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BEGIN:VEVENT
SUMMARY:A. Raghuram (Fordham University)
DTSTART:20230127T153000Z
DTEND:20230127T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/1
DESCRIPTION:Title: Special values of Rankin-Selberg L-functions over a totally imaginary
field\nby A. Raghuram (Fordham University) as part of Columbia - Autom
orphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics Hal
l.\n\nAbstract\nI will talk about my recent rationality results on the rat
ios of critical values for Rankin-Selberg L-functions for GL(n) x GL(m) ov
er a totally imaginary base field. In contrast to a totally real base fiel
d\, when the base field is totally imaginary\, some delicate signatures en
ter the reciprocity laws for these special values. These signatures depend
on whether or not the totally imaginary base field contains a CM subfield
. This is a generalization of my work with Günter Harder on rank-one Eise
nstein cohomology for GL(N)\, where N = n + m. The rationality result come
s from interpreting Langlands's constant term theorem in terms of an arith
metically defined intertwining operator between Hecke summands in the coho
mology of the Borel-Serre boundary of a locally symmetric space for GL(N).
The signatures arise from Galois action on certain local systems that int
ervene in boundary cohomology.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Weinstein (Boston University)
DTSTART:20230203T153000Z
DTEND:20230203T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/2
DESCRIPTION:Title: Higher Modularity of Elliptic Curves\nby J. Weinstein (Boston Univ
ersity) as part of Columbia - Automorphic Forms and Arithmetic Seminar\n\n
Lecture held in 520 Mathematics Hall.\n\nAbstract\nElliptic curves E over
the rational numbers are modular: this means there is a nonconstant map fr
om a modular curve to E. When instead the coefficients of E belong to a fu
nction field\, it still makes sense to talk about the modularity of E (and
this is known)\, but one can also extend the idea further and ask whether
E is 'r-modular' for r=2\,3.... To define this generalization\, the modul
ar curve gets replaced with Drinfeld's concept of a 'shtuka space'. The r-
modularity of E is predicted by Tate's conjecture. In joint work with Adam
Logan\, we give some classes of elliptic curves E which are 2- and 3-modu
lar.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. E. Rodríguez Camargo (Max Planck (Bonn))
DTSTART:20230210T153000Z
DTEND:20230210T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/3
DESCRIPTION:Title: Solid locally analytic representations\, D-modules and applications to
p-adic automorphic forms\nby J. E. Rodríguez Camargo (Max Planck (Bo
nn)) as part of Columbia - Automorphic Forms and Arithmetic Seminar\n\nLec
ture held in 520 Mathematics Hall.\n\nAbstract\nIn this talk I will presen
t a project in progress with Joaquín Rodrigues Jacinto concerning the stu
dy of locally analytic\nrepresentations of p-adic Lie groups and its relat
ion with p-adic D-modules of rigid spaces à la Ardakov. I will sketch\nho
w both theories are essentially two different looks of the same kind of ob
jects and how they can be interpreted in\nterms of sheaves in suitable sta
cks on analytic rings. If time permits I will mention two possible applica
tions in the\ncohomology of Shimura varieties.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Cass (University of Michigan)
DTSTART:20230217T153000Z
DTEND:20230217T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/4
DESCRIPTION:Title: Geometrization of the mod p Satake transform\nby Robert Cass (Univ
ersity of Michigan) as part of Columbia - Automorphic Forms and Arithmetic
Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nThe classic
al Satake isomorphism relates the spherical Hecke algebra of a reductive g
roup $G$ over a local field $F$ to representations of the Langlands dual g
roup. \nWhen $F$ is of mixed characteristic $(0\,p)$ and the Hecke algebra
has characteristic prime to p\, the Satake isomorphism has been geometriz
ed by X. Zhu\, J. Yu\, Fargues-Scholze\, and Richarz-Scholbach using techn
iques 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 formulas for
the mod p Satake isomorphism of Herzig and Henniart-Vignéras using mod p
étale sheaves on Witt vector affine flag varieties.\nOur methods involve
the constant term functors inspired from the geometric Langlands program\,
especially the geometry of certain generalized Mirković-Vilonen cycles.
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://researchseminars.org/talk/AutoFoArith/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yujie Xu (MIT)
DTSTART:20230224T153000Z
DTEND:20230224T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/5
DESCRIPTION:Title: Hecke algebras for p-adic groups and the explicit Local Langlands Corr
espondence for $G_2$\nby Yujie Xu (MIT) as part of Columbia - Automorp
hic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\
n\nAbstract\nI will talk about my recent joint work with Aubert where we p
rove the Local Langlands Conjecture for $G_2$ (explicitly). This uses our
earlier results on Hecke algebras attached to Bernstein components of redu
ctive $p$-adic groups\, as well as an expected property on cuspidal suppor
t\, along with a list of characterizing properties. In particular\, we obt
ain "mixed" L-packets containing F-singular supercuspidals and non-supercu
spidals.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier (McGill)
DTSTART:20230303T153000Z
DTEND:20230303T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/6
DESCRIPTION:Title: Counting non-tempered automorphic forms using endoscopy\nby Mathil
de Gerbelli-Gauthier (McGill) as part of Columbia - Automorphic Forms and
Arithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nH
ow many automorphic representations of level n have a specified local fact
or at the infinite places? When this local factor is a discrete series rep
resentation\, this questions is asymptotically well-understood as n grows.
Non-tempered local factors\, on the other hand\, violate the Ramanujan co
njecture and should be very rare. We use the endoscopic classification for
representations to quantify this rarity in the case of cohomological repr
esentations of unitary groups\, and discuss some applications to the growt
h of cohomology of Shimura varieties.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Patrikis (Ohio State University)
DTSTART:20230310T153000Z
DTEND:20230310T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/7
DESCRIPTION:Title: Compatibility of canonical l-adic local systems on some Shimura variet
ies of non-abelian type\nby Stefan Patrikis (Ohio State University) as
part of Columbia - Automorphic Forms and Arithmetic Seminar\n\nLecture he
ld 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 Shimura var
iety $Sh_K(G\, X)$ 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-abelian typ
e Shimura varieties the points (over number fields\, say) at least yield c
ompatible systems of l-adic representations (to be precise\, after project
ion to the adjoint group of G). These should be the l-adic realizations of
the conjectural motives.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasho Kaletha (University of Michigan)
DTSTART:20230324T143000Z
DTEND:20230324T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/8
DESCRIPTION:Title: Covers of reductive groups and functoriality\nby Tasho Kaletha (Un
iversity of Michigan) as part of Columbia - Automorphic Forms and Arithmet
ic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nTo a conn
ected reductive group $G$ over a local field $F$ we\ndefine a compact topo
logical group $\\tilde\\pi_1(G)$ and an extension\n$G(F)_\\infty$ of $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 group $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 deduce from
the linear case a refined local Langlands correspondence\nbetween genuine
representations of $G(F)_x$ and L-parameters valued in\nthis L-group.\n\nT
his construction is motivated by Langlands functoriality. We show that\na
subgroup of the L-group of $G$ of a certain kind naturally lead to a\nsmal
ler quasi-split group $H$ and a double cover of $H(F)$. Genuine\nrepresent
ations of this double cover are expected to be in functorial\nrelationship
with representations of $G(F)$. We will present two concrete\napplication
s of this\, one that gives a characterization of the local\nLanglands corr
espondence for supercuspidal L-parameters when p is\nsufficiently large\,
and one to the theory of endoscopy.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregorio Baldi (IHES)
DTSTART:20230331T143000Z
DTEND:20230331T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/9
DESCRIPTION:Title: The Hodge locus\nby Gregorio Baldi (IHES) as part of Columbia - Au
tomorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics
Hall.\n\nAbstract\nI will report on a joint work with Klingler and Ullmo.
Given a polarizable variation of Hodge structures on a smooth complex quas
i-projective variety S (e.g. the one associated to a family of pure motive
s over S)\, Cattani\, Deligne and Kaplan proved that its Hodge locus (the
locus of closed points of S where exceptional Hodge tensors appear) is a *
countable* union of closed algebraic subvarieties of S. In this talk I wil
l discuss when this Hodge locus is actually algebraic.\n\nThe first part o
f the talk will introduce the Hodge theoretic formalism and highlight diff
erences and similarities with the world of Shimura varieties. If time perm
its I will present some applications of such a viewpoint to either the Law
rence-Venkatesh method or to the existence of genus four curves of "Mumfor
d's type".\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yihang Zhu (University of Maryland)
DTSTART:20230407T143000Z
DTEND:20230407T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/10
DESCRIPTION:Title: Zeta Functions of Shimura Varieties\nby Yihang Zhu (University of
Maryland) as part of Columbia - Automorphic Forms and Arithmetic Seminar\
n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nI will first recall
the general expectations of Shimura\, Langlands\, and Kottwtiz on the shap
e of the zeta function of a Shimura variety\, or more generally its étale
cohomology. I will then report on some recent progress which partially fu
lfills these expectations\, for Shimura varieties of unitary groups and sp
ecial orthogonal groups. Finally\, I will give a preview of some foreseeab
le developments in the near future.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haruzo Hida (UCLA)
DTSTART:20230414T143000Z
DTEND:20230414T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/11
DESCRIPTION:Title: Adjoint L-value formula and Tate conjecture\nby Haruzo Hida (UCLA
) as part of Columbia - Automorphic Forms and Arithmetic Seminar\n\nLectur
e held in 520 Mathematics Hall.\n\nAbstract\nFor a Hecke eigenform $f$\,
we state an adjoint L-value formula relative to each quaternion algebra $
D$ over $\\mathbb{Q}$ with discriminant $\\partial$ and reduced norm
$N$.\nA key to prove the formula is the theta correspondence for the quad
ratic $\\mathbb{Q}$-space $(D\,N)$. Under the $R=\\mathbb{T}$-theorem\,
the $p$-part of the Bloch-Kato conjecture is known\; so\, the formula is\n
an adjoint Selmer class number formula. We also describe how to relate th
e formula to a consequence of the Tate conjecture for quaternionic Shimura
varieties.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Groechenig (University of Toronto)
DTSTART:20230421T143000Z
DTEND:20230421T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/12
DESCRIPTION:Title: p-adic points of stacks and applications\nby Michael Groechenig (
University of Toronto) as part of Columbia - Automorphic Forms and Arithme
tic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nThe firs
t half of this talk will be devoted to describing the structural propertie
s of the set of local field valued points of a certain class of algebraic
stacks. I will then describe two applications in the second half\, one joi
nt with Wyss and Ziegler\, and the other one with Esnault. The first appli
cation relates the p-adic volume of certain moduli spaces to BPS invariant
s and the second application is an elementary proof of the existence of a
Fontaine-Laffaille structure for rigid flat connections.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Sangiovanni Vincentelli (Princeton University)
DTSTART:20230908T143000Z
DTEND:20230908T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/13
DESCRIPTION:Title: A Unified Framework for the Construction of Euler Systems\nby Mar
co Sangiovanni Vincentelli (Princeton University) as part of Columbia - Au
tomorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics
Hall.\n\nAbstract\nEuler Systems (ESs) are collections of Galois cohomolog
y 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\, Kolyva
gin\, and Kato. In this talk\, I will present joint work with C. Skinner\,
in which we develop a new method for constructing Euler Systems and apply
it to build an ES for the Galois representation attached to the symmetric
square of an elliptic modular form. I will stress how this method gives a
unifying approach to constructing ESs\, in that it can be successfully ap
plied to retrieve most classical ESs (the cyclotomic units ES\, the ellipt
ic units ES\, Kato's ES\, Lei-Loeffler-Zerbes ES for the Rankin-Selberg co
nvolution of two elliptic modular forms...).\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tongmu He (Institute for Advanced Study)
DTSTART:20230915T143000Z
DTEND:20230915T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/14
DESCRIPTION:Title: Sen Operators and Lie Algebras arising from Galois Representations ov
er p-adic Varieties\nby Tongmu He (Institute for Advanced Study) as pa
rt of Columbia - Automorphic Forms and Arithmetic Seminar\n\nLecture held
in 520 Mathematics Hall.\n\nAbstract\nAny finite-dimensional $p$-adic repr
esentation of the absolute Galois group of a $p$-adic local field with imp
erfect residue field is characterized by its arithmetic and geometric Sen
operators defined by Sen and Brinon. We generalize their construction to t
he fundamental group of a $p$-adic affine variety with a semi-stable chart
\, and prove that the module of Sen operators is canonically defined\, ind
ependently of the choice of the chart. When the representation comes from
a $\\mathbb{Q}_p$-representation of the fundamental group\, we relate the
infinitesimal action of inertia subgroups with Sen operators\, which is a
generalization of a result of Sen and Ohkubo. These Sen operators can be e
xtended continuously to certain infinite-dimensional representations. As a
n application\, we prove that the geometric Sen operators annihilate local
ly analytic vectors\, generalizing a result of Pan.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Preston Wake (Michigan State University)
DTSTART:20230922T143000Z
DTEND:20230922T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/15
DESCRIPTION:Title: Rational torsion in modular Jacobians\nby Preston Wake (Michigan
State University) as part of Columbia - Automorphic Forms and Arithmetic S
eminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nFor a prime n
umber $N$\, Ogg's conjecture states that the torsion in the Jacobian of th
e modular curve $X_0(N)$ is generated by the cusps. Mazur proved Ogg's con
jecture 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 p
roof using the Eisenstein ideal. This is joint work with Ken Ribet.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Kramer-Miller (Lehigh University)
DTSTART:20230929T143000Z
DTEND:20230929T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/16
DESCRIPTION:Title: Geometric Iwasawa theory and p-adic families of motives over function
fields\nby Joe Kramer-Miller (Lehigh University) as part of Columbia
- Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathemat
ics Hall.\n\nAbstract\nGeometric Iwasawa theory studies the behavior of p-
adic towers of curves. Classically\, the focus has been on the p-part of c
lass groups\, mirroring Iwasawa theory for number fields. However\, there
are many interesting features of Iwasawa theory for curves that have no nu
mber field analogy. The p-part of the class group is only a small part 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 also dis
cuss what geometric Iwasawa theory for motives should look like and explai
n new results in this direction.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daxin Xu (Morningside Center of Mathematics)
DTSTART:20231006T143000Z
DTEND:20231006T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/17
DESCRIPTION:Title: $p$-adic non-abelian Hodge theory over curves via moduli stacks\n
by Daxin Xu (Morningside Center of Mathematics) as part of Columbia - Auto
morphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics Ha
ll.\n\nAbstract\nThe $p$-adic Simpson correspondence aims to establish an
equivalence between generalized representations and Higgs bundles over a p
-adic variety. In this talk\, we will explain how to upgrade such an equiv
alence to a twisted isomorphism of moduli stacks in the curve case. This i
s based on a joint work in progress with Heuer.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Howe (University of Utah)
DTSTART:20231013T143000Z
DTEND:20231013T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/18
DESCRIPTION:Title: Differential topology for diamonds\nby Sean Howe (University of U
tah) as part of Columbia - Automorphic Forms and Arithmetic Seminar\n\nLec
ture held in 520 Mathematics Hall.\n\nAbstract\nScholze's category of diam
onds gives a robust framework for p-adic geometry that bridges the gap bet
ween Tate's classical theory of rigid analytic varieties and the modern th
eory of perfectoid spaces. This flexibility is crucial\, for example\, if
one wants to study Hodge-Tate period maps or other natural period maps tha
t arise in the study of p-adic cohomology. However\, this flexibility also
comes at a price: many diamonds that appear naturally\, including perfect
oid spaces\, are of a fundamentally topological rather than analytic natur
e. This topological nature eliminates some basic tools that we might expec
t to have available to us based on our experience in complex analytic geom
etry: for example\, the existence of approximate p-power roots in a perfec
toid algebra guarantees that it will admit no continuous derivations and t
hus 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 t
he extra data of a Tangent Space. An important motivating example comes fr
om the Fargues-Scholze Jacobian Criterion\, but we will go well beyond thi
s case. In particular\, we construct Tangent Spaces for p-adic Lie torsors
over rigid analytic varieties and differentiate the Hodge-Tate period map
in the de Rham case. The key tools in the construction and computations a
re the theory of coherent sheaves on the Fargues-Fontaine curve and its re
lation to the theory of Banach-Colmez spaces due to le Bras\, the geometri
c Sen theory of Pan and Camargo\, and the p-adic Simpson/Riemann-Hilbert c
orrespondence of Liu and Zhu. Motivated by the success of the Fargues-Scho
lze criterion\, it is natural to ask: after these Tangent Spaces and deriv
atives are constructed\, what can they tell us about the topological prope
rties of diamonds and morphisms between them? We will address this by form
ulating two general conjectures in the spirit of a "differential topology
for diamonds" and then conclude by exploring some examples.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziquan Yang (University of Wisconsin\, Madison)
DTSTART:20231020T143000Z
DTEND:20231020T160000Z
DTSTAMP:20260422T225726Z
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 - Auto
morphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics Ha
ll.\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 Zhao. Na
mely\, we prove the conjecture for elliptic curves of height 1 over a glob
al function field of genus 1 under a mild assumption. This is obtained by
specializing a more general theorem on the Tate conjecture. The key geomet
ric idea is an application of rigidity properties of the variations of Hod
ge structures to study deformation of line bundles in positive and mixed c
haracteristic. Then I will talk about a generalization of such deformation
results recently obtained with Urbanik. Namely\, we show that for a suffi
ciently big arithmetic family of smooth projective varieties\, there is an
open dense subscheme of the base over which all line bundles in positive
characteristics can be obtained by specializing those in characteristic 0.
\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Gros (Université de Rennes 1)
DTSTART:20231027T143000Z
DTEND:20231027T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/20
DESCRIPTION:Title: Functoriality of the p-adic Simpson correspondence by proper direct i
mage\nby Michel Gros (Université de Rennes 1) as part of Columbia - A
utomorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics
Hall.\n\nAbstract\nFaltings has initiated in 2005 a p-adic analogue of th
e (complex) Simpson's correspondence whose construction has been taken up
by different\nauthors\, according to several approaches. After a presentat
ion of the one Ahmed Abbes and I have developed\, I will explain how we es
tablish the\nfunctoriality of the p-adic Simpson correspondence by proper
direct image\, which leads to a generalization of the relative Hodge-Tate
spectral sequence.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsao-Hsien Chen (University of Minnesota\, Twin Cities)
DTSTART:20231103T143000Z
DTEND:20231103T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/21
DESCRIPTION:Title: On a vanishing conjecture appearing in the Braverman-Kazhdan program<
/a>\nby Tsao-Hsien Chen (University of Minnesota\, Twin Cities) as part of
Columbia - Automorphic Forms and Arithmetic Seminar\n\nLecture held in 52
0 Mathematics Hall.\n\nAbstract\nMotivated by the Langlands functoriality
conjecture and the work of Godement-Jacquet on automorphic L-functions\, B
raverman and Kazhdan introduced a non-linear version of the Fourier-Delig
ne transform on reductive groups over finite fields and they conjecture t
hat this new type of non-linear Fourier-transform satisfies several remark
able properties similar to the linear case. It was shown that their conjec
ture follows from a certain vanishing conjecture (a generalization of the
well-known acyclicity of Artin-Schreier sheaf on affine line to reductive
groups). I will give an introduction to the work of Braverman and Kazhdan
on non-linear version Fourier transforms and explain a proof of their vani
shing conjecture. Time permitting I will also discuss applications to stab
le Bernstein center conjecture.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xinwen Zhu (Stanford University)
DTSTART:20231110T153000Z
DTEND:20231110T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/22
DESCRIPTION:Title: The unipotent categorical local Langlands correspondence\nby Xinw
en Zhu (Stanford University) as part of Columbia - Automorphic Forms and A
rithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nI
will discuss a conjectural categorical form of the local Langlands corresp
ondence for p-adic groups and establish the unipotent part of such corresp
ondence (for characteristic zero coefficient field).\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deepam Patel (Purdue University)
DTSTART:20231201T153000Z
DTEND:20231201T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/24
DESCRIPTION:Title: Motivic Properties of Generalized Alexander Modules\nby Deepam Pa
tel (Purdue University) as part of Columbia - Automorphic Forms and Arithm
etic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nThis wi
ll be a survey of some joint work with Madhav Nori on the theory of Gamma
Motives. Classical Alexander modules are examples\, and we will explain th
e analogs of the classical monodromy theorem and period isomorphisms in th
is context. If time permits\, we will discuss some motivation coming from
Beilinson's conjectures on special values of L-functions.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Xu (University of California\, Los Angeles)
DTSTART:20231208T153000Z
DTEND:20231208T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/25
DESCRIPTION:Title: Combinatorial Eisenstein cocycles\nby Peter Xu (University of Cal
ifornia\, Los Angeles) as part of Columbia - Automorphic Forms and Arithme
tic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nWe expla
in how one can define special cocycles for arithmetic groups via explicit
maps of complexes parameterizing linear algebraic data\, in a framework si
multaneously generalizing work of Bergeron-Charollois-Garcia and Sharifi-V
enkatesh. We explain some representation-theoretic aspects of these cocycl
es\, and point towards some ongoing and future arithmetic applications.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (McGill University)
DTSTART:20240119T153000Z
DTEND:20240119T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/26
DESCRIPTION:Title: Kudla-Millson lift of toric cycles and diagonal restriction of Hilber
t modular forms\nby Romain Branchereau (McGill University) as part of
Columbia - Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520
Mathematics Hall.\n\nAbstract\nLet $Y$ be a locally symmetric space assoc
iated to an even dimensional rational quadratic space $(V\,Q)$ of signatur
e $(p\,q)$. The Kudla-Millson lift is a lift from the $q$-th homology of $
Y$ to modular forms of weight $\\frac{p+q}{2}$.\n\nA natural way of constr
ucting a homology class is by embedding an algebraic torus in the orthogon
al group of $V$. I will discuss the Kudla-Millson lift of such cycles\, an
d in particular show that it is the diagonal restriction of a Hilbert modu
lar form. In low rank\, one can recover a result of Darmon-Pozzi-Vonk and
a trace identity due to Darmon-Harris-Rotger-Venkatesh.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyu Zhang (Stanford University)
DTSTART:20240126T153000Z
DTEND:20240126T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/27
DESCRIPTION:Title: Asai motives\, Asai L-functions and twisted arithmetic fundamental le
mmas\nby Zhiyu Zhang (Stanford University) as part of Columbia - Autom
orphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics Hal
l.\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 stu
dying (a twist of) central Asai L-values via descents and period integrals
. Firstly\, I will prove new cases of twisted GGP conjecture (joint work w
ith Weixiao Lu and Danielle Wang)\, based on the relative trace formula ap
proach in the thesis work of Wang. Secondly\, I will formulate an arithmet
ic twisted GGP conjecture on central derivatives. As a key ingredient\, I
will formulate and prove a twisted arithmetic fundamental lemma. For the p
roof\, I will introduce new special cycles and Rapoport-Zink spaces relate
d to mirabolic and parabolic groups.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Kountouridis (University of Chicago)
DTSTART:20240202T153000Z
DTEND:20240202T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/28
DESCRIPTION:Title: Monodromy of simple singularities and mixed-characteristic degenerati
ons\nby Jason Kountouridis (University of Chicago) as part of Columbia
- Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathema
tics Hall.\n\nAbstract\nGiven a smooth proper surface $X$ over a $p$-adic
field\, we study the monodromy action on its $\\ell$-adic cohomology when
$X$ degenerates to a surface in characteristic $p$ with simple singulariti
es\, otherwise known as rational double points. This class of singularitie
s is a generalization of ordinary double points and has natural incarnatio
ns in arithmetic geometry and in Lie theory. We will use a mixed-character
istic version of the Grothendieck-Brieskorn resolution to investigate redu
ction properties of models of $X$\, and we will describe the associated lo
cal monodromy via certain Springer representations attached to an appropri
ate nearby cycles sheaf. Time permitting\, we may see some applications on
derived equivalences of K3 surfaces.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Bellovin (University of Glasgow)
DTSTART:20240209T153000Z
DTEND:20240209T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/29
DESCRIPTION:Title: Modularity of trianguline Galois representations\nby Rebecca Bell
ovin (University of Glasgow) as part of Columbia - Automorphic Forms and A
rithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nTh
e Fontaine-Mazur conjecture (proved by Kisin and Emerton) says that (under
certain technical hypotheses) a Galois representation $\\rho:\\mathrm{Gal
}_{\\mathbb{Q}}\\rightarrow \\mathrm{GL}_{2}(\\overline{\\mathbb{Q}}_{p})$
is modular if it is unramified outside finitely many places and de Rham a
t $p$. I will talk about what this means\, and I will discuss an analogous
modularity result for Galois representations $\\rho:\\mathrm{Gal}_{\\math
bb{Q}}\\rightarrow \\mathrm{GL}_{2}(L)$ when $L$ is instead a non-archimed
ean local field of characteristic $p$.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shizhang Li (Morningside Center of Mathematics)
DTSTART:20240216T153000Z
DTEND:20240216T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/30
DESCRIPTION:Title: General relative Poincare duality in nonarchimedean geometry\nby
Shizhang Li (Morningside Center of Mathematics) as part of Columbia - Auto
morphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics Ha
ll.\n\nAbstract\nIn this talk we'll explain a strategy to deduce general r
elative Poincare duality in p-adic geometry (previously conjectured by Bha
tt--Hansen) in a diagramatic manner\, whose special cases were previously
obtained respectively by Lan--Liu--Zhu\, Gabber--Zavyalov\, Mann. This is
a joint work in preparation with Emanuel Reinecke and Bogdan Zavyalov.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Sage (University at Buffalo)
DTSTART:20240223T153000Z
DTEND:20240223T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/31
DESCRIPTION:Title: Meromorphic connections on the projective line with specified local b
ehavior\nby Daniel Sage (University at Buffalo) as part of Columbia -
Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematic
s Hall.\n\nAbstract\nA fundamental problem in the theory of meromorphic co
nnections on $\\mathbb{P}^1$ is to understand the space of such systems wi
th given local behavior. Here\, the local behavior of a connection at a si
ngular point means the "formal type" there--the isomorphism class of the i
nduced formal connection. Given a collection of singular points and corres
ponding formal types\, there are several natural questions one might 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 one const
ruct an explicit moduli space of such connections?\n\nClassically\, these
questions were studied under the assumption that all singularities are reg
ular singular (i.e. simple poles). For example\, in 2003\, Crawley-Boevey
solved the Deligne-Simpson problem for Fuchsian connections (a variant of
question 1) by reinterpreting the problem in terms of quiver varieties. La
ter\, mathematicians including Boalch\, Hiroe\, and Yamakawa investigated
these questions when "unramified" irregular singularities are allowed. (Un
ramified means that the formal types can be expressed in upper triangular
form without introducing roots of the local parameter.) In recent years\,
there has been increasing interest in meromorphic connections (and G-conne
ctions where G is a reductive group) with ramified singularities due to de
velopments in the geometric Langlands program. In this talk\, I will give
an overview of recent progress on the ramified version of these problems d
ue to myself and various collaborators. Time permitting\, I will also talk
about some related work of myself and Kamgarpour on differential Galois g
roups of G-connections.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vaidehee Thatte (King's College London)
DTSTART:20240301T153000Z
DTEND:20240301T170000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/32
DESCRIPTION:Title: Understanding the Defect via Ramification Theory\nby Vaidehee Tha
tte (King's College London) as part of Columbia - Automorphic Forms and Ar
ithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nCla
ssical ramification theory deals with complete discrete valuation fields $
k((X))$ with perfect residue fields $k$. Invariants such as the Swan condu
ctor capture important information about extensions of these fields. Many
fascinating complications arise when we allow non-discrete valuations and
imperfect residue fields $k$. Particularly in positive residue characteris
tic\, we encounter the mysterious phenomenon of the \\textit{defect} (or r
amification deficiency). The occurrence of a non-trivial defect is one of
the main obstacles to long-standing problems\, such as obtaining resolutio
n of singularities in positive characteristic.\n\nDegree $p$ extensions of
valuation fields are building blocks of the general case. In this talk\,
we will present a generalization of ramification invariants for such exten
sions and discuss how this leads to a better understanding of the defect.
If time permits\, we will briefly discuss their connection with some recen
t work (joint with K. Kato) on upper ramification groups.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Miller (Rutgers University)
DTSTART:20240308T153000Z
DTEND:20240308T170000Z
DTSTAMP:20260422T225726Z
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 Semina
r\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nI'll discuss recen
t progress on the problem of classifying all unitary representations of a
real reductive Lie group\, particularly the exceptional groups. The talk
will focus on applications of techniques/intuition from string theory\, au
tomorphic forms\, and intertwining operators (joint work with: Michael Gre
en and Pierre Vanhove\; Joseph Hundley\; and Jeff Adams\, Marc van Leeuwen
\, and David Vogan.)\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toby Gee (Imperial College London)
DTSTART:20240322T143000Z
DTEND:20240322T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/34
DESCRIPTION:Title: Modularity of genus 2 curves\nby Toby Gee (Imperial College Londo
n) as part of Columbia - Automorphic Forms and Arithmetic Seminar\n\nLectu
re held in 520 Mathematics Hall.\n\nAbstract\nI will give an overview (and
some details) of my proof with George Boxer\, Frank Calegari\, and Vincen
t Pilloni of the modularity of a positive proportion of curves over Q of g
enus 2.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zheng Liu (University of California\, Santa Barbara)
DTSTART:20240329T143000Z
DTEND:20240329T160000Z
DTSTAMP:20260422T225726Z
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 Columb
ia - Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathe
matics Hall.\n\nAbstract\nI'll explain a construction of p-adic L-function
s for $\\mathrm{GSp}(4)\\times \\mathrm{GL}(2)$ by using Furusawa's integr
al and the proof of its interpolation formula. I'll describe how local fun
ctional equations are used to compute the zeta intgerals at p and how 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 congruences for Y
oshida lifts.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Chan (University of Michigan)
DTSTART:20240405T143000Z
DTEND:20240405T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/36
DESCRIPTION:Title: Generic character sheaves on parahoric subgroups\nby Charlotte Ch
an (University of Michigan) as part of Columbia - Automorphic Forms and Ar
ithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\n\nAbstract\nLus
ztig's theory of character sheaves for connected\nreductive groups is one
of the most important developments in\nrepresentation theory in the last f
ew decades. I will give an overview\nof this theory and explain the need\,
from the perspective of the\nrepresentation theory of p-adic groups\, of
a theory of character\nsheaves on jet schemes. Recently\, R. Bezrukavnikov
and I have\ndeveloped the "generic" part of this desired theory. In the s
implest\nnon trivial case\, this resolves a conjecture of Lusztig and prod
uces\nperverse sheaves on jet schemes compatible with parahoric\nDeligne--
Lusztig induction. This talk is intended to describe in broad\nstrokes wha
t we know about these generic character sheaves\, especially\nwithin the c
ontext of the Langlands program.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Nagloo (University of Illinois Chicago)
DTSTART:20240412T143000Z
DTEND:20240412T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/37
DESCRIPTION:Title: Fuchsian automorphic functions and functional transcendence\nby J
oel Nagloo (University of Illinois Chicago) as part of Columbia - Automorp
hic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics Hall.\
n\nAbstract\nOver the last decades\, following works around the Pila-Wilki
e counting theorem in the context of o-minimality\, there has been a surge
in interest around functional transcendence results\, in part due to thei
r connection with special points conjectures. A prime example is the Ax-Li
ndemann-Weierstrass (ALW) Theorem and its role in his proof of the André-
Oort conjecture.\n\nIn this talk we will discuss how an entirely new appro
ach\, using the model theory of differential fields as well as other diffe
rential tools\, can be used to prove functional transcendence results (inc
luding ALW) for Fuchsian automorphic functions and other covering maps. We
will also explain how cases of the André-Pink conjecture can be obtained
using this new approach. This is joint work with D. Blazquez-Sanz\, G. Ca
sale and J. Freitag.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruofan Jiang (University of Wisconsin-Madison)
DTSTART:20240419T143000Z
DTEND:20240419T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/38
DESCRIPTION:Title: mod $p$ analogues of the Mumford-Tate and André-Oort conjectures
\nby Ruofan Jiang (University of Wisconsin-Madison) as part of Columbia -
Automorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematic
s Hall.\n\nAbstract\nFor a smooth projective variety $Y$ over complex numb
ers\, one has the notion of Hodge structure. Associated to the Hodge stru
cture is a $\\mathbb{Q}$-reductive group $\\mathrm{MT}(Y)$\, called the Mu
mford-Tate group. If the $Y$ is defined over a number field\, then its $p$
-adic étale cohomology is a Galois representation. There is a notion of $
p$-adic étale monodromy group $G_p(Y)$. The Mumford-Tate conjecture claim
s that the base change to $\\mathbb{Q}_p$ of $\\mathrm{MT}(Y)$ has the sam
e 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 Shimura va
rieties. Important special cases of orthogonal Shimura varieties include
moduli spaces of polarized Abelian and K3 surfaces. The result has an inte
resting application to a mod $p$ analogue of the André-Oort conjecture: i
f a subvariety of a Shimura variety contains a Zariski dense collection of
special curves\, then the subvariety is "almost" a Shimura subvariety.\n
LOCATION:https://researchseminars.org/talk/AutoFoArith/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Le Hung (Northwestern University)
DTSTART:20240426T143000Z
DTEND:20240426T160000Z
DTSTAMP:20260422T225726Z
UID:AutoFoArith/39
DESCRIPTION:Title: Equivariant homology of affine Springer fibers and Breuil-Mezard cycl
es\nby Bao Le Hung (Northwestern University) as part of Columbia - Aut
omorphic Forms and Arithmetic Seminar\n\nLecture held in 520 Mathematics H
all.\n\nAbstract\nBreuil and Mezard conjecture that the Hilbert-Samuel mul
tiplicities of deformation rings of rank $n$ representations of a $p$-adic
field $K$ with $p$-adic Hodge theoretic conditions are controlled by cert
ain decomposition numbers the group $\\mathrm{GL}_{n}(O_{K})$. More recent
ly\, as part of the categorical $p$-adic Langlands program\, Emerton and G
ee gave a geometric interpretation of this phenomena as the (conjectural)
existence of highly constrained Breuil-Mezard cycles in the Emerton-Gee st
ack. I will explain how the equivariant homology of certain affine Springe
r fibers gives a proposal for these cycles (at least in a generic regime)\
, 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://researchseminars.org/talk/AutoFoArith/39/
END:VEVENT
END:VCALENDAR