BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Tobias Berger (The University of Sheffield)
DTSTART:20240116T200000Z
DTEND:20240116T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/1
DESCRIPTION:Title: Pseudomodularity of residually reducible Galois repr
esentations\nby Tobias Berger (The University of Sheffield) as part of
The Graduate Center Arithmetic Geometry Seminar\n\nLecture held in The Gr
aduate Center.\n\nAbstract\nAfter a survey of previous work I will present
new results on pseudomodularity of residually reducible Galois representa
tions with 3 residual pieces. I will discuss applications to proving modul
arity of Galois representations arising from abelian surfaces and Picard c
urves. This is joint work with Krzysztof Klosin (CUNY).\n\nPasscode for Zo
om link: 169\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/1
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dorota Blinkiewicz (University of A. Mickiewicz)
DTSTART:20240507T190000Z
DTEND:20240507T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/8
DESCRIPTION:Title: Linear relations in semiabelian varieties\nby Do
rota Blinkiewicz (University of A. Mickiewicz) as part of The Graduate Cen
ter Arithmetic Geometry Seminar\n\nLecture held in The Graduate Center.\n\
nAbstract\nIn the lecture I will discuss results concerning the detecting
linear dependence problem\, with torsion ambiguity\, for a family of semia
belian varieties G over a number field F and for any finitely generated su
bgroup H of a Mordell-Weil group G(F). For more than 40 years\, this probl
em has been investigated for abelian varieties and tori by numerous author
s. In the lecture I will show results concerning the problem for semiabeli
an varieties and I will also show counterexamples leading to families of w
ild 1-motives.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/8
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kalyani Kansal (Institute for Advanced Study)
DTSTART:20240206T200000Z
DTEND:20240206T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/17
DESCRIPTION:Title: Irregular loci in the Emerton-Gee stack for GL2
\nby Kalyani Kansal (Institute for Advanced Study) as part of The Graduate
Center Arithmetic Geometry Seminar\n\nLecture held in The Graduate Center
.\n\nAbstract\nLet K be a finite extension of $\\mathbb Q_p$. The Emerton-
Gee stack for GL2 is a stack of etale (phi\, Gamma)-modules of rank two. I
ts reduced part\, X\, is an algebraic stack of finite type over a finite f
ield\, and can be viewed as a moduli stack of two dimensional mod p repres
entations of the absolute Galois group of K. By the work of Caraiani\, Eme
rton\, Gee and Savitt\, it is known that in most cases\, the locus of mod
p representations admitting crystalline lifts with specified regular Hodge
-Tate weights is an irreducible component of X. Their work relied on a det
ailed study of a closely related stack of etale phi-modules which admits a
map from a stack of Breuil-Kisin modules with descent data. In our work\,
we assume K is unramfied and further study this map with a view to studyi
ng the loci of mod p representations admitting crystalline lifts with smal
l\, irregular Hodge-Tate weights. We identify these loci as images of cert
ain irreducible components of the stack of Breuil-Kisin modules and obtain
several inclusions of the non-regular loci into the irreducible component
s of X. This is joint work with Rebecca Bellovin\, Neelima Borade\, Anton
Hilado\, Heejong Lee\, Brandon Levin\, David Savitt and Hanneke Wiersema.\
n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/1
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Brown (Occidental College)
DTSTART:20240220T200000Z
DTEND:20240220T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/18
DESCRIPTION:Title: Coding theory\, lattices\, and theta functions\
nby Jim Brown (Occidental College) as part of The Graduate Center Arithmet
ic Geometry Seminar\n\nLecture held in The Graduate Center.\n\nAbstract\nC
oding theory is the branch of mathematics that strives to find efficient w
ays to transmit information reliably. In particular\, when information is
transmitted over noisy channels there will inevitably be errors during th
e transmission. We wish to employ methods to detect these errors\, and ul
timately\, correct the errors. In fact\, there is a great deal of algebra
ic geometry and number theory that goes into this endeavor. In this talk
I will discuss some work with undergraduate research students showing how
to construct lattices in number fields from codes\, the theta series asso
ciated to the lattices\, and then some interesting results on those theta
series.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/1
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ila Varma (University of Toronto)
DTSTART:20240227T200000Z
DTEND:20240227T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/19
DESCRIPTION:Title: Counting number fields and predicting asymptotics\nby Ila Varma (University of Toronto) as part of The Graduate Center Ar
ithmetic Geometry Seminar\n\nLecture held in The Graduate Center.\n\nAbstr
act\nA guiding question in number theory\, specifically in arithmetic stat
istics\, is: Fix a degree n and a Galois group G in S_n. How does the coun
t of number fields of degree n whose normal closure has Galois group G gro
w as their discriminants tend to infinity? In this talk\, we will discuss
the history of this question and take a closer look at the story in the ca
se that n = 4\, i.e. the counts of quartic fields.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/1
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Chen (Columbia University)
DTSTART:20240305T200000Z
DTEND:20240305T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/20
DESCRIPTION:Title: Low degree maps and points\nby Nathan Chen (Col
umbia University) as part of The Graduate Center Arithmetic Geometry Semin
ar\n\nLecture held in The Graduate Center.\n\nAbstract\nTwo powerful tools
for studying degree d > 1 points on algebraic curves over Q are the Abel-
Jacobi map and Falting's theorem. However\, for higher dimensional varieti
es there is very little that has been explored. This talk will focus on me
asures of irrationality for algebraic surfaces\, which are geometric analo
gues of having many degree d points. We will then present some geometric c
onstructions that give rise to many degree d points.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/2
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Emory (Oklahoma State University)
DTSTART:20240402T190000Z
DTEND:20240402T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/21
DESCRIPTION:Title: On determining Sato-Tate groups\nby Melissa Emo
ry (Oklahoma State University) as part of The Graduate Center Arithmetic G
eometry Seminar\n\nLecture held in The Graduate Center.\n\nAbstract\nThe o
riginal Sato-Tate conjecture was posed around 1960 by Mikio Sato and John
Tate (independently) and is a statistical conjecture regarding the distrib
ution of the normalized traces of Frobenius on an elliptic curve. In 2012\
, the conjecture was generalized to higher genus curves by Serre. In recen
t years classifications of Sato-Tate groups in dimensions 1\, 2\, and 3 ha
ve been given\, but there are obstacles to providing classifications in hi
gher dimension. In this talk\, I will describe work to prove nondegeneracy
and determine Sato-Tate groups for two families of Jacobian varieties. T
his work is joint with Heidi Goodson.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/2
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wanlin Li (Washington University in St. Louis)
DTSTART:20240416T190000Z
DTEND:20240416T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/22
DESCRIPTION:Title: The nontriviality of the Ceresa cycle\nby Wanli
n Li (Washington University in St. Louis) as part of The Graduate Center A
rithmetic Geometry Seminar\n\nLecture held in The Graduate Center.\n\nAbst
ract\nThe Ceresa cycle is an algebraic 1-cycle in the Jacobian of a smooth
algebraic curve with a chosen base point. It is algebraically trivial for
a hyperelliptic curve and non-trivial for a very general complex curve of
genus $\\ge 3$. Given a pointed algebraic curve\, there is no general met
hod to determine whether the Ceresa cycle associated to it is rationally o
r algebraically trivial. In this talk\, I will discuss some methods and to
ols to study this problem.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/2
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Dillery (University of Maryland)
DTSTART:20240319T190000Z
DTEND:20240319T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/23
DESCRIPTION:Title: Comparing local Langlands correspondences\nby P
eter Dillery (University of Maryland) as part of The Graduate Center Arith
metic Geometry Seminar\n\nLecture held in The Graduate Center.\n\nAbstract
\nBroadly speaking\, for G a connected reductive group over a local field
F\, the Langlands program is the endeavor of relating Galois representatio
ns (more precisely\, "L-parameters"---certain homomorphisms from the Weil-
Deligne group of F to the dual group of G) to admissible smooth representa
tions of G(F). There is conjectured to be a finite-to-one map from irreduc
ible smooth representations of G(F) to L-parameters\, and there are many d
ifferent approaches to parametrizing the fibers of such a map. \n\nThe goa
l of this talk is to explain some of these approaches\; a special focus w
ill be placed on the so-called "isocrystal" and "rigid" local Langlands co
rrespondences. The former is best suited for building on the recent breakt
hroughs of Fargues-Scholze\, while the latter is the broadest and is well-
suited to endoscopy (a version of functoriality). We will discuss a proof
of the equivalence of these two approaches\, initiated by Kaletha for p-ad
ic fields and extended to arbitrary nonarchimedean local fields in my rece
nt work.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/2
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Schwein (University of Bonn)
DTSTART:20240514T190000Z
DTEND:20240514T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/24
DESCRIPTION:Title: Tame supercuspidals at bad primes\nby David Sch
wein (University of Bonn) as part of The Graduate Center Arithmetic Geomet
ry Seminar\n\nLecture held in The Graduate Center - room 4433.\n\nAbstract
\nSupercuspidal representations are the elementary particles in the repres
entation theory of reductive p-adic groups and play an important role in n
umber theory as local factors of cuspidal automorphic representations. Con
structing such representations explicitly\, via (compact) induction\, is a
longstanding open problem which has been solved for large p but not in ge
neral. I'll discuss work in progress joint with Jessica Fintzen towards co
nstructing some of these missing supercuspidals when p is (very!) small.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/2
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anwesh Ray (Chennai Mathematical Institute in India)
DTSTART:20241008T190000Z
DTEND:20241008T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/28
DESCRIPTION:Title: Iwasawa theory and connections with arithmetic stat
istics and Hilbert's tenth problem\nby Anwesh Ray (Chennai Mathematica
l Institute in India) as part of The Graduate Center Arithmetic Geometry S
eminar\n\nLecture held in The Graduate Center - room 4433.\n\nAbstract\nIw
asawa theory\, originally developed from the study of L-functions and the
structure of class groups\, has become a cornerstone of modern number theo
ry. In this talk\, I will focus on the Iwasawa theory of elliptic curves\,
delving into some of the profound conjectures that shape the field. By ap
plying techniques from the arithmetic statistics of elliptic curves\, we c
an investigate these conjectures "on average." The statistical study of el
liptic curves reveals patterns and behaviors in large families\, offering
new insights that may lead to partial resolutions or alternative perspecti
ves on long-standing open problems. If time allows\, I will also explore h
ow these investigations contribute to broader developments in arithmetic g
eometry and their implications for Hilbert's Tenth Problem over number rin
gs\, a fundamental problem at the intersection of number theory and logic.
\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/2
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Kozioł (Baruch College and CUNY Graduate Center)
DTSTART:20241029T190000Z
DTEND:20241029T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/29
DESCRIPTION:Title: A gentle introduction to the mod p Local Langlands
Program\nby Karol Kozioł (Baruch College and CUNY Graduate Center) as
part of The Graduate Center Arithmetic Geometry Seminar\n\nLecture held i
n The Graduate Center - room 9116.\n\nAbstract\nI'll give some motivation
and background on the origins of the mod p version of the local Langlands
conjectures. In particular\, I'll try to point out connections between c
ongruences between modular forms\, Serre's philosophy of weights\, and coh
omology of modular curves.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/2
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deewang Bhamidipati (University of California\, Santa Cruz)
DTSTART:20241105T200000Z
DTEND:20241105T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/30
DESCRIPTION:Title: q-Frobenius Trace Distributions of Abelian Varietie
s\nby Deewang Bhamidipati (University of California\, Santa Cruz) as p
art of The Graduate Center Arithmetic Geometry Seminar\n\nLecture held in
The Graduate Center - room 9116.\n\nAbstract\nElliptic curves over a finit
e field \\(\\mathbf{F}_q\\) famously come in two flavours: ordinary and su
persingular. As q varies over powers of a fixed prime p\, the eigenvalues
of Frobenius of an ordinary elliptic curve are uniformly distributed on a
circle\, while those of a supersingular elliptic curve are supported in fi
nitely many places. In joint work with Santiago Arango-Piñeros and Soumya
Sankar\, we study this phenomenon for abelian varieties in higher dimensi
ons and provide a classification of the possible scenarios in low dimensio
ns. This phenomenon is informed by the angle rank of an abelian variety ov
er a finite field\, which measures the algebraic independence of the eigen
values of the Frobenius. In this talk\, I will discuss some of our results
and some open questions in this area.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/3
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Cullinan (Bard College)
DTSTART:20241119T200000Z
DTEND:20241119T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/31
DESCRIPTION:Title: Explicit Arithmetic in Isogeny-Torsion Graphs\n
by John Cullinan (Bard College) as part of The Graduate Center Arithmetic
Geometry Seminar\n\nLecture held in The Graduate Center - room 9116.\n\nAb
stract\nLet E and E’ be isogenous elliptic curves defined over Q. Then t
heir associated L-functions are equal\; in particular\, their leading Tayl
or coefficients are equal. However (assuming the conjecture of Birch and S
winnerton-Dyer)\, the individual arithmetic invariants that comprise the l
eading terms may not be. In this talk we explore how the individual BSD te
rms change under a prime-degree isogeny and how to quantify the “likelih
ood” that such changes occur. This is joint work with Meagan Kenney and
John Voight and\, separately\, Alexander Barrios.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/3
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jen Berg (Bucknell University)
DTSTART:20241126T200000Z
DTEND:20241126T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/32
DESCRIPTION:Title: Brauer-Manin obstructions requiring arbitrarily man
y Brauer classes\nby Jen Berg (Bucknell University) as part of The Gra
duate Center Arithmetic Geometry Seminar\n\nLecture held in The Graduate C
enter - room 9116.\n\nAbstract\nIf a variety X over the rationals has p-ad
ic (local) points for each p\, then one might ask whether X has any (globa
l) rational points. To start\, we can impose conditions on the collection
of all local points on X to narrow down the possible subset of global poin
ts\, should any exist. One fruitful approach uses an algebro-geometric obj
ect called the Brauer group of X which defines an obstruction set\; if thi
s set is empty\, then it guarantees the set of rational points is empty\,
too. \nFor some nice classes of surfaces\, if X is locally soluble for all
p but does not have a rational point\, then the Brauer group of X is conj
ectured to be the cause. In general\, when such an obstruction occurs\, it
arises from a finite number of classes in the Brauer group. One might won
der whether properties of this finite subset can be determined in advance\
, i.e.\, without computing the obstruction set. In the case of cubic surfa
ces\, for example\, it is known that just one Brauer class is needed to de
tect an obstruction. In this talk\, we’ll discuss work that shows we can
not always hope to give such quantitative bounds\; for any integer N > 0\,
we construct conic bundles over the projective line for which the Brauer
group modulo constants is generated by N classes\, all of which are requir
ed to witness an obstruction. (This is joint work with Pagano\, Poonen\, S
toll\, Triantafillou\, Viray\, Vogt.)\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/3
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asimina Hamakiotes (University of Connecticut)
DTSTART:20241203T200000Z
DTEND:20241203T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/33
DESCRIPTION:Title: Abelian extensions arising from elliptic curves wit
h complex multiplication\nby Asimina Hamakiotes (University of Connect
icut) as part of The Graduate Center Arithmetic Geometry Seminar\n\nLectur
e held in The Graduate Center - room 9116.\n\nAbstract\nLet $K$ be an im
aginary quadratic field\, and let $\\mathcal{O}_{K\,f}$ be an order in
$K$ of conductor $f \\geq 1$. Let $E$ be an elliptic curve with comple
x multiplication by $\\mathcal{O}_{K\,f}$\, such that $E$ is defined by
a model over $\\mathbb{Q}(j(E))$\, where $j(E)$ is the $j$-invariant
of $E$. Let $N\\geq 2$ be an integer. The extension $\\mathbb{Q}(j(E)\
, E[N])/\\mathbb{Q}(j(E))$ is usually not abelian\; it is only abelian fo
r $N=2\,3$\, and $4$. Let $p$ be a prime and let $n\\geq 1$ be an in
teger. In this talk\, we will classify the maximal abelian extension conta
ined in $\\mathbb{Q}(E[p^n])/\\mathbb{Q}$.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/3
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Bellovin (University of Connecticut)
DTSTART:20250128T200000Z
DTEND:20250128T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/34
DESCRIPTION:Title: Perfectoid covers of abelian varieties\nby Rebe
cca Bellovin (University of Connecticut) as part of The Graduate Center Ar
ithmetic Geometry Seminar\n\nLecture held in The Graduate Center - room 91
16.\n\nAbstract\nPerfectoid spaces have emerged as a key tool in p-adic Ho
dge theory over the past decade\, generalizing earlier ideas due to people
like Fontaine and Wintenberger. I will discuss some history and applica
tions of this circle of ideas\, before talking about recent work character
izing perfectoid covers of certain abelian varieties. This is joint work
with Hanlin Cai and Sean Howe.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/3
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Eischen (University of Oregon/IAS)
DTSTART:20250204T200000Z
DTEND:20250204T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/35
DESCRIPTION:Title: Algebraicity of Spin L-functions for GSp_6\nby
Ellen Eischen (University of Oregon/IAS) as part of The Graduate Center Ar
ithmetic Geometry Seminar\n\nLecture held in The Graduate Center - room 91
16.\n\nAbstract\nI will discuss recent results for algebraicity of critica
l values of Spin L-functions for GSp_6. I will also discuss ongoing work
toward the construction of p-adic L-functions interpolating these values.
I will explain how this work fits into the context of earlier developme
nts\, while also indicating where new technical challenges arise. This i
s joint work with Giovanni Rosso and Shrenik Shah. All who are curious a
bout this topic are welcome at this talk\, even without prior experience w
ith Spin L-functions.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/3
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Sangiovanni Vincentelli (Columbia University)
DTSTART:20250422T190000Z
DTEND:20250422T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/40
DESCRIPTION:Title: A Base Change of Kato’s Euler System\nby Marc
o Sangiovanni Vincentelli (Columbia University) as part of The Graduate Ce
nter Arithmetic Geometry Seminar\n\nLecture held in The Graduate Center -
room 9116.\n\nAbstract\nThe Bloch–Kato conjecture predicts a strong rela
tionship between L-functions and Selmer groups. A powerful tool in the stu
dy of Selmer groups is the theory of Euler systems\, pioneered by Thaine\,
Kolyvagin\, and Rubin. In this talk\, I will present joint work with A. B
urungale on the construction of a new Euler system for the base change of
an elliptic modular form to a quadratic imaginary field K. This Euler syst
em exhibits remarkably good p-adic deformation properties and specializes
to Kato’s Euler system\, thereby establishing a direct link between (uni
versal) Iwasawa theory over K and over Q. I will argue that it can be vie
wed as the “base change” of Kato’s Euler system\, as anticipated by
the analytic side of the Bloch–Kato conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/4
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoyu Huang (Coco) (Temple University)
DTSTART:20250304T200000Z
DTEND:20250304T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/45
DESCRIPTION:Title: Learning Euler Factors of Elliptic Curves and Recen
t Machine Learning Applications to Number Theory\nby Xiaoyu Huang (Coc
o) (Temple University) as part of The Graduate Center Arithmetic Geometry
Seminar\n\nLecture held in The Graduate Center - room 9116.\n\nAbstract\nI
n this talk\, we will discuss recent applications of machine learning to n
umber theory. In particular\, we will introduce the recent results of appl
ying transformer models and feedforward neural networks to predict Frobeni
us traces a_p from elliptic curves given other traces a_q. We train additi
onal models to predict a_p (mod 2) from a_q (mod 2)\, and cross-analysis s
uch as a_p (mod 2) from a_q. Our experiments reveal that these models achi
eve high accuracy\, even in the absence of explicit number-theoretic tools
like functional equations of L-functions. We also present partial interpr
etability findings on the patterns learned by the machine learning models.
\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/4
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaclyn Lang (Temple University)
DTSTART:20250325T190000Z
DTEND:20250325T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/47
DESCRIPTION:Title: Eisenstein congruences in prime-square level\nb
y Jaclyn Lang (Temple University) as part of The Graduate Center Arithmeti
c Geometry Seminar\n\nLecture held in The Graduate Center - room 9116.\n\n
Abstract\nIn his celebrated Eisenstein ideal paper\, Mazur studied congrue
nces modulo a prime p between Eisenstein series and cusp forms in prime le
vel N. If p is at least 5\, he showed that such congruences exist if and
only if N is congruent to 1 modulo p. I will discuss recent work with Pre
ston Wake in which we investigate Eisenstein-cuspidal congruences when the
level is N^2\, where N is a prime congruent to -1 modulo p. We show that
such congruences exist in this case\, and that they are remarkably unifor
m compared with Mazur’s setting. Moreover\, one can use a mild extensio
n of Ribet’s method to produce from our congruences nontrivial elements
in the class group of Q(N^{1/p}).\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/4
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Groen (Lehigh University)
DTSTART:20250401T190000Z
DTEND:20250401T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/48
DESCRIPTION:Title: The Schottky problem in characteristic 2\nby St
even Groen (Lehigh University) as part of The Graduate Center Arithmetic G
eometry Seminar\n\nLecture held in The Graduate Center - room 9116.\n\nAbs
tract\nThis talk explores the relation between curves and abelian varietie
s in characteristic 2. Abelian varieties are ubiquitous objects in number
theory and algebraic geometry\, possessing the structure both of a project
ive variety and of a group. Important examples of abelian varieties are Ja
cobians of curves\, but most abelian varieties are not Jacobians. Hence a
natural ambition\, called the Schottky problem\, is to characterize the J
acobians among abelian varieties. It can be beneficial to approach this pr
oblem from the angle of p-torsion group schemes in characteristic p. Equiv
alently\, it is fruitful to study which p-torsion group schemes can occur
as the p-torsion of the Jacobian of a (specific type of) curve. In this ta
lk\, we treat the 2-torsion group schemes of Jacobians of curves in charac
teristic 2 that admit a double cover to another curve. Through an analysis
of the first De Rham cohomology\, we prove that the 2-torsion group schem
e of a double cover of an ordinary curve is determined by the ramification
invariants of the cover\, generalizing a result of Elkin and Pries. Moreo
ver\, when the base curve is not ordinary\, we prove restrictions on the p
ossible 2-torsion group schemes of the double cover. As an application\, w
e obtain asymptotics for the 2-torsion group scheme of a one point cover w
hose ramification invariant goes off to infinity.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/4
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Austin Myer (CUNY Graduate Center)
DTSTART:20250506T190000Z
DTEND:20250506T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/51
DESCRIPTION:Title: (Toward) An Algorithm to Construct (Explicitly) a R
egular Model of a Hyperelliptic Curve in (Bad) Characteristic (0\, 2)\
nby James Austin Myer (CUNY Graduate Center) as part of The Graduate Cente
r Arithmetic Geometry Seminar\n\nLecture held in The Graduate Center - roo
m 9116.\n\nAbstract\nI’ll discuss progress toward my thesis project advi
sed by Andrew Obus to construct (explicitly) a regular model of a hyperell
iptic curve over a complete\, discretely-valued field of characteristic 0
whose ring of integers has algebraically closed residue field of (bad) cha
racteristic 2. We regard the hyperelliptic curve (by definition) as a bran
ched double cover of the projective line. The strategy thus proceeds via n
ormalization (in the function field of the hyperelliptic curve\, and alway
s in the sequel) of a candidate semistable “Obus-Srinivasan” model of
the projective line (described explicitly via inductive “(Saunders) Mac
Lane” valuations) obtained via semistable reduction (and possible furthe
r modification). The regularity of the normalization of such a candidate s
emistable “Obus-Srinivasan” model of the projective line may be verifi
ed via a criterion I’ve somewhat recently established\, which seems now
strengthened by melding with nascent work of Andrew Obus &\n\nPadmavathi S
rinivasan. Currently\, an obscure lemma of Ofer Gabber seems to assuage th
e singularities along the special fiber born of the quotient of the semist
able model by the facilitatory Galois action.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/5
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hatley (Union College)
DTSTART:20251021T190000Z
DTEND:20251021T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/57
DESCRIPTION:Title: Ranks of elliptic curves in quadratic twist familie
s via Iwasawa theory\nby Jeff Hatley (Union College) as part of The Gr
aduate Center Arithmetic Geometry Seminar\n\nLecture held in The Graduate
Center - room 8203.\n\nAbstract\nFor a fixed elliptic curve E/Q\, Goldfeld
's Conjecture predicts that half of its quadratic twists have rank 0 and h
alf have rank 1. This conjecture is now a theorem in most cases\, due to r
ecent work of Alex Smith. However\, it is still interesting to ask for eff
ective versions of this theorem\; for instance\, if one considers only twi
sts by prime numbers which are 1 mod 4\, what can be said about the rank d
istribution? In this talk\, we will discuss joint work with Anwesh Ray whi
ch uses Iwasawa theory to study some of these sorts of questions.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/5
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qiao He (Columbia University)
DTSTART:20251118T200000Z
DTEND:20251118T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/60
DESCRIPTION:Title: Height pairing on Shimura curve revisited and a gen
eral conjecture for GSpin Shimura varieties\nby Qiao He (Columbia Univ
ersity) as part of The Graduate Center Arithmetic Geometry Seminar\n\nLect
ure held in The Graduate Center - room 9116.\n\nAbstract\nIn their paper "
Height pairings on Shimura curves and p-adic uniformization" (Invent\, 200
0)\, Kudla and Rapoport studied intersections of special cycles on Shimura
curves and related it with derivative of Eisenstein series\, which is one
of the key ingredient to prove arithmetic inner product formula for Shimu
ra curves (a variant/generalization of Gross-Zagier formula). In this talk
\, we will revisit Kudla and Rapoport's formula by incorporating it into a
general conjecture for the GSpin Shimura variety. As evidence of the conj
ecture\, we also discuss the proof for the self product of Shimura curves
case. This is a joint work with Baiqing Zhu.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/6
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leah Sturman (Southern Connecticut State University)
DTSTART:20251125T200000Z
DTEND:20251125T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/61
DESCRIPTION:Title: Hypergeometric Decompositions of K3 Surface Pencils
\nby Leah Sturman (Southern Connecticut State University) as part of T
he Graduate Center Arithmetic Geometry Seminar\n\nLecture held in The Grad
uate Center - room 8203.\n\nAbstract\nIn this talk we will look at five pe
ncils of projective quartic surfaces with the aim of giving explicit formu
las for the point counts over finite fields of each. These point counts ar
e written in terms of hypergeometric sums. Given time\, we will discuss ho
w to obtain a decomposition of the incomplete L-function of each pencil in
terms of hypergeometric L-series and Dedekind zeta functions. This is joi
nt work with Rachel Davis\, Jessamyn Dukes\, Thais Gomes Ribeiro\, Eli Orv
is\, Adriana Salerno\, and Ursula Whitcher.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/6
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ariel Weiss (Trinity College)
DTSTART:20251202T200000Z
DTEND:20251202T210000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/62
DESCRIPTION:Title: The distribution of 2-Selmer groups in quadratic tw
ist families\nby Ariel Weiss (Trinity College) as part of The Graduate
Center Arithmetic Geometry Seminar\n\nLecture held in The Graduate Center
- room 9116.\n\nAbstract\nThe Poonen–Rains and Bhargava–Kane–Lenstr
a–Poonen–Rains give striking predictions for the distribution of Selme
r groups in the family of all elliptic curves over $\\mathbb{Q}$. In parti
cular\, they predict that the average size of the $p$-Selmer group is $1+p
$\, a result proved for $p=2\,3\,5$ by Bhargava and Shankar. \n\nHowever\,
these models do not accurately describe families of elliptic curves with
isogenies\, where the average $p$-Selmer size can even be infinite. In thi
s talk\, I will report on work in progress to determine the distribution o
f $2$-Selmer groups in the family of quadratic twists of an elliptic curve
with a $2$-torsion point. I will present a theorem that shows that the di
stribution of the $2$-Selmer groups coincides with a distribution arising
from the kernels of random matrices. This work is joint with Harald Helfgo
tt\, Zev Klagsbrun\, and Jennifer Park.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/6
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Connor Stewart (CUNY Graduate Center)
DTSTART:20260331T190000Z
DTEND:20260331T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/66
DESCRIPTION:Title: Conductor-Discriminant Inequality for Tamely Ramifi
ed Cyclic Covers\nby Connor Stewart (CUNY Graduate Center) as part of
The Graduate Center Arithmetic Geometry Seminar\n\nLecture held in The Gra
duate Center - room 8203.\n\nAbstract\nWe consider $\\mathbb{Z}/n$-covers
$X\\to\\mathbb{P}^1$ defined over discretely valued fields $K$ with excell
ent valuation ring $\\mathcal{O}_K$ and perfect residue field of character
istic not dividing\n$n$. Two standard measures of bad reduction for such a
curve $X$ are the Artin conductor of its minimal regular model over\n$\\m
athcal{O}_K$ and the valuation of the discriminant of a Weierstrass equati
on for $X$. We prove an inequality relating these two measures. Specifical
ly\, if $X$ is given by an affine equation $y^n = f(x)$ with $f(x) \\in \\
mathcal{O}_K[x]$\,\nand if $\\mathcal{X}$ is its minimal regular model ove
r\n$\\mathcal{O}_K$\, then the negative of the Artin conductor of $\\mathc
al{X}$ is bounded\nabove by $(n-1)v_K(\\disc(\\rad f))$. This extends\npre
vious work of Ogg\, Saito\, Liu\, Srinivisan\, and Obus-Srinivasan on elli
ptic and hyperelliptic curves. (Joint work with Andrew Obus and Padmavathi
Srinivasan.)\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/6
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Yelton (Wesleyan University)
DTSTART:20260310T190000Z
DTEND:20260310T200000Z
DTSTAMP:20260404T094340Z
UID:gc-arithmetic-geometry/68
DESCRIPTION:Title: Mumford superelliptic curves and cluster data\n
by Jeffrey Yelton (Wesleyan University) as part of The Graduate Center Ari
thmetic Geometry Seminar\n\nLecture held in The Graduate Center - room 820
3.\n\nAbstract\nLet K be a field with a nonarchimedean valuation\, and let
C be a curve over K defined by an equation of the form y^p = f(x)\, where
p is any prime (which is allowed to be the residue characteristic of K).
Much information about the arithmetic of such a curve can be determined f
rom the cluster data of the roots of the polynomial f. I will demonstrate
a way to encode such cluster data as a metric graph which is a subspace o
f the Berkovich projective line and\, using this framework\, provide a cri
terion for C to have the geometric property of being a Mumford curve\; thi
s property means that the curve has a nonarchimedean uniformization.\n
LOCATION:https://stable.researchseminars.org/talk/gc-arithmetic-geometry/6
8/
END:VEVENT
END:VCALENDAR