiver variet
ies. Later\, mathematicians including Boalch\, Hiroe\, and Yamakawa invest
igated these questions when "unramified" irregular singularities are allow
ed. (Unramified means that the formal types can be expressed in upper tria
ngular form without introducing roots of the local parameter.) In recent y
ears\, there has been increasing interest in meromorphic connections (and
G-connections where G is a reductive group) with ramified singularities du
e to developments in the geometric Langlands program. In this talk\, I wil
l give an overview of recent progress on the ramified version of these pro
blems due to myself and various collaborators. Time permitting\, I will al
so talk about some related work of myself and Kamgarpour on differential G
alois groups of G-connections.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vaidehee Thatte (King's College London)
DTSTART:20240301T153000Z
DTEND:20240301T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/32
DESCRIPTION:Title: Understanding the Defect via Ramification Theory\nby Vaide
hee Thatte (King's College London) as part of Columbia - Automorphic Forms
and Arithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstra
ct\nClassical ramification theory deals with complete discrete valuation f
ields $k((X))$ with perfect residue fields $k$. Invariants such as the Swa
n conductor capture important information about extensions of these fields
. Many fascinating complications arise when we allow non-discrete valuatio
ns and imperfect residue fields $k$. Particularly in positive residue char
acteristic\, we encounter the mysterious phenomenon of the \\textit{defect
} (or ramification deficiency). The occurrence of a non-trivial defect is
one of the main obstacles to long-standing problems\, such as obtaining re
solution of singularities in positive characteristic.\n\nDegree $p$ extens
ions of valuation fields are building blocks of the general case. In this
talk\, we will present a generalization of ramification invariants for suc
h extensions and discuss how this leads to a better understanding of the d
efect. If time permits\, we will briefly discuss their connection with som
e recent work (joint with K. Kato) on upper ramification groups.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Miller (Rutgers University)
DTSTART:20240308T153000Z
DTEND:20240308T170000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/33
DESCRIPTION:Title: An update on the unitary dual problem\nby Stephen Miller (
Rutgers University) as part of Columbia - Automorphic Forms and Arithmetic
Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nI'll discus
s recent progress on the problem of classifying all unitary representation
s of a real reductive Lie group\, particularly the exceptional groups. Th
e talk will focus on applications of techniques/intuition from string theo
ry\, automorphic forms\, and intertwining operators (joint work with: Mich
ael Green and Pierre Vanhove\; Joseph Hundley\; and Jeff Adams\, Marc van
Leeuwen\, and David Vogan.)\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toby Gee (Imperial College London)
DTSTART:20240322T143000Z
DTEND:20240322T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/34
DESCRIPTION:Title: Modularity of genus 2 curves\nby Toby Gee (Imperial Colleg
e London) as part of Columbia - Automorphic Forms and Arithmetic Seminar\n
\nLecture held in 520 Mathematics Hall.\n\nAbstract\nI will give an overvi
ew (and some details) of my proof with George Boxer\, Frank Calegari\, and
Vincent Pilloni of the modularity of a positive proportion of curves over
Q of genus 2.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zheng Liu (University of California\, Santa Barbara)
DTSTART:20240329T143000Z
DTEND:20240329T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/35
DESCRIPTION:Title: p-adic L-functions for $\\mathrm{GSp}(4)\\times \\mathrm{GL}(2
)$\nby Zheng Liu (University of California\, Santa Barbara) as part of
Columbia - Automorphic Forms and Arithmetic Seminar\n\nLecture held in 52
0 Mathematics Hall.\n\nAbstract\nI'll explain a construction of p-adic L-f
unctions for $\\mathrm{GSp}(4)\\times \\mathrm{GL}(2)$ by using Furusawa's
integral and the proof of its interpolation formula. I'll describe how lo
cal functional equations are used to compute the zeta intgerals at p and h
ow the archimedean integrals are computed by using Yoshida lifts together
with p-adic Rankin-Selberg L-function and p-adic standard L-function of $\
\mathrm{Sp}(4)$. I'll also discuss its applications in studying congruence
s for Yoshida lifts.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Chan (University of Michigan)
DTSTART:20240405T143000Z
DTEND:20240405T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/36
DESCRIPTION:Title: Generic character sheaves on parahoric subgroups\nby Charl
otte Chan (University of Michigan) as part of Columbia - Automorphic Forms
and Arithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstra
ct\nLusztig's theory of character sheaves for connected\nreductive groups
is one of the most important developments in\nrepresentation theory in the
last few decades. I will give an overview\nof this theory and explain the
need\, from the perspective of the\nrepresentation theory of p-adic group
s\, of a theory of character\nsheaves on jet schemes. Recently\, R. Bezruk
avnikov and I have\ndeveloped the "generic" part of this desired theory. I
n the simplest\nnon trivial case\, this resolves a conjecture of Lusztig a
nd produces\nperverse sheaves on jet schemes compatible with parahoric\nDe
ligne--Lusztig induction. This talk is intended to describe in broad\nstro
kes what we know about these generic character sheaves\, especially\nwithi
n the context of the Langlands program.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Nagloo (University of Illinois Chicago)
DTSTART:20240412T143000Z
DTEND:20240412T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/37
DESCRIPTION:Title: Fuchsian automorphic functions and functional transcendence\nby Joel Nagloo (University of Illinois Chicago) as part of Columbia - A
utomorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics
Hall.\n\nAbstract\nOver the last decades\, following works around the Pil
a-Wilkie counting theorem in the context of o-minimality\, there has been
a surge in interest around functional transcendence results\, in part due
to their connection with special points conjectures. A prime example is th
e Ax-Lindemann-Weierstrass (ALW) Theorem and its role in his proof of the
André-Oort conjecture.\n\nIn this talk we will discuss how an entirely ne
w approach\, using the model theory of differential fields as well as othe
r differential tools\, can be used to prove functional transcendence resul
ts (including ALW) for Fuchsian automorphic functions and other covering m
aps. We will also explain how cases of the André-Pink conjecture can be o
btained using this new approach. This is joint work with D. Blazquez-Sanz\
, G. Casale and J. Freitag.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruofan Jiang (University of Wisconsin-Madison)
DTSTART:20240419T143000Z
DTEND:20240419T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/38
DESCRIPTION:Title: mod $p$ analogues of the Mumford-Tate and André-Oort conjectu
res\nby Ruofan Jiang (University of Wisconsin-Madison) as part of Colu
mbia - Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mat
hematics Hall.\n\nAbstract\nFor a smooth projective variety $Y$ over compl
ex numbers\, one has the notion of Hodge structure. Associated to the Hod
ge structure is a $\\mathbb{Q}$-reductive group $\\mathrm{MT}(Y)$\, called
the Mumford-Tate group. If the $Y$ is defined over a number field\, then
its $p$-adic étale cohomology is a Galois representation. There is a noti
on of $p$-adic étale monodromy group $G_p(Y)$. The Mumford-Tate conjectur
e claims that the base change to $\\mathbb{Q}_p$ of $\\mathrm{MT}(Y)$ has
the same neutral component as $G_p(Y)$. \n\nIn my talk\, I will formulate
a mod $p$ analogue of the conjecture and sketch a proof for orthogonal Shi
mura varieties. Important special cases of orthogonal Shimura varieties i
nclude moduli spaces of polarized Abelian and K3 surfaces. The result has
an interesting application to a mod $p$ analogue of the André-Oort conjec
ture: if a subvariety of a Shimura variety contains a Zariski dense collec
tion of special curves\, then the subvariety is "almost" a Shimura subvari
ety.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Le Hung (Northwestern University)
DTSTART:20240426T143000Z
DTEND:20240426T160000Z
DTSTAMP:20260404T100034Z
UID:AutoFoArith/39
DESCRIPTION:Title: Equivariant homology of affine Springer fibers and Breuil-Meza
rd cycles\nby Bao Le Hung (Northwestern University) as part of Columbi
a - Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathem
atics Hall.\n\nAbstract\nBreuil and Mezard conjecture that the Hilbert-Sam
uel multiplicities of deformation rings of rank $n$ representations of a $
p$-adic field $K$ with $p$-adic Hodge theoretic conditions are controlled
by certain decomposition numbers the group $\\mathrm{GL}_{n}(O_{K})$. More
recently\, as part of the categorical $p$-adic Langlands program\, Emerto
n and Gee gave a geometric interpretation of this phenomena as the (conjec
tural) existence of highly constrained Breuil-Mezard cycles in the Emerton
-Gee stack. I will explain how the equivariant homology of certain affine
Springer fibers gives a proposal for these cycles (at least in a generic r
egime)\, and how it elucidates their internal structures. This is based on
joint work with Tony Feng\, and work in progress with Zhongyipan Lin.\n
LOCATION:https://stable.researchseminars.org/talk/AutoFoArith/39/
END:VEVENT
END:VCALENDAR