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BEGIN:VEVENT
SUMMARY:Tobias Berger (The University of Sheffield)
DTSTART:20240116T200000Z
DTEND:20240116T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/1
DESCRIPTION:Title: Pseudomodularity of residually reducible Galois representat
ions\nby Tobias Berger (The University of Sheffield) as part of The Gr
aduate Center Arithmetic Geometry Seminar\n\nLecture held in The Graduate
Center.\n\nAbstract\nAfter a survey of previous work I will present new re
sults on pseudomodularity of residually reducible Galois representations w
ith 3 residual pieces. I will discuss applications to proving modularity o
f Galois representations arising from abelian surfaces and Picard curves.
This is joint work with Krzysztof Klosin (CUNY).\n\nPasscode for Zoom link
: 169\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dorota Blinkiewicz (University of A. Mickiewicz)
DTSTART:20240507T190000Z
DTEND:20240507T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/8
DESCRIPTION:Title: Linear relations in semiabelian varieties\nby Dorota Bl
inkiewicz (University of A. Mickiewicz) as part of The Graduate Center Ari
thmetic Geometry Seminar\n\nLecture held in The Graduate Center.\n\nAbstra
ct\nIn the lecture I will discuss results concerning the detecting linear
dependence problem\, with torsion ambiguity\, for a family of semiabelian
varieties G over a number field F and for any finitely generated subgroup
H of a Mordell-Weil group G(F). For more than 40 years\, this problem has
been investigated for abelian varieties and tori by numerous authors. In t
he lecture I will show results concerning the problem for semiabelian vari
eties and I will also show counterexamples leading to families of wild 1-m
otives.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kalyani Kansal (Institute for Advanced Study)
DTSTART:20240206T200000Z
DTEND:20240206T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/17
DESCRIPTION:Title: Irregular loci in the Emerton-Gee stack for GL2\nby Ka
lyani Kansal (Institute for Advanced Study) as part of The Graduate Center
Arithmetic Geometry Seminar\n\nLecture held in The Graduate Center.\n\nAb
stract\nLet K be a finite extension of $\\mathbb Q_p$. The Emerton-Gee sta
ck for GL2 is a stack of etale (phi\, Gamma)-modules of rank two. Its redu
ced part\, X\, is an algebraic stack of finite type over a finite field\,
and can be viewed as a moduli stack of two dimensional mod p representatio
ns of the absolute Galois group of K. By the work of Caraiani\, Emerton\,
Gee and Savitt\, it is known that in most cases\, the locus of mod p repre
sentations admitting crystalline lifts with specified regular Hodge-Tate w
eights is an irreducible component of X. Their work relied on a detailed s
tudy of a closely related stack of etale phi-modules which admits a map fr
om a stack of Breuil-Kisin modules with descent data. In our work\, we ass
ume K is unramfied and further study this map with a view to studying the
loci of mod p representations admitting crystalline lifts with small\, irr
egular Hodge-Tate weights. We identify these loci as images of certain irr
educible components of the stack of Breuil-Kisin modules and obtain severa
l inclusions of the non-regular loci into the irreducible components 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://researchseminars.org/talk/gc-arithmetic-geometry/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Brown (Occidental College)
DTSTART:20240220T200000Z
DTEND:20240220T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/18
DESCRIPTION:Title: Coding theory\, lattices\, and theta functions\nby Jim
Brown (Occidental College) as part of The Graduate Center Arithmetic Geom
etry Seminar\n\nLecture held in The Graduate Center.\n\nAbstract\nCoding t
heory is the branch of mathematics that strives to find efficient ways to
transmit information reliably. In particular\, when information is transm
itted over noisy channels there will inevitably be errors during the trans
mission. We wish to employ methods to detect these errors\, and ultimatel
y\, correct the errors. In fact\, there is a great deal of algebraic geom
etry and number theory that goes into this endeavor. In this talk I will
discuss some work with undergraduate research students showing how to con
struct lattices in number fields from codes\, the theta series associated
to the lattices\, and then some interesting results on those theta series.
\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ila Varma (University of Toronto)
DTSTART:20240227T200000Z
DTEND:20240227T210000Z
DTSTAMP:20260422T212927Z
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 Arithmeti
c Geometry Seminar\n\nLecture held in The Graduate Center.\n\nAbstract\nA
guiding question in number theory\, specifically in arithmetic statistics\
, is: Fix a degree n and a Galois group G in S_n. How does the count of nu
mber fields of degree n whose normal closure has Galois group G grow as th
eir discriminants tend to infinity? In this talk\, we will discuss the his
tory of this question and take a closer look at the story in the case that
n = 4\, i.e. the counts of quartic fields.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Chen (Columbia University)
DTSTART:20240305T200000Z
DTEND:20240305T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/20
DESCRIPTION:Title: Low degree maps and points\nby Nathan Chen (Columbia U
niversity) as part of The Graduate Center Arithmetic Geometry Seminar\n\nL
ecture held in The Graduate Center.\n\nAbstract\nTwo powerful tools for st
udying degree d > 1 points on algebraic curves over Q are the Abel-Jacobi
map and Falting's theorem. However\, for higher dimensional varieties ther
e is very little that has been explored. This talk will focus on measures
of irrationality for algebraic surfaces\, which are geometric analogues of
having many degree d points. We will then present some geometric construc
tions that give rise to many degree d points.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Emory (Oklahoma State University)
DTSTART:20240402T190000Z
DTEND:20240402T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/21
DESCRIPTION:Title: On determining Sato-Tate groups\nby Melissa Emory (Okl
ahoma State University) as part of The Graduate Center Arithmetic Geometry
Seminar\n\nLecture held in The Graduate Center.\n\nAbstract\nThe original
Sato-Tate conjecture was posed around 1960 by Mikio Sato and John Tate (i
ndependently) and is a statistical conjecture regarding the distribution o
f the normalized traces of Frobenius on an elliptic curve. In 2012\, the c
onjecture was generalized to higher genus curves by Serre. In recent years
classifications of Sato-Tate groups in dimensions 1\, 2\, and 3 have been
given\, but there are obstacles to providing classifications in higher di
mension. In this talk\, I will describe work to prove nondegeneracy and de
termine Sato-Tate groups for two families of Jacobian varieties. This wor
k is joint with Heidi Goodson.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wanlin Li (Washington University in St. Louis)
DTSTART:20240416T190000Z
DTEND:20240416T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/22
DESCRIPTION:Title: The nontriviality of the Ceresa cycle\nby Wanlin Li (W
ashington University in St. Louis) as part of The Graduate Center Arithmet
ic Geometry Seminar\n\nLecture held in The Graduate Center.\n\nAbstract\nT
he Ceresa cycle is an algebraic 1-cycle in the Jacobian of a smooth algebr
aic curve with a chosen base point. It is algebraically trivial for a hype
relliptic curve and non-trivial for a very general complex curve of genus
$\\ge 3$. Given a pointed algebraic curve\, there is no general method to
determine whether the Ceresa cycle associated to it is rationally or algeb
raically trivial. In this talk\, I will discuss some methods and tools to
study this problem.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Dillery (University of Maryland)
DTSTART:20240319T190000Z
DTEND:20240319T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/23
DESCRIPTION:Title: Comparing local Langlands correspondences\nby Peter Di
llery (University of Maryland) as part of The Graduate Center Arithmetic G
eometry Seminar\n\nLecture held in The Graduate Center.\n\nAbstract\nBroad
ly speaking\, for G a connected reductive group over a local field F\, the
Langlands program is the endeavor of relating Galois representations (mor
e precisely\, "L-parameters"---certain homomorphisms from the Weil-Deligne
group of F to the dual group of G) to admissible smooth representations o
f G(F). There is conjectured to be a finite-to-one map from irreducible sm
ooth representations of G(F) to L-parameters\, and there are many differen
t approaches to parametrizing the fibers of such a map. \n\nThe goal of th
is talk is to explain some of these approaches\; a special focus will be
placed on the so-called "isocrystal" and "rigid" local Langlands correspon
dences. The former is best suited for building on the recent breakthroughs
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-adic fiel
ds and extended to arbitrary nonarchimedean local fields in my recent work
.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Schwein (University of Bonn)
DTSTART:20240514T190000Z
DTEND:20240514T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/24
DESCRIPTION:Title: Tame supercuspidals at bad primes\nby David Schwein (U
niversity of Bonn) as part of The Graduate Center Arithmetic Geometry Semi
nar\n\nLecture held in The Graduate Center - room 4433.\n\nAbstract\nSuper
cuspidal representations are the elementary particles in the representatio
n theory of reductive p-adic groups and play an important role in number t
heory as local factors of cuspidal automorphic representations. Constructi
ng such representations explicitly\, via (compact) induction\, is a longst
anding open problem which has been solved for large p but not in general.
I'll discuss work in progress joint with Jessica Fintzen towards construct
ing some of these missing supercuspidals when p is (very!) small.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anwesh Ray (Chennai Mathematical Institute in India)
DTSTART:20241008T190000Z
DTEND:20241008T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/28
DESCRIPTION:Title: Iwasawa theory and connections with arithmetic statistics
and Hilbert's tenth problem\nby Anwesh Ray (Chennai Mathematical Insti
tute in India) as part of The Graduate Center Arithmetic Geometry Seminar\
n\nLecture held in The Graduate Center - room 4433.\n\nAbstract\nIwasawa t
heory\, originally developed from the study of L-functions and the structu
re of class groups\, has become a cornerstone of modern number theory. In
this talk\, I will focus on the Iwasawa theory of elliptic curves\, delvin
g into some of the profound conjectures that shape the field. By applying
techniques from the arithmetic statistics of elliptic curves\, we can inve
stigate these conjectures "on average." The statistical study of elliptic
curves reveals patterns and behaviors in large families\, offering new ins
ights that may lead to partial resolutions or alternative perspectives on
long-standing open problems. If time allows\, I will also explore how thes
e investigations contribute to broader developments in arithmetic geometry
and their implications for Hilbert's Tenth Problem over number rings\, a
fundamental problem at the intersection of number theory and logic.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Kozioł (Baruch College and CUNY Graduate Center)
DTSTART:20241029T190000Z
DTEND:20241029T200000Z
DTSTAMP:20260422T212927Z
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 o
f The Graduate Center Arithmetic Geometry Seminar\n\nLecture held in The G
raduate Center - room 9116.\n\nAbstract\nI'll give some motivation and bac
kground on the origins of the mod p version of the local Langlands conject
ures. In particular\, I'll try to point out connections between congruen
ces between modular forms\, Serre's philosophy of weights\, and cohomology
of modular curves.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deewang Bhamidipati (University of California\, Santa Cruz)
DTSTART:20241105T200000Z
DTEND:20241105T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/30
DESCRIPTION:Title: q-Frobenius Trace Distributions of Abelian Varieties\n
by Deewang Bhamidipati (University of California\, Santa Cruz) as part of
The Graduate Center Arithmetic Geometry Seminar\n\nLecture held in The Gra
duate Center - room 9116.\n\nAbstract\nElliptic curves over a finite field
\\(\\mathbf{F}_q\\) famously come in two flavours: ordinary and supersing
ular. As q varies over powers of a fixed prime p\, the eigenvalues of Frob
enius of an ordinary elliptic curve are uniformly distributed on a circle\
, while those of a supersingular elliptic curve are supported in finitely
many places. In joint work with Santiago Arango-Piñeros and Soumya Sankar
\, we study this phenomenon for abelian varieties in higher dimensions and
provide a classification of the possible scenarios in low dimensions. Thi
s phenomenon is informed by the angle rank of an abelian variety over a fi
nite field\, which measures the algebraic independence of the eigenvalues
of the Frobenius. In this talk\, I will discuss some of our results and so
me open questions in this area.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Cullinan (Bard College)
DTSTART:20241119T200000Z
DTEND:20241119T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/31
DESCRIPTION:Title: Explicit Arithmetic in Isogeny-Torsion Graphs\nby John
Cullinan (Bard College) as part of The Graduate Center Arithmetic Geometr
y Seminar\n\nLecture held in The Graduate Center - room 9116.\n\nAbstract\
nLet E and E’ be isogenous elliptic curves defined over Q. Then their as
sociated L-functions are equal\; in particular\, their leading Taylor coef
ficients are equal. However (assuming the conjecture of Birch and Swinnert
on-Dyer)\, the individual arithmetic invariants that comprise the leading
terms may not be. In this talk we explore how the individual BSD terms cha
nge under a prime-degree isogeny and how to quantify the “likelihood”
that such changes occur. This is joint work with Meagan Kenney and John Vo
ight and\, separately\, Alexander Barrios.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jen Berg (Bucknell University)
DTSTART:20241126T200000Z
DTEND:20241126T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/32
DESCRIPTION:Title: Brauer-Manin obstructions requiring arbitrarily many Braue
r classes\nby Jen Berg (Bucknell University) as part of The Graduate C
enter Arithmetic Geometry Seminar\n\nLecture held in The Graduate Center -
room 9116.\n\nAbstract\nIf a variety X over the rationals has p-adic (loc
al) points for each p\, then one might ask whether X has any (global) rati
onal points. To start\, we can impose conditions on the collection of all
local points on X to narrow down the possible subset of global points\, sh
ould any exist. One fruitful approach uses an algebro-geometric object cal
led the Brauer group of X which defines an obstruction set\; if this set i
s empty\, then it guarantees the set of rational points is empty\, too. \n
For 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 conjectured
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 wonder whe
ther properties of this finite subset can be determined in advance\, i.e.\
, without computing the obstruction set. In the case of cubic surfaces\, f
or example\, it is known that just one Brauer class is needed to detect an
obstruction. In this talk\, we’ll discuss work that shows we cannot alw
ays hope to give such quantitative bounds\; for any integer N > 0\, we con
struct conic bundles over the projective line for which the Brauer group m
odulo constants is generated by N classes\, all of which are required to w
itness an obstruction. (This is joint work with Pagano\, Poonen\, Stoll\,
Triantafillou\, Viray\, Vogt.)\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asimina Hamakiotes (University of Connecticut)
DTSTART:20241203T200000Z
DTEND:20241203T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/33
DESCRIPTION:Title: Abelian extensions arising from elliptic curves with compl
ex multiplication\nby Asimina Hamakiotes (University of Connecticut) a
s part of The Graduate Center Arithmetic Geometry Seminar\n\nLecture held
in The Graduate Center - room 9116.\n\nAbstract\nLet $K$ be an imaginary
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 complex multi
plication by $\\mathcal{O}_{K\,f}$\, such that $E$ is defined by a mode
l 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 for $N=2
\,3$\, and $4$. Let $p$ be a prime and let $n\\geq 1$ be an integer.
In this talk\, we will classify the maximal abelian extension contained in
$\\mathbb{Q}(E[p^n])/\\mathbb{Q}$.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Bellovin (University of Connecticut)
DTSTART:20250128T200000Z
DTEND:20250128T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/34
DESCRIPTION:Title: Perfectoid covers of abelian varieties\nby Rebecca Bel
lovin (University of Connecticut) as part of The Graduate Center Arithmeti
c Geometry Seminar\n\nLecture held in The Graduate Center - room 9116.\n\n
Abstract\nPerfectoid spaces have emerged as a key tool in p-adic Hodge the
ory over the past decade\, generalizing earlier ideas due to people like F
ontaine and Wintenberger. I will discuss some history and applications o
f this circle of ideas\, before talking about recent work characterizing p
erfectoid covers of certain abelian varieties. This is joint work with H
anlin Cai and Sean Howe.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Eischen (University of Oregon/IAS)
DTSTART:20250204T200000Z
DTEND:20250204T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/35
DESCRIPTION:Title: Algebraicity of Spin L-functions for GSp_6\nby Ellen E
ischen (University of Oregon/IAS) as part of The Graduate Center Arithmeti
c Geometry Seminar\n\nLecture held in The Graduate Center - room 9116.\n\n
Abstract\nI will discuss recent results for algebraicity of critical value
s 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 wi
ll explain how this work fits into the context of earlier developments\, w
hile also indicating where new technical challenges arise. This is joint
work with Giovanni Rosso and Shrenik Shah. All who are curious about th
is topic are welcome at this talk\, even without prior experience with Spi
n L-functions.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Sangiovanni Vincentelli (Columbia University)
DTSTART:20250422T190000Z
DTEND:20250422T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/40
DESCRIPTION:Title: A Base Change of Kato’s Euler System\nby Marco Sangi
ovanni Vincentelli (Columbia University) as part of The Graduate Center Ar
ithmetic Geometry Seminar\n\nLecture held in The Graduate Center - room 91
16.\n\nAbstract\nThe Bloch–Kato conjecture predicts a strong relationshi
p between L-functions and Selmer groups. A powerful tool in the study of S
elmer groups is the theory of Euler systems\, pioneered by Thaine\, Kolyva
gin\, and Rubin. In this talk\, I will present joint work with A. Burungal
e on the construction of a new Euler system for the base change of an elli
ptic modular form to a quadratic imaginary field K. This Euler system exhi
bits remarkably good p-adic deformation properties and specializes to Kato
’s Euler system\, thereby establishing a direct link between (universal)
Iwasawa theory over K and over Q. I will argue that it can be viewed as
the “base change” of Kato’s Euler system\, as anticipated by the ana
lytic side of the Bloch–Kato conjecture.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoyu Huang (Coco) (Temple University)
DTSTART:20250304T200000Z
DTEND:20250304T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/45
DESCRIPTION:Title: Learning Euler Factors of Elliptic Curves and Recent Machi
ne Learning Applications to Number Theory\nby Xiaoyu Huang (Coco) (Tem
ple University) as part of The Graduate Center Arithmetic Geometry Seminar
\n\nLecture held in The Graduate Center - room 9116.\n\nAbstract\nIn this
talk\, we will discuss recent applications of machine learning to number t
heory. In particular\, we will introduce the recent results of applying tr
ansformer models and feedforward neural networks to predict Frobenius trac
es a_p from elliptic curves given other traces a_q. We train additional mo
dels to predict a_p (mod 2) from a_q (mod 2)\, and cross-analysis such as
a_p (mod 2) from a_q. Our experiments reveal that these models achieve hig
h accuracy\, even in the absence of explicit number-theoretic tools like f
unctional equations of L-functions. We also present partial interpretabili
ty findings on the patterns learned by the machine learning models.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaclyn Lang (Temple University)
DTSTART:20250325T190000Z
DTEND:20250325T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/47
DESCRIPTION:Title: Eisenstein congruences in prime-square level\nby Jacly
n Lang (Temple University) as part of The Graduate Center Arithmetic Geome
try Seminar\n\nLecture held in The Graduate Center - room 9116.\n\nAbstrac
t\nIn his celebrated Eisenstein ideal paper\, Mazur studied congruences mo
dulo a prime p between Eisenstein series and cusp forms in prime level 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 Preston Wa
ke 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 c
ongruences exist in this case\, and that they are remarkably uniform compa
red with Mazur’s setting. Moreover\, one can use a mild extension of Ri
bet’s method to produce from our congruences nontrivial elements in the
class group of Q(N^{1/p}).\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Groen (Lehigh University)
DTSTART:20250401T190000Z
DTEND:20250401T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/48
DESCRIPTION:Title: The Schottky problem in characteristic 2\nby Steven Gr
oen (Lehigh University) as part of The Graduate Center Arithmetic Geometry
Seminar\n\nLecture held in The Graduate Center - room 9116.\n\nAbstract\n
This talk explores the relation between curves and abelian varieties in ch
aracteristic 2. Abelian varieties are ubiquitous objects in number theory
and algebraic geometry\, possessing the structure both of a projective var
iety and of a group. Important examples of abelian varieties are Jacobians
of curves\, but most abelian varieties are not Jacobians. Hence a natura
l ambition\, called the Schottky problem\, is to characterize the Jacobian
s among abelian varieties. It can be beneficial to approach this problem f
rom the angle of p-torsion group schemes in characteristic p. Equivalently
\, 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 talk\, we
treat the 2-torsion group schemes of Jacobians of curves in characteristi
c 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 scheme of a
double cover of an ordinary curve is determined by the ramification invari
ants of the cover\, generalizing a result of Elkin and Pries. Moreover\, w
hen the base curve is not ordinary\, we prove restrictions on the possible
2-torsion group schemes of the double cover. As an application\, we obtai
n asymptotics for the 2-torsion group scheme of a one point cover whose ra
mification invariant goes off to infinity.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Austin Myer (CUNY Graduate Center)
DTSTART:20250506T190000Z
DTEND:20250506T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/51
DESCRIPTION:Title: (Toward) An Algorithm to Construct (Explicitly) a Regular
Model of a Hyperelliptic Curve in (Bad) Characteristic (0\, 2)\nby Jam
es Austin Myer (CUNY Graduate Center) as part of The Graduate Center Arith
metic Geometry Seminar\n\nLecture held in The Graduate Center - room 9116.
\n\nAbstract\nI’ll discuss progress toward my thesis project advised by
Andrew Obus to construct (explicitly) a regular model of a hyperelliptic c
urve over a complete\, discretely-valued field of characteristic 0 whose r
ing of integers has algebraically closed residue field of (bad) characteri
stic 2. We regard the hyperelliptic curve (by definition) as a branched do
uble cover of the projective line. The strategy thus proceeds via normaliz
ation (in the function field of the hyperelliptic curve\, and always in th
e sequel) of a candidate semistable “Obus-Srinivasan” model of the pro
jective line (described explicitly via inductive “(Saunders) Mac Lane”
valuations) obtained via semistable reduction (and possible further modif
ication). The regularity of the normalization of such a candidate semistab
le “Obus-Srinivasan” model of the projective line may be verified via
a criterion I’ve somewhat recently established\, which seems now strengt
hened by melding with nascent work of Andrew Obus &\n\nPadmavathi Srinivas
an. Currently\, an obscure lemma of Ofer Gabber seems to assuage the singu
larities along the special fiber born of the quotient of the semistable mo
del by the facilitatory Galois action.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hatley (Union College)
DTSTART:20251021T190000Z
DTEND:20251021T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/57
DESCRIPTION:Title: Ranks of elliptic curves in quadratic twist families via I
wasawa theory\nby Jeff Hatley (Union College) as part of The Graduate
Center Arithmetic Geometry Seminar\n\nLecture held in The Graduate Center
- room 8203.\n\nAbstract\nFor a fixed elliptic curve E/Q\, Goldfeld's Conj
ecture predicts that half of its quadratic twists have rank 0 and half hav
e rank 1. This conjecture is now a theorem in most cases\, due to recent w
ork of Alex Smith. However\, it is still interesting to ask for effective
versions of this theorem\; for instance\, if one considers only twists by
prime numbers which are 1 mod 4\, what can be said about the rank distribu
tion? In this talk\, we will discuss joint work with Anwesh Ray which uses
Iwasawa theory to study some of these sorts of questions.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qiao He (Columbia University)
DTSTART:20251118T200000Z
DTEND:20251118T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/60
DESCRIPTION:Title: Height pairing on Shimura curve revisited and a general co
njecture for GSpin Shimura varieties\nby Qiao He (Columbia University)
as part of The Graduate Center Arithmetic Geometry Seminar\n\nLecture hel
d in The Graduate Center - room 9116.\n\nAbstract\nIn their paper "Height
pairings on Shimura curves and p-adic uniformization" (Invent\, 2000)\, Ku
dla 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 Shimura curv
es (a variant/generalization of Gross-Zagier formula). In this talk\, we w
ill revisit Kudla and Rapoport's formula by incorporating it into a genera
l conjecture for the GSpin Shimura variety. As evidence of the conjecture\
, we also discuss the proof for the self product of Shimura curves case. T
his is a joint work with Baiqing Zhu.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leah Sturman (Southern Connecticut State University)
DTSTART:20251125T200000Z
DTEND:20251125T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/61
DESCRIPTION:Title: Hypergeometric Decompositions of K3 Surface Pencils\nb
y Leah Sturman (Southern Connecticut State University) as part of The Grad
uate Center Arithmetic Geometry Seminar\n\nLecture held in The Graduate Ce
nter - room 8203.\n\nAbstract\nIn this talk we will look at five pencils o
f projective quartic surfaces with the aim of giving explicit formulas for
the point counts over finite fields of each. These point counts are writt
en in terms of hypergeometric sums. Given time\, we will discuss how to ob
tain a decomposition of the incomplete L-function of each pencil in terms
of hypergeometric L-series and Dedekind zeta functions. This is joint work
with Rachel Davis\, Jessamyn Dukes\, Thais Gomes Ribeiro\, Eli Orvis\, Ad
riana Salerno\, and Ursula Whitcher.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ariel Weiss (Trinity College)
DTSTART:20251202T200000Z
DTEND:20251202T210000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/62
DESCRIPTION:Title: The distribution of 2-Selmer groups in quadratic twist fam
ilies\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–Lenstra–Poo
nen–Rains give striking predictions for the distribution of Selmer group
s in the family of all elliptic curves over $\\mathbb{Q}$. In particular\,
they predict that the average size of the $p$-Selmer group is $1+p$\, a r
esult proved for $p=2\,3\,5$ by Bhargava and Shankar. \n\nHowever\, these
models do not accurately describe families of elliptic curves with isogeni
es\, where the average $p$-Selmer size can even be infinite. In this talk\
, I will report on work in progress to determine the distribution of $2$-S
elmer 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 distribut
ion of the $2$-Selmer groups coincides with a distribution arising from th
e kernels of random matrices. This work is joint with Harald Helfgott\, Ze
v Klagsbrun\, and Jennifer Park.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Connor Stewart (CUNY Graduate Center)
DTSTART:20260331T190000Z
DTEND:20260331T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/66
DESCRIPTION:Title: Conductor-Discriminant Inequality for Tamely Ramified Cycl
ic Covers\nby Connor Stewart (CUNY Graduate Center) as part of The Gra
duate Center Arithmetic Geometry Seminar\n\nLecture held in The Graduate C
enter - room 8203.\n\nAbstract\nWe consider $\\mathbb{Z}/n$-covers $X\\to\
\mathbb{P}^1$ defined over discretely valued fields $K$ with excellent val
uation ring $\\mathcal{O}_K$ and perfect residue field of characteristic n
ot 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$\\mathcal{
O}_K$ and the valuation of the discriminant of a Weierstrass equation for
$X$. We prove an inequality relating these two measures. Specifically\, 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 over\n$\\m
athcal{O}_K$\, then the negative of the Artin conductor of $\\mathcal{X}$
is bounded\nabove by $(n-1)v_K(\\disc(\\rad f))$. This extends\nprevious w
ork of Ogg\, Saito\, Liu\, Srinivisan\, and Obus-Srinivasan on elliptic an
d hyperelliptic curves. (Joint work with Andrew Obus and Padmavathi Sriniv
asan.)\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Yelton (Wesleyan University)
DTSTART:20260310T190000Z
DTEND:20260310T200000Z
DTSTAMP:20260422T212927Z
UID:gc-arithmetic-geometry/68
DESCRIPTION:Title: Mumford superelliptic curves and cluster data\nby Jeff
rey Yelton (Wesleyan University) as part of The Graduate Center Arithmetic
Geometry Seminar\n\nLecture held in The Graduate Center - room 8203.\n\nA
bstract\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 a
ny prime (which is allowed to be the residue characteristic of K). Much i
nformation about the arithmetic of such a curve can be determined from 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 of the B
erkovich projective line and\, using this framework\, provide a criterion
for C to have the geometric property of being a Mumford curve\; this prope
rty means that the curve has a nonarchimedean uniformization.\n
LOCATION:https://researchseminars.org/talk/gc-arithmetic-geometry/68/
END:VEVENT
END:VCALENDAR