BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Jishnu Ray (University of British Columbia)
DTSTART:20200423T210000Z
DTEND:20200423T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/1
DESCRIPTION:Title: Conjectures in Iwasawa Theory of Selmer groups and Iwasawa Algebra
s\nby Jishnu Ray (University of British Columbia) as part of UCSD numb
er theory seminar\n\n\nAbstract\nThe Iwasawa Theory of Selmer groups provi
des a natural way for p-adic approach to the celebrated Birch and Swinnert
on Dyer conjecture. Over a non-commutative p-adic Lie extension\, the (dua
l) Selmer group becomes a module over a non-commutative Iwasawa algebra an
d its structure can be understood by analyzing “(left) reflexive ideals
” in the Iwasawa algebra. In this talk\, we will start by recalling seve
ral existing conjectures in Iwasawa Theory and then we will give an explic
it ring-theoretic presentation\, by generators and relations\, of such Iwa
sawa algebras and sketch its implications in understanding the (two-sides)
reflexive ideals. Generalizing Clozel’s work for SL(2)\, we will also s
how that such an explicit presentation of Iwasawa algebras can be obtained
for a much wider class of p-adic Lie groups viz. uniform pro-p groups and
the pro-p Iwahori of GL(n\,Z_p). Further\, if time permits\, I will also
sketch some of my recent Iwasawa theoretic results joint with Sujatha Ramd
orai.\n\npretalk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jize Yu (California Institute of Technology)
DTSTART:20200430T210000Z
DTEND:20200430T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/2
DESCRIPTION:Title: The integral geometric Satake equivalence in mixed characteristic<
/a>\nby Jize Yu (California Institute of Technology) as part of UCSD numbe
r theory seminar\n\nLecture held in APM 7321.\n\nAbstract\nThe geometric S
atake equivalence establishes a link between two monoidal categories: the
category of perverse sheaves on the local Hecke stack and the category of
finitely generated representations of the Langlands dual group. It has man
y important applications in the study of the geometric Langlands program a
nd number theory. In this talk\, I will discuss the integral coefficient g
eometric Satake equivalence in the mixed characteristic setting. It genera
lizes the previous results of Lusztig\, Ginzburg\, Mirkovic-Vilonen\, and
Zhu. Time permitting\, I will discuss an application of this result in con
structing a Jacquet-Langlands transfer.\n\nThere will be a pretalk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Wang-Erickson (University of Pittsburgh)
DTSTART:20200507T210000Z
DTEND:20200507T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/3
DESCRIPTION:Title: The Eisenstein ideal with squarefree level\nby Carl Wang-Erick
son (University of Pittsburgh) as part of UCSD number theory seminar\n\nLe
cture held in APM 7321.\n\nAbstract\nIn his landmark paper "Modular forms
and the Eisenstein ideal\," Mazur studied congruences modulo a prime p bet
ween the Hecke eigenvalues of an Eisenstein series and the Hecke eigenvalu
es of cusp forms\, assuming these modular forms have weight 2 and prime le
vel N. He asked about generalizations to squarefree levels N. I will prese
nt some work on such generalizations\, which is joint with Preston Wake an
d Catherine Hsu.\n\nThere will be a pretalk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jack Thorne (Cambridge University)
DTSTART:20200521T210000Z
DTEND:20200521T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/5
DESCRIPTION:Title: Symmetric power functoriality for holomorphic modular forms\nb
y Jack Thorne (Cambridge University) as part of UCSD number theory seminar
\n\nLecture held in APM 7321.\n\nAbstract\nLanglands’s functoriality con
jectures predict the existence of “liftings” of automorphic representa
tions along morphisms of L-groups. A basic case of interest comes from the
irreducible algebraic representations of GL(2)\, thought of as the L-grou
p of the reductive group GL(2) over Q. I will discuss the proof\, joint wi
th James Newton\, of the existence of the corresponding functorial liftin
gs for a broad class of holomorphic modular forms\, including Ramanujan’
s Delta function.\n\nThere will be a pre-talk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Fuchs (University of California\, Davis)
DTSTART:20200528T210000Z
DTEND:20200528T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/6
DESCRIPTION:Title: Prime components in integral circle packings\nby Elena Fuchs (
University of California\, Davis) as part of UCSD number theory seminar\n\
nLecture held in APM 7321.\n\nAbstract\nCircle packings in which all circl
es have integer curvature\, particularly Apollonian circle packings\, have
in the last decade become objects of great interest in number theory. In
this talk\, we explore some of their most fascinating arithmetic features\
, from local to global properties to prime components in the packings\, go
ing from theorems\, to widely believed conjectures\, to wild guesses as to
what might be true.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niccolo Ronchetti (University of California\, Los Angeles)
DTSTART:20200604T210000Z
DTEND:20200604T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/7
DESCRIPTION:Title: A derived Hecke action on the ordinary Hida tower\nby Niccolo
Ronchetti (University of California\, Los Angeles) as part of UCSD number
theory seminar\n\nLecture held in APM 7321.\n\nAbstract\nWhen studying the
cohomology of Shimura varieties and arithmetic manifolds\, one encounters
the following phenomenon: the same Hecke eigensystem shows up in multiple
degrees around the middle dimension\, and its multiplicities in these deg
rees resembles that of an exterior algebra.\n\nIn a series of recent paper
s\, Venkatesh and his collaborators provide an explanation: they construct
graded objects having a graded action on the cohomology\, and show that u
nder good circumstances this action factors through that of an explicit ex
terior algebra\, which in turn acts faithfully and generate the entire Hec
ke eigenspace.\n\nIn this talk\, we discuss joint work with Khare where we
investigate the $p=p$ situation (as opposed to the $l \\neq p$ situation\
, which is the main object of study of Venkatesh’s Derived Hecke Algebra
paper): we construct a degree-raising action on the cohomology of the ord
inary Hida tower and show that (under some technical assumptions)\, this a
ction generates the full Hecke eigenspace under its lowest nonzero degree.
Then\, we bring Galois representations into the picture\, and show that t
he derived Hecke action constructed before is in fact related to the actio
n of a certain dual Selmer group.\n\nThere will be a pre-talk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Pellarin (U. Jean Monnet\, Saint-Etienne\, France)
DTSTART:20200514T170000Z
DTEND:20200514T180000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/8
DESCRIPTION:Title: On Drinfeld modular forms in Tate algebras\nby Federico Pellar
in (U. Jean Monnet\, Saint-Etienne\, France) as part of UCSD number theory
seminar\n\nLecture held in APM 7321.\n\nAbstract\nIn this talk we will de
scribe some recent works on Drinfeld modular forms with values in Tate alg
ebras (in 'equal positive characteristic'). In particular\, we will discus
s some remarkable identities (proved or conjectural) for Eisenstein and Po
incaré series\, and the problem of analytically interpolate families of D
rinfeld modular forms for congruence subgroups at the infinity place.\n\nT
he pre-talk will begin 30 minutes prior (09:30 local time).\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Tong (University of California\, San Diego)
DTSTART:20200514T210000Z
DTEND:20200514T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/10
DESCRIPTION:Title: Towards a Hodge-Iwasawa theory\nby Xin Tong (University of Ca
lifornia\, San Diego) as part of UCSD number theory seminar\n\n\nAbstract\
nWith the motivation of generalizing the corresponding geometrization of T
amagawa-Iwasawa theory after Kedlaya-Pottharst\, and with motivation of es
tablishing the corresponding equivariant version of the relative p-adic Ho
dge theory after Kedlaya-Liu aiming at the deformation of representations
of profinite fundamental groups and the family of étale local systems\, w
e initiate the corresponding Hodge-Iwasawa theory with deep point of view
and philosophy in mind from early work of Kato and Fukaya-Kato. In this ta
lk\, we are going to discuss some foundational results on the Hodge-Iwasaw
a modules and Hodge-Iwasawa sheaves\, as well as some interesting investig
ation towards the goal in our mind\, which are taken from our first paper
in this series project.\n\nThere will be a pre-talk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Organizational meeting (UCSD)
DTSTART:20201001T210000Z
DTEND:20201001T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/11
DESCRIPTION:Title: Organizational meeting\nby Organizational meeting (UCSD) as p
art of UCSD number theory seminar\n\nLecture held in normally APM 7321\, c
urrently online.\n\nAbstract\nThis is an organizational meeting for the re
mainder of the term. The seminar itself will begin one week later.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Pollack (UCSD)
DTSTART:20201008T210000Z
DTEND:20201008T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/12
DESCRIPTION:Title: Singular modular forms on quaternionic E_8\nby Aaron Pollack
(UCSD) as part of UCSD number theory seminar\n\nLecture held in normally A
PM 7321\, currently online.\n\nAbstract\nThe exceptional group $E_{7\,3}$
has a symmetric space with Hermitian tube structure. On it\, Henry Kim wr
ote down low weight holomorphic modular forms that are "singular" in the s
ense that their Fourier expansion has many terms equal to zero. The symme
tric space associated to the exceptional group $E_{8\,4}$ does not have a
Hermitian structure\, but it has what might be the next best thing: a quat
ernionic structure and associated "modular forms". I will explain the cons
truction of singular modular forms on $E_{8\,4}$\, and the proof that thes
e special modular forms have rational Fourier expansions\, in a precise se
nse. This builds off of work of Wee Teck Gan and uses key input from Gord
an Savin.\n\npre-talk at 1:30pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Mundy (Columbia)
DTSTART:20201105T220000Z
DTEND:20201105T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/13
DESCRIPTION:Title: Archimedean components of Eisenstein series and CAP forms for $G_
2$\nby Samuel Mundy (Columbia) as part of UCSD number theory seminar\n
\nLecture held in normally APM 7321\, currently online.\n\nAbstract\nI wil
l talk about some recent work determining the archimedean components of ce
rtain Eisenstein series and CAP forms induced from the long root parabolic
of $G_2$. I will also discuss how these results are being used in some wo
rk in progress on producing nonzero classes in symmetric cube Selmer group
s.\n\npre-talk at 1:30\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brandon Alberts (UCSD)
DTSTART:20201029T210000Z
DTEND:20201029T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/14
DESCRIPTION:Title: Modeling Malle's Conjecture with Random Groups\nby Brandon Al
berts (UCSD) as part of UCSD number theory seminar\n\nLecture held in norm
ally APM 7321\, currently online.\n\nAbstract\nWe construct a random group
with a local structure that models the behavior of the absolute Galois gr
oup ${\\rm Gal}(\\overline{K}/K)$\, and prove that this random group satis
fies Malle's conjecture for counting number fields ordered by discriminant
with probability 1. This work is motivated by the use of random groups to
model class group statistics in families of number fields (and generaliza
tions). We take care to address the known counter-examples to Malle's conj
ecture and how these may be incorporated into the random group.\n\npre-tal
k at 1:30\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Upton (UCSD)
DTSTART:20201112T220000Z
DTEND:20201112T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/15
DESCRIPTION:Title: Newton Slopes in $\\mathbb{Z}_p$-Towers of Curves\nby James U
pton (UCSD) as part of UCSD number theory seminar\n\nLecture held in norma
lly APM 7321\, currently online.\n\nAbstract\nLet $X/\\mathbb{F}_q$ be a s
mooth affine curve over a finite field of characteristic $p > 2$. In this
talk we discuss the $p$-adic variation of zeta functions $Z(X_n\,s)$ in a
pro-covering $X_\\infty:\\cdots \\to X_1 \\to X_0 = X$ with total Galois g
roup $\\mathbb{Z}_p$. For certain ``monodromy stable'' coverings over an o
rdinary curve $X$\, we prove that the $q$-adic Newton slopes of $Z(X_n\,s)
/Z(X\,s)$ approach a uniform distribution in the interval $[0\,1]$\, confi
rming a conjecture of Daqing Wan. We also prove a ``Riemann hypothesis'' f
or a family of Galois representations associated to $X_\\infty/X$\, analog
ous to the Riemann hypothesis for equicharacteristic $L$-series as posed
by David Goss. This is joint work with Joe Kramer-Miller.\n\npre-talk at 1
:30\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yifeng Liu (Yale University)
DTSTART:20201120T000000Z
DTEND:20201120T010000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/16
DESCRIPTION:Title: Beilinson-Bloch conjecture and arithmetic inner product formula\nby Yifeng Liu (Yale University) as part of UCSD number theory seminar\
n\nLecture held in normally APM 7321\, currently online.\n\nAbstract\nIn t
his talk\, we study the Chow group of the motive associated to a tempered
global L-packet \\pi of unitary groups of even rank with respect to a CM e
xtension\, whose global root number is -1. We show that\, under some restr
ictions on the ramification of \\pi\, if the central derivative L'(1/2\,\\
pi) is nonvanishing\, then the \\pi-nearly isotypic localization of the Ch
ow group of a certain unitary Shimura variety over its reflex field does n
ot vanish. This proves part of the Beilinson--Bloch conjecture for Chow gr
oups and L-functions. Moreover\, assuming the modularity of Kudla's genera
ting functions of special cycles\, we explicitly construct elements in a c
ertain \\pi-nearly isotypic subspace of the Chow group by arithmetic theta
lifting\, and compute their heights in terms of the central derivative L'
(1/2\,\\pi) and local doubling zeta integrals. This is a joint work with C
hao Li.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Mornev (ETHZ)
DTSTART:20201203T180000Z
DTEND:20201203T190000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/17
DESCRIPTION:Title: Local monodromy of Drinfeld modules\nby Maxim Mornev (ETHZ) a
s part of UCSD number theory seminar\n\nLecture held in normally APM 7321\
, currently online.\n\nAbstract\nThe theory of Drinfeld modules is remarka
bly similar to the theory of abelian varieties\, but their local monodromy
behaves differently and is poorly understood. In this talk I will present
a research program which aims to fully describe this monodromy. The corne
rstone of this program is a "z-adic" variant of Grothendieck's l-adic mono
dromy theorem.\n\nThe talk is aimed at a general audience of number theori
sts and arithmetic geometers. No special knowledge of monodromy theory or
Drinfeld modules is assumed.\n\nThere will be a pre-talk introducing the t
heory of t-motives.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Popescu (UCSD)
DTSTART:20201015T210000Z
DTEND:20201015T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/18
DESCRIPTION:Title: An equivariant Tamagawa number formula for Drinfeld modules and b
eyond\nby Cristian Popescu (UCSD) as part of UCSD number theory semina
r\n\nLecture held in normally APM 7321\, currently online.\n\nAbstract\nI
will present a vast generalization of Taelman's 2012 celebrated class-numb
er formula for Drinfeld modules to the setting of (rigid analytic) L-funct
ions of Drinfeld module motives with Galois equivariant coefficients. I wi
ll discuss applications and potential extensions of this formula to the ca
tegory of t-modules and t-motives. This is based on joint work with Ferrar
a\, Green and Higgins\, and a result of meetings in the UCSD Drinfeld Modu
le Seminar.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Van Koughnett (Purdue)
DTSTART:20201022T210000Z
DTEND:20201022T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/19
DESCRIPTION:Title: Topological modular forms for number theorists\nby Paul Van K
oughnett (Purdue) as part of UCSD number theory seminar\n\nLecture held in
normally APM 7321\, currently online.\n\nAbstract\nThis will be a mainly
expository talk about some recent applications of number theory to topolog
y. The crux of these applications is the construction of a cohomology theo
ry called topological modular forms (TMF) out of the moduli of elliptic cu
rves. I'll explain what TMF is\, what we have been doing with it\, and wha
t we'd still like to know\; I'll also discuss more recent attempts to exte
nd the theory using level structures\, higher-dimensional abelian varietie
s\, and K3 surfaces. Time permitting\, I'll talk about my work with Domini
c Culver on some partial number-theoretic interpretations of TMF co-operat
ions.\n\nI'll give a pre-talk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Le Hung (Northwestern University)
DTSTART:20201210T220000Z
DTEND:20201210T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/20
DESCRIPTION:Title: Moduli of Fontaine-Laffaille modules and mod p local-global compa
tibility.\nby Bao Le Hung (Northwestern University) as part of UCSD nu
mber theory seminar\n\nLecture held in normally APM 7321\, currently onlin
e.\n\nAbstract\nThe mod p cohomology of locally symmetric spaces for defin
ite unitary groups at infinite level is expected to realize the mod p loca
l Langlands correspondence for GL_n. In particular\, one expects the (comp
onent at p) of the associated Galois representation to be determined by co
homology as a smooth representation. I will describe how one can establish
this expectation in many cases when the local Galois representation is Fo
ntaine-Laffaille.\nThis is joint work with D. Le\, S. Morra\, C. Park and
Z. Qian.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Lam (Harvard University)
DTSTART:20210107T220000Z
DTEND:20210107T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/21
DESCRIPTION:Title: Calabi-Yau varieties and Shimura varieties\nby Joshua Lam (Ha
rvard University) as part of UCSD number theory seminar\n\nLecture held in
normally APM 7321\, currently online.\n\nAbstract\nI will discuss the Att
ractor Conjecture for Calabi-Yau varieties\, which was formulated by Moore
in the nineties\, highlighting the difference between Calabi-Yau varietie
s with and without Shimura moduli. In the Shimura case\, I show that the c
onjecture holds and gives rise to an explicit parametrization of CM points
on certain Shimura varieties\; in the case without Shimura moduli\, I’l
l present counterexamples to the conjecture using unlikely intersection th
eory. Part of this is joint work with Arnav Tripathy.\n\nThere will be a 3
0 minute pre-talk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aranya Lahiri (Indiana University)
DTSTART:20210114T220000Z
DTEND:20210114T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/22
DESCRIPTION:Title: Resolutions of locally analytic principal series representations
of GL_2(F)\nby Aranya Lahiri (Indiana University) as part of UCSD numb
er theory seminar\n\nLecture held in normally APM 7321\, currently online.
\n\nAbstract\nLocally analytic representations of $p$-adic analytic groups
have played a crucial role in many areas of arithmetic and representation
theory (including in $p$-adic local Langlands program) since their intro
duction by Schneider and Teitelbaum. In this talk we will briefly review s
ome aspects of the theory of locally analytic representations. Then\, for
a locally analytic representation $V$ of $GL_2(F)$ we will construct a co
efficient system attached to the Bruhat-Tits tree of $Gl_2(F)$. Finally we
will use this coefficient system to construct a resolution for locally an
alytic principal series of $GL_2(F)$.\n\npre-talk at 1:30. I will discuss
basics and some key examples of locally analytic representations in the pr
e-talk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naomi Sweeting (Harvard University)
DTSTART:20210204T220000Z
DTEND:20210204T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/23
DESCRIPTION:Title: Kolyvagin's conjecture and higher congruences of modular forms\nby Naomi Sweeting (Harvard University) as part of UCSD number theory se
minar\n\nLecture held in normally APM 7321\, currently online.\n\nAbstract
\nGiven an elliptic curve E\, Kolyvagin used CM points on modular curves
to construct a system of classes valued in the Galois cohomology of the to
rsion points of E. Under the conjecture that not all of these classes van
ish\, he gave a description for the Selmer group of E. This talk will rep
ort on recent work proving new cases of Kolyvagin's conjecture. The metho
ds follow in the footsteps of Wei Zhang\, who used congruences between mod
ular forms to prove Kolyvagin's conjecture under some technical hypotheses
. We remove many of these hypotheses by considering congruences modulo hi
gher powers of p. The talk will explain the difficulties associated with
higher congruences of modular forms and how they can be overcome. I will a
lso provide an introduction to the conjecture and its consequences\, inclu
ding a 'converse theorem': algebraic rank one implies analytic rank one.\n
\npre-talk at 1:30\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kwun Angus Chung (University of Michigan)
DTSTART:20210121T220000Z
DTEND:20210121T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/24
DESCRIPTION:Title: $v$-adic convergence for exp and log in function fields and appli
cations to $v$-adic $L$-values\nby Kwun Angus Chung (University of Mic
higan) as part of UCSD number theory seminar\n\nLecture held in normally A
PM 7321\, currently online.\n\nAbstract\nClassically over the rational num
bers\, the exponential and logarithm series converge $p$-adically within s
ome open disc of $\\mathbb{C}_p$. For function fields\, exponential and lo
garithm series arise naturally from Drinfeld modules\, which are objects c
onstructed by Drinfeld in his thesis to prove the Langlands conjecture for
$\\mathrm{GL}_2$ over function fields. For a "finite place" $v$ on such a
curve\, one can ask if the exp and log possess similar $v$-adic convergen
ce properties. For the most basic case\, namely that of the Carlitz module
over $\\mathbb{F}_q[T]$\, this question has been long understood. In this
talk\, we will show the $v$-adic convergence for Drinfeld-(Hayes) modules
on elliptic curves and a certain class of hyperelliptic curves. As an app
lication\, we are then able to obtain a formula for the $v$-adic $L$-value
$L_v(1\,\\Psi)$ for characters in these cases\, analogous to Leopoldt's f
ormula in the number field case.\n\npre-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashwin Iyengar (King's College\, London)
DTSTART:20210128T220000Z
DTEND:20210128T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/25
DESCRIPTION:Title: The Iwasawa Main Conjecture over the Extended Eigencurve\nby
Ashwin Iyengar (King's College\, London) as part of UCSD number theory sem
inar\n\nLecture held in normally APM 7321\, currently online.\n\nAbstract\
nI will give a brief historical motivation for the Iwasawa main conjecture
\, and then I will talk about a construction of a $p$-adic $L$-function in
families over the extended eigencurve\, and how to formulate a two-variab
le Iwasawa main conjecture. If time permits\, I will state some open quest
ions about this family of functions.\n\nI will give a pre-talk beforehand
at 1:30.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allechar Serrano Lopez (University of Utah)
DTSTART:20210211T220000Z
DTEND:20210211T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/26
DESCRIPTION:Title: Counting elliptic curves with prescribed torsion over imaginary q
uadratic fields\nby Allechar Serrano Lopez (University of Utah) as par
t of UCSD number theory seminar\n\nLecture held in normally APM 7321\, cur
rently online.\n\nAbstract\nA generalization of Mazur's theorem states tha
t there are 26 possibilities for the torsion subgroup of an elliptic curve
over a quadratic extension of $\\mathbb{Q}$. If $G$ is one of these group
s\, we count the number of elliptic curves of bounded naive height whose t
orsion subgroup is isomorphic to $G$ in the case of imaginary quadratic fi
elds.\n\npre-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zuhair Mullath (University of Massachusetts\, Amherst)
DTSTART:20210218T220000Z
DTEND:20210218T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/27
DESCRIPTION:Title: Unobstructed Galois deformation problems associated to GSp(4)
\nby Zuhair Mullath (University of Massachusetts\, Amherst) as part of UCS
D number theory seminar\n\nLecture held in normally APM 7321\, currently o
nline.\n\nAbstract\nTo a cuspidal automorphic representation of GSp(4) ove
r $\\mathbb Q$\, one can associate a compatible system of Galois represent
ations $\\{\\rho_p\\}_{p \\\; \\mathrm{prime}}$. For $p$ sufficiently larg
e\, the deformation theory of the mod-$p$ reduction $\\overline \\rho_p$ i
s expected to be unobstructed -- meaning the universal deformation ring is
a power series ring. The global obstructions to deforming $\\overline \\r
ho_p$ is controlled by certain adjoint Bloch-Kato Selmer groups\, which ar
e expected to be trivial for $p$ large enough.\n\nI will talk about some r
ecent results showing that there are no local obstructions to the deformat
ion theory of $\\overline \\rho_p$ for almost all $p$. This is joint work
with M. Broshi\, C. Sorensen\, and T. Weston.\n\nPre-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Trudgian (UNSW Canberra at ADFA)
DTSTART:20210225T220000Z
DTEND:20210225T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/28
DESCRIPTION:Title: Verifying the Riemann hypothesis to a new height\nby Tim Trud
gian (UNSW Canberra at ADFA) as part of UCSD number theory seminar\n\nLect
ure held in normally APM 7321\, currently online.\n\nAbstract\nSadly\, I w
on’t have time to prove the Riemann hypothesis in this talk. However\, I
do hope to outline recent work in a record partial-verification of RH. Th
is is joint work with Dave Platt\, in Bristol\, UK.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soumya Sankar (The Ohio State University)
DTSTART:20210304T220000Z
DTEND:20210304T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/29
DESCRIPTION:Title: Counting elliptic curves with a rational $N$-isogeny\nby Soum
ya Sankar (The Ohio State University) as part of UCSD number theory semina
r\n\nLecture held in normally APM 7321\, currently online.\n\nAbstract\nTh
e classical problem of counting elliptic curves with a rational N-isogeny
can be phrased in terms of counting rational points on certain moduli stac
ks of elliptic curves. Counting points on stacks poses various challenges\
, and I will discuss these along with a few ways to overcome them. I will
also talk about the theory of heights on stacks developed in recent work o
f Ellenberg\, Satriano and Zureick-Brown and use it to count elliptic curv
es with an $N$-isogeny for certain $N$. The talk assumes no prior knowledg
e of stacks and is based on joint work with Brandon Boggess.\n\nThere will
be a 30 minute pre-talk for graduate students and postdocs preceding the
main talk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Organizational meeting (UCSD)
DTSTART:20210311T220000Z
DTEND:20210311T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/30
DESCRIPTION:Title: Organizational meeting\nby Organizational meeting (UCSD) as p
art of UCSD number theory seminar\n\nLecture held in normally APM 7321\, c
urrently online.\n\nAbstract\nOrganizational meeting to plan for next quar
ter. No talk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Koymans (MPIM)
DTSTART:20210401T180000Z
DTEND:20210401T190000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/31
DESCRIPTION:Title: Malle's conjecture for nonic Heisenberg extensions\nby Peter
Koymans (MPIM) as part of UCSD number theory seminar\n\nLecture held in no
rmally APM 7321\, currently online.\n\nAbstract\nIn 2002 Malle conjectured
an asymptotic formula for the number of $G$-extensions of a number field
$K$ with discriminant bounded by $X$. In this talk I will discuss recent j
oint work with Etienne Fouvry on this conjecture. Our main result proves M
alle's conjecture in the special case of nonic Heisenberg extensions.\n\np
re-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahesh Kakde (IISc\, Bangalore)
DTSTART:20210408T170000Z
DTEND:20210408T180000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/32
DESCRIPTION:Title: On the Brumer-Stark conjecture and applications to Hilbert's 12th
problem\nby Mahesh Kakde (IISc\, Bangalore) as part of UCSD number th
eory seminar\n\nLecture held in normally APM 7321\, currently online.\n\nA
bstract\nI will report on my joint work with Samit Dasgupta on the Brumer-
Stark conjecture proving existence of the Brumer-Stark units and on a conj
ecture of Dasgupta giving a p-adic analytic formula for these units. I wil
l present a sketch of our proof of the Brumer-Stark conjecture and also me
ntion applications to Hilbert's 12th problem\, or explicit class field the
ory.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lance Miller (University of Arkansas)
DTSTART:20210415T210000Z
DTEND:20210415T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/33
DESCRIPTION:Title: Finiteness of quasi-canonical lifts of elliptic curves\nby La
nce Miller (University of Arkansas) as part of UCSD number theory seminar\
n\nLecture held in normally APM 7321\, currently online.\n\nAbstract\nFix
a prime integer $p$. Set $R$ the completed valuation ring of the maximal u
nramified extension of $\\mathbb{Q}_p$. For $X := X_1(N)$ the modular cur
ve with $N$ at least 4 and coprime to $p$\, Buium-Poonen in 2009 showed th
at the locus of canonical lifts enjoys finite intersection with preimages
of finite rank subgroups of $E(R)$ when $E$ is an elliptic curve with a su
rjection from $X$. This is done using Buium's theory of arithmetic ODEs\,
in particular interesting homomorphisms $E(R) \\to R$ which are arithmetic
analogues of Manin maps. \n\nIn this talk\, I will review the general ide
a behind this result and other applications of arithmetic jet spaces to Di
ophantine geometry and discuss a recent analogous result for quasi-canonic
al lifts\, i.e.\, those curves with Serre-Tate parameter a root of unity.
Here the ODE Manin maps are insufficient\, so we introduce a PDE version o
f Buium's theory to provide the needed maps. All of this is joint work wit
h A. Buium.\n\npre-talk at 1:30\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Owen Barrett (University of Chicago)
DTSTART:20210422T210000Z
DTEND:20210422T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/34
DESCRIPTION:Title: The derived category of the abelian category of constructible she
aves\nby Owen Barrett (University of Chicago) as part of UCSD number t
heory seminar\n\nLecture held in normally APM 7321\, currently online.\n\n
Abstract\nNori proved in 2002 that given a complex algebraic variety $X$\,
the bounded\nderived category of the abelian category of constructible sh
eaves on $X$ is\nequivalent to the usual triangulated category $D(X)$ of b
ounded\nconstructible complexes on $X$.\nHe moreover showed that given any
constructible sheaf $\\mathcal F$ on\n$\\A^n$\, there is an injection $\\
mathcal F\\hookrightarrow\\mathcal G$ with\n$\\mathcal G$ constructible an
d $H^i(\\A^n\,\\mathcal G)=0$ for $i>0$.\n\nIn this talk\, I'll discuss ho
w to extend Nori's theorem to the case of a\nvariety over an algebraically
closed field of positive characteristic\, with\nBetti constructible sheav
es replaced by $\\ell$-adic sheaves.\nThis is the case $p=0$ of the genera
l problem which asks whether the bounded\nderived category of $p$-perverse
sheaves is equivalent to $D(X)$\, resolved\naffirmatively for the middle
perversity by Beilinson.\n\npre-talk at 1:30pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Klevdal (University of Utah)
DTSTART:20210429T210000Z
DTEND:20210429T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/35
DESCRIPTION:Title: Integrality of G-local systems\nby Christian Klevdal (Univers
ity of Utah) as part of UCSD number theory seminar\n\nLecture held in norm
ally APM 7321\, currently online.\n\nAbstract\nSimpson conjectured that fo
r a reductive group $G$\, rigid $G$-local systems on a smooth projective c
omplex variety are integral. I will discuss a proof of integrality for coh
omologically rigid $G$-local systems. This generalizes and is inspired by
work of Esnault and Groechenig for $GL_n$. Surprisingly\, the main tools u
sed in the proof (for general $G$ and $GL_n$) are the work of L. Lafforgue
on the Langlands program for curves over function fields\, and work of Dr
infeld on companions of $\\ell$-adic sheaves. The major differences betwee
n general $G$ and $GL_n$ are first to make sense of companions for $G$-loc
al systems\, and second to show that the monodromy group of a rigid G-loca
l system is semisimple. All work is joint with Stefan Patrikis.\n\npre-tal
k\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Fox (University of Oregon)
DTSTART:20210506T210000Z
DTEND:20210506T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/36
DESCRIPTION:Title: Supersingular Loci of Some Unitary Shimura Varieties\nby Mari
a Fox (University of Oregon) as part of UCSD number theory seminar\n\nLect
ure held in normally APM 7321\, currently online.\n\nAbstract\nUnitary Shi
mura varieties are moduli spaces of abelian varieties with an action of a
quadratic imaginary field\, and extra structure. In this talk\, we'll disc
uss specific examples of unitary Shimura varieties whose supersingular loc
i can be concretely described in terms of Deligne-Lusztig varieties. By Ra
poport-Zink uniformization\, much of the structure of these supersingular
loci can be understood by studying an associated moduli space of p-divisib
le groups (a Rapoport-Zink space). We'll discuss the geometric structure o
f these associated Rapoport-Zink spaces as well as some techniques for stu
dying them.\n\nThere will be a pre-talk!\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Howe (University of Utah)
DTSTART:20210513T210000Z
DTEND:20210513T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/37
DESCRIPTION:Title: Bialgebraicity in local Shimura varieties\nby Sean Howe (Univ
ersity of Utah) as part of UCSD number theory seminar\n\nLecture held in n
ormally APM 7321\, currently online.\n\nAbstract\nA classical transcendenc
e result of Schneider on the modular $j$-invariant states that\, for $\\ta
u \\in \\mathbb{H}$\, both $\\tau$ and $j(\\tau)$ are in $\\overline{\\mat
hbb{Q}}$ if and only if $\\tau$ is contained in an imaginary quadratic ext
ension of $\\mathbb{Q}$. The space $\\mathbb{H}$ has a natural interpretat
ion as a parameter space for $\\mathbb{Q}$-Hodge structures (or\, in this
case\, elliptic curves)\, and from this perspective the imaginary quadrati
c points are distinguished as corresponding to objects with maximal symmet
ry. This result has been generalized by Cohen and Shiga-Wolfart to more ge
neral moduli of Hodge structures (corresponding to abelian-type Shimura va
rieties)\, and by Ullmo-Yafaev to higher dimensional loci of extra symmetr
y (special subvarieties)\, where bialgebraicity is intimately connected wi
th the Pila-Zannier approach to the Andre-Oort conjecture.\n\nIn this talk
\, I will discuss work in progress with Christian Klevdal on an analogous
bialgebraicity characterization of special subvarieties in Scholze's local
Shimura varieties and more general diamond moduli of $p$-adic Hodge struc
tures.\n\nThere will be a pretalk!\n\npre-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nahid Walji (University of British Columbia)
DTSTART:20210520T210000Z
DTEND:20210520T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/38
DESCRIPTION:Title: On the conjectural decomposition of symmetric powers of automorph
ic representations for GL(3) and GL(4)\nby Nahid Walji (University of
British Columbia) as part of UCSD number theory seminar\n\nLecture held in
normally APM 7321\, currently online.\n\nAbstract\nLet $\\Pi$ be a cuspid
al automorphic representation for GL(3) over a number field. We fix an int
eger $k \\geq 2$ and we assume that the symmetric $m$th power lifts of $\\
Pi$ are automorphic for $m \\leq k$\, cuspidal for $m < k$\, and that cert
ain associated Rankin–Selberg products are automorphic. In this setting\
, we bound the number of cuspidal isobaric summands in the $k$th symmetric
power lift. In particular\, we show it is bounded above by 3 for $k \\geq
7$\, and bounded above by 2 when $k \\geq 19$ with $k$ congruent to 1 mod
3. We will also discuss the analogous problem for GL(4).\n\nThis will inc
lude a pre-talk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evan O'Dorney (Princeton University)
DTSTART:20210527T210000Z
DTEND:20210527T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/39
DESCRIPTION:Title: Arithmetic statistics of $H^1(K\, T)$\nby Evan O'Dorney (Prin
ceton University) as part of UCSD number theory seminar\n\nLecture held in
normally APM 7321\, currently online.\n\nAbstract\nCoclasses in a Galois
cohomology group $H^1(K\, T)$ parametrize extensions of a number field wit
h certain Galois group. It is natural to want to count these coclasses wit
h general local conditions and with respect to a discriminant-like invaria
nt. In joint work with Brandon Alberts\, I present a novel tool for studyi
ng this: harmonic analysis on adelic cohomology\, modeled after the celebr
ated use of harmonic analysis on the adeles in Tate's thesis. This leads t
o a more illuminating explanation of a fact previously noticed by Alberts\
, namely that the Dirichlet series counting such coclasses is a finite sum
of Euler products\; and we nail down the asymptotic count of coclasses in
satisfying generality.\n\nIn the pre-talk\, I will give a rundown on the
needed background in Galois cohomology\, etale algebras\, the local Tate p
airing\, and Poitou-Tate duality.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kelly Isham (University of California Irvine)
DTSTART:20210603T210000Z
DTEND:20210603T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/40
DESCRIPTION:Title: Asymptotic growth of orders in a fixed number field via subrings
in $\\mathbb{Z}^n$\nby Kelly Isham (University of California Irvine) a
s part of UCSD number theory seminar\n\nLecture held in normally APM 7321\
, currently online.\n\nAbstract\nLet $K$ be a number field of degree $n$ a
nd $\\mathcal{O}_K$ be its ring of integers. An order in $\\mathcal{O}_K$
is a finite index subring that contains the identity. A major open questio
n in arithmetic statistics asks for the asymptotic growth of orders in $K$
. In this talk\, we will give the best known lower bound for this asymptot
ic growth. The main strategy is to relate orders in $\\mathcal{O}_K$ to su
brings in $\\mathbb{Z}^n$ via zeta functions. Along the way\, we will give
lower bounds for the asymptotic growth of subrings in $\\mathbb{Z}^n$ and
for the number of index $p^e$ subrings in $\\mathbb{Z}^n$. We will also d
iscuss analytic properties of these zeta functions.\n\nThere will be a pre
talk at 1:30 Pacific time.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiran Kedlaya (UCSD)
DTSTART:20211007T210000Z
DTEND:20211007T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/42
DESCRIPTION:Title: Orders of abelian varieties over F_2\nby Kiran Kedlaya (UCSD)
as part of UCSD number theory seminar\n\nLecture held in APM 7321 and onl
ine.\n\nAbstract\nWe describe several recent results on orders of abelian
varieties over $\\mathbb{F}_2$: every positive integer occurs as the order
of an ordinary abelian variety over $\\mathbb{F}_2$ (joint with E. Howe)\
; every positive integer occurs infinitely often as the order of a simple
abelian variety over $\\mathbb{F}_2$\; the geometric decomposition of the
simple abelian varieties over $\\mathbb{F}_2$ can be described explicitly
(joint with T. D'Nelly-Warady)\; and the relative class number one problem
for function fields is reduced to a finite computation (work in progress)
.\n\nAll of these results rely on the relationship between isogeny classes
of abelian varieties over finite fields and Weil polynomials given by the
work of Weil and Honda-Tate. With these results in hand\, most of the wor
k is to construct algebraic integers satisfying suitable archimedean const
raints.\n\nTalk to be given in person and streamed via Zoom.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Lagarias (Michigan)
DTSTART:20211014T210000Z
DTEND:20211014T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/43
DESCRIPTION:Title: Complex Equiangular Lines and the Stark Conjectures\nby Jeff
Lagarias (Michigan) as part of UCSD number theory seminar\n\nLecture held
in APM 7321 and online.\n\nAbstract\nThis talk is expository. It describes
the history of an exciting connection made by physicists between an unso
lved \nproblem in combinatorial design theory- the existence of maximal se
ts of $d^2$ complex equiangular lines in ${\\mathbb C}^d$-\nrephrased as
a problem in quantum information theory\, and topics\n in algebraic number
theory involving class fields of real quadratic fields. Work of my former
student\nGene Kopp recently uncovered a surprising\, deep (unproved!) co
nnection with\nthe Stark conjectures. For infinitely many dimensions $d$
he predicts the existence of maximal equiangular sets\, \nconstructible by
a specific recipe starting from suitable Stark units\, in the rank one ca
se. Numerically computing\nspecial values at $s=0$ of suitable L-functions
then permits recovering the units numerically to high precision\, \nthen
reconstructing them exactly\, then testing they satisfy suitable extra alg
ebraic identities to yield a construction\nof the set of equiangular line
s. It has been carried out for $d=5\, 11\, 17$ and $23$.\n\npre-talk at 1:
20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Grubb (UCSD)
DTSTART:20211021T210000Z
DTEND:20211021T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/44
DESCRIPTION:Title: A cut-by-curves criterion for overconvergence of $F$-isocrystals<
/a>\nby Thomas Grubb (UCSD) as part of UCSD number theory seminar\n\nLectu
re held in APM 7321 and online.\n\nAbstract\nLet $X$ be a smooth\, geometr
ically irreducible scheme over a finite field of characteristic $p > 0$. W
ith respect to rigid cohomology\, $p$-adic coefficient objects on $X$ come
in two types: convergent $F$-isocrystals and the subcategory of overconve
rgent $F$-isocrystals. Overconvergent isocrystals are related to $\\ell$-a
dic etale objects ($\\ell\\neq p$) via companions theory\, and as such it
is desirable to understand when an isocrystal is overconvergent. We show (
under a geometric tameness hypothesis) that a convergent $F$-isocrystal $E
$ is overconvergent if and only if its restriction to all smooth curves on
$X$ is. The technique reduces to an algebraic setting where we use skelet
on sheaves and crystalline companions to compare $E$ to an isocrystal whic
h is patently overconvergent. Joint with Kiran Kedlaya and James Upton.\n\
npre-talk at 1:30\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Dalal (Johns Hopkins)
DTSTART:20211028T210000Z
DTEND:20211028T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/45
DESCRIPTION:Title: Counting level-1\, quaternionic automorphic representations on $G
_2$\nby Rahul Dalal (Johns Hopkins) as part of UCSD number theory semi
nar\n\nLecture held in APM 7321 and online.\n\nAbstract\nQuaternionic auto
morphic representations are one attempt to generalize to other groups the
special place holomorphic modular forms have among automorphic representat
ions of $GL_2$. Like holomorphic modular forms\, they are defined by havin
g their real component be one of a particularly nice class (in this case\,
called quaternionic discrete series). We count quaternionic automorphic r
epresentations on the exceptional group $G_2$ by developing a $G_2$ versio
n of the classical Eichler-Selberg trace formula for holomorphic modular f
orms. \n\nThere are two main technical difficulties. First\, quaternionic
discrete series come in L-packets with non-quaternionic members and standa
rd invariant trace formula techniques cannot easily distinguish between di
screte series with real component in the same L-packet. Using the more mod
ern stable trace formula resolves this issue. Second\, quaternionic discre
te series do not satisfy a technical condition of being "regular"\, so the
trace formula can a priori pick up unwanted contributions from automorphi
c representations with non-tempered components at infinity. Applying some
computations of Mundy\, this miraculously does not happen for our specific
case of quaternionic representations on $G_2$. \n\nFinally\, we are only
studying level-1 forms\, so we can apply some tricks of Chenevier and Taï
bi to reduce the problem to counting representations on the compact form o
f $G_2$ and certain pairs of modular forms. This avoids involved computati
ons on the geometric side of the trace formula.\n\n30 min pre-talk before\
n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linus Hamann (Princeton)
DTSTART:20211104T210000Z
DTEND:20211104T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/46
DESCRIPTION:Title: Compatibility of the Fargues-Scholze and Gan-Takeda local Langlan
ds\nby Linus Hamann (Princeton) as part of UCSD number theory seminar\
n\nLecture held in APM 6402 and online.\n\nAbstract\nGiven a prime $p$\, a
finite extension $L/\\mathbb{Q}_{p}$\, a connected $p$-adic reductive gro
up $G/L$\, and a smooth irreducible representation $\\pi$ of $G(L)$\, Farg
ues-Scholze recently attached a semisimple Weil parameter to such $\\pi$\,
giving a general candidate for the local Langlands correspondence. It is
natural to ask whether this construction is compatible with known instance
s of the correspondence after semisimplification. For $G = GL_{n}$ and its
inner forms\, Fargues-Scholze and Hansen-Kaletha-Weinstein show that the
correspondence is compatible with the correspondence of Harris-Taylor/Hen
niart. We verify a similar compatibility for $G = GSp_{4}$ and its unique
non-split inner form $G = GU_{2}(D)$\, where $D$ is the quaternion divisio
n algebra over $L$\, assuming that $L/\\mathbb{Q}_{p}$ is unramified and $
p > 2$. In this case\, the local Langlands correspondence has been constru
cted by Gan-Takeda and Gan-Tantono. Analogous to the case of $GL_{n}$ and
its inner forms\, this compatibility is proven by describing the Weil grou
p action on the cohomology of a local Shimura variety associated to $GSp_{
4}$\, using basic uniformization of abelian type Shimura varieties due to
Shen\, combined with various global results of Kret-Shin and Sorensen on G
alois representations in the cohomology of global Shimura varieties associ
ated to inner forms of $GSp_{4}$ over a totally real field. After showing
the parameters are the same\, we apply some ideas from the geometry of the
Fargues-Scholze construction explored recently by Hansen\, to give a more
precise description of the cohomology of this local Shimura variety\, ver
ifying a strong form of the Kottwitz conjecture in the process.\n\npre-tal
k at 1:20pm.\n\nThe talk will be given via Zoom\, but we will meet in the
lecture hall as usual.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Dorfsman-Hopkins (UC Berkeley)
DTSTART:20211118T220000Z
DTEND:20211118T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/47
DESCRIPTION:Title: Untilting Line Bundles on Perfectoid Spaces\nby Gabriel Dorfs
man-Hopkins (UC Berkeley) as part of UCSD number theory seminar\n\nLecture
held in APM 7321 and online.\n\nAbstract\nLet $X$ be a perfectoid space w
ith tilt $X^\\flat$. We build a natural map $\\theta:\\Pic X^\\flat\\to\\
lim\\Pic X$ where the (inverse) limit is taken over the $p$-power map\, an
d show that $\\theta$ is an isomorphism if $R = \\Gamma(X\,\\sO_X)$ is a p
erfectoid ring. As a consequence we obtain a characterization of when the
Picard groups of $X$ and $X^\\flat$ agree in terms of the $p$-divisibilit
y of $\\Pic X$. The main technical ingredient is the vanishing of higher
derived limits of the unit group $R^*$\, whence the main result follows fr
om the Grothendieck spectral sequence.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Upton (UC San Diego)
DTSTART:20211202T220000Z
DTEND:20211202T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/48
DESCRIPTION:Title: Newton Polygons of Abelian $L$-Functions on Curves\nby James
Upton (UC San Diego) as part of UCSD number theory seminar\n\nLecture held
in APM 7321 and online.\n\nAbstract\nLet $X$ be a smooth\, affine\, geome
trically connected curve over a finite field of characteristic $p > 2$. Le
t $\\rho:\\pi_1(X) \\to \\mathbb{C}^\\times$ be a character of finite orde
r $p^n$. If $\\rho\\neq 1$\, then the Artin $L$-function $L(\\rho\,s)$ is
a polynomial\, and a theorem of Kramer-Miller states that its $p$-adic New
ton polygon $\\mathrm{NP}(\\rho)$ is bounded below by a certain Hodge poly
gon $\\mathrm{HP}(\\rho)$ which is defined in terms of local monodromy inv
ariants. In this talk we discuss the interaction between the polygons $\\m
athrm{NP}(\\rho)$ and $\\mathrm{HP}(\\rho)$. Our main result states that i
f $X$ is ordinary\, then $\\mathrm{NP}(\\rho)$ and $\\mathrm{HP}(\\rho)$ s
hare a vertex if and only if there is a corresponding vertex shared by cer
tain "local" Newton and Hodge polygons associated to each ramified point o
f $\\rho$. As an application\, we give a local criterion that is necessary
and sufficient for $\\mathrm{NP}(\\rho)$ and $\\mathrm{HP}(\\rho)$ to coi
ncide. This is joint work with Joe Kramer-Miller.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Organizational meeting (UCSD)
DTSTART:20210923T210000Z
DTEND:20210923T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/49
DESCRIPTION:Title: Organizational meeting (Zoom only)\nby Organizational meeting
(UCSD) as part of UCSD number theory seminar\n\nLecture held in APM 7321
and online.\n\nAbstract\nThis meeting will take place exclusively over Zoo
m.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Organizational meeting
DTSTART:20220106T220000Z
DTEND:20220106T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/50
DESCRIPTION:Title: Organizational meeting (Zoom only)\nby Organizational meeting
as part of UCSD number theory seminar\n\nLecture held in APM 6402 and onl
ine.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tong Liu (Purdue)
DTSTART:20220113T220000Z
DTEND:20220113T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/51
DESCRIPTION:Title: Prismatic F-crystal and lattice in crystalline representation
\nby Tong Liu (Purdue) as part of UCSD number theory seminar\n\n\nAbstract
\nIn this talk\, I will explain a theorem of Bhatt-Scholze: the equivalenc
e between prismatic $F$-crystal and $\\mathbb Z_p$-lattices inside crystal
line representation\, and how to extend this theorem to allow more general
types of base ring like Tate algebra ${\\mathbb Z}_p \\langle t^{\\pm 1}\
\rangle$. This is a joint work with Heng Du\, Yong-Suk Moon and Koji Shim
izu. \n\nThis is a talk in integral $p$-adic Hodge theory. So in the pre
-talk\, I will explain the motivations and base ideas in integral $p$-adic
Hodge theory.\n\nonline only\; pre-talk at 1:30\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudius Heyer (Münster)
DTSTART:20220120T220000Z
DTEND:20220120T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/52
DESCRIPTION:Title: The left adjoint of derived parabolic induction\nby Claudius
Heyer (Münster) as part of UCSD number theory seminar\n\n\nAbstract\nRece
nt advances in the theory of smooth mod $p$ representations of a $p$-adic\
nreductive group $G$ involve more and more derived methods. It becomes\ni
ncreasingly clear that the proper framework to study smooth mod $p$\nrepre
sentations is the derived category $D(G)$.\n\nI will talk about smooth mod
$p$ representations and highlight their\nshortcomings compared to\, say\,
smooth complex representations of $G$. After\nexplaining how the situati
on improves in the derived category\, I will spend the\nremaining time on
the left adjoint of the derived parabolic induction functor.\n\nThere will
be a pre-talk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petar Bakic (Utah)
DTSTART:20220127T220000Z
DTEND:20220127T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/53
DESCRIPTION:Title: Howe duality for exceptional theta correspondences\nby Petar
Bakic (Utah) as part of UCSD number theory seminar\n\nLecture held in onli
ne.\n\nAbstract\nThe theory of local theta correspondence is built up from
two main ingredients: a reductive dual pair inside a symplectic group\, a
nd a Weil representation of its metaplectic cover. Exceptional corresponde
nces arise similarly: dual pairs inside exceptional groups can be construc
ted using so-called Freudenthal Jordan algebras\, while the minimal repres
entation provides a suitable replacement for the Weil representation. The
talk will begin by recalling these constructions. Focusing on a particular
dual pair\, we will explain how one obtains Howe duality for the correspo
ndence in question. Finally\, we will discuss applications of these result
s. The new work in this talk is joint with Gordan Savin.\n\npre-talk at 1:
30pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Smith (Stanford)
DTSTART:20220203T220000Z
DTEND:20220203T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/54
DESCRIPTION:Title: $2^k$-Selmer groups and Goldfeld's conjecture\nby Alex Smith
(Stanford) as part of UCSD number theory seminar\n\nLecture held in APM 64
02 and online.\n\nAbstract\nTake $E$ to be an elliptic curve over a number
field whose four torsion obeys certain technical conditions. In this talk
\, we will outline a proof that 100% of the quadratic twists of $E$ have r
ank at most one. To do this\, we will find the distribution of $2^k$-Selme
r ranks in this family for every positive $k$. We will also show how are t
echniques may be applied to find the distribution of $2^k$-class groups of
quadratic fields.\n\nThe pre-talk will focus on the definition of Selmer
groups. We will also give some context for the study of the arithmetic sta
tistics of these groups.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabrielle De Micheli (UCSD)
DTSTART:20220210T220000Z
DTEND:20220210T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/55
DESCRIPTION:Title: Lattice Enumeration for Tower NFS: a 521-bit Discrete Logarithm C
omputation\nby Gabrielle De Micheli (UCSD) as part of UCSD number theo
ry seminar\n\nLecture held in APM 6402 and online.\n\nAbstract\nThe Tower
variant of the Number Field Sieve (TNFS) is known to be asymptotically the
most efficient algorithm to solve the discrete logarithm problem in finit
e fields of medium characteristics\, when the extension degree is composit
e. A major obstacle to an efficient implementation of TNFS is the collecti
on of algebraic relations\, as it happens in dimensions greater than 2. Th
is requires the construction of new sieving algorithms which remain effici
ent as the dimension grows. In this talk\, I will present how we overcome
this difficulty by considering a lattice enumeration algorithm which we a
dapt to this specific context. We also consider a new sieving area\, a hig
h-dimensional sphere\, whereas previous sieving algorithms for the classic
al NFS considered an orthotope. Our new sieving technique leads to a much
smaller running time\, despite the larger dimension of the search space\,
and even when considering a larger target\, as demonstrated by a record co
mputation we performed in a 521-bit finite field GF(p^6). The target finit
e field is of the same form as finite fields used in recent zero-knowledge
proofs in some blockchains. This is the first reported implementation of
TNFS.\n\nIn the pre-talk\, I will briefly present the core ideas of the qu
adratic sieve algorithm and its evolution to the Number Field Sieve algori
thm.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Pollack (UCSD)
DTSTART:20220217T220000Z
DTEND:20220217T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/56
DESCRIPTION:Title: A Cohen-Zagier modular form on G_2\nby Aaron Pollack (UCSD) a
s part of UCSD number theory seminar\n\nLecture held in APM 6402 and onlin
e.\n\nAbstract\nI will report on joint work with Spencer Leslie where we d
efine an analogue of the Cohen-Zagier Eisenstein series to the exceptional
group $G_2$. Recall that the Cohen-Zagier Eisenstein series is a weight $
3/2$ modular form whose Fourier coefficients see the class numbers of imag
inary quadratic fields. We define a particular modular form of weight $1/2
$ on $G_2$\, and prove that its Fourier coefficients see (certain torsors
for) the 2-torsion in the narrow class groups of totally real cubic fields
. In particular: 1) we define a notion of modular forms of half-integral w
eight on certain exceptional groups\, 2) we prove that these modular forms
have a nice theory of Fourier coefficients\, and 3) we partially compute
the Fourier coefficients of a particular nice example on G_2.\n\npre-talk
at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paulina Fust (Duisburg-Essen)
DTSTART:20220224T220000Z
DTEND:20220224T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/57
DESCRIPTION:Title: Continuous group cohomology and Ext-groups\nby Paulina Fust (
Duisburg-Essen) as part of UCSD number theory seminar\n\nLecture held in A
PM 6402 and online.\n\nAbstract\nWe prove that the continuous cohomology g
roups of a $p$-adic reductive group with coefficients in an admissible uni
tary $\\mathbb{Q}_p$-Banach space representation $\\Pi$ are finite-dimensi
onal and compare them to certain Ext-groups. As an application of this res
ult\, we show that the continuous cohomology of $SL_2(\\mathbb{Q}_p) $ wit
h values in non-ordinary irreducible $\\mathbb{Q}_p$-Banach space represen
tations of $GL_2(\\mathbb{Q}_p)$ vanishes.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annie Carter (UCSD)
DTSTART:20220303T170000Z
DTEND:20220303T180000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/58
DESCRIPTION:Title: Two-variable polynomials with dynamical Mahler measure zero\n
by Annie Carter (UCSD) as part of UCSD number theory seminar\n\n\nAbstract
\nIntroduced by Lehmer in 1933\, the classical Mahler measure of a complex
rational function $P$ in one or more variables is given by integrating $\
\log|P(x_1\, \\ldots\, x_n)|$ over the unit torus. Lehmer asked whether th
e Mahler measures of integer polynomials\, when nonzero\, must be bounded
away from zero\, a question that remains open to this day. In this talk we
generalize Mahler measure by associating it with a discrete dynamical sys
tem $f: \\mathbb{C} \\to \\mathbb{C}$\, replacing the unit torus by the $n
$-fold Cartesian product of the Julia set of $f$ and integrating with resp
ect to the equilibrium measure on the Julia set. We then characterize thos
e two-variable integer polynomials with dynamical Mahler measure zero\, co
nditional on a dynamical version of Lehmer's conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Urbanik (Toronto)
DTSTART:20220310T220000Z
DTEND:20220310T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/59
DESCRIPTION:Title: Effective Methods for Shafarevich Problems\nby David Urbanik
(Toronto) as part of UCSD number theory seminar\n\nLecture held in APM 732
1.\n\nAbstract\nGiven a smooth projective family $f : X \\to S$ defined ov
er\nthe ring of integers of a number field\, the Shafarevich problem is to
\ndescribe those fibres of f which have everywhere good reduction. This\nc
an be interpreted as asking for the dimension of the Zariski closure\nof t
he set of integral points of $S$\, and is ultimately a difficult\ndiophant
ine question about which little is known as soon as the\ndimension of $S$
is at least 2. Recently\, Lawrence and Venkatesh gave a\ngeneral strategy
for addressing such problems which requires as input\nlower bounds on the
monodromy of f over essentially arbitrary closed\nsubvarieties of $S$. In
this talk we review their ideas\, and describe\nrecent work which gives a
fully effective method for computing these\nlower bounds. This gives a ful
ly effective strategy for solving\nShafarevich-type problems for essential
ly arbitrary families $f$.\n\nThis week's talk is in APM 7321 rather than
APM 6402.\n\npre-talk at 1:20 pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amit Ophir (Hebrew U.)
DTSTART:20220414T170000Z
DTEND:20220414T180000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/60
DESCRIPTION:Title: Invariant norms on the p-adic Schrödinger representation\nby
Amit Ophir (Hebrew U.) as part of UCSD number theory seminar\n\nLecture h
eld in online.\n\nAbstract\nMotivated by questions about a p-adic Fourier
transform\, we study invariant norms on the p-adic Schrödinger representa
tions of Heisenberg groups. These Heisenberg groups are p-adic\, and the S
chrodinger representations are explicit irreducible smooth representations
that play an important role in their representation theory. \nClassically
\, the field of coefficients is taken to be the complex numbers and\, amon
g other things\, one studies the unitary completions of the representation
s (which are well understood). By taking the field of coefficients to be a
n extension of the p-adic numbers\, we can consider completions that bette
r capture the p-adic topology\, but at the cost of losing the Haar measure
and the $L^2$-norm. Nevertheless\, we establish a rigidity property for a
family of norms (parametrized by a Grassmannian) that are invariant under
the action of the Heisenberg group.\nThe irreducibility of some Banach re
presentations follows as a result. The proof uses "q-arithmetics".\n\npre-
talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Lawrence (UCLA)
DTSTART:20220428T210000Z
DTEND:20220428T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/61
DESCRIPTION:Title: Sparsity of Integral Points on Moduli Spaces of Varieties\nby
Brian Lawrence (UCLA) as part of UCSD number theory seminar\n\nLecture he
ld in APM 6402 and online.\n\nAbstract\nInteresting moduli spaces don't ha
ve many integral points. More precisely\, if X is a variety over a number
field\, admitting a variation of Hodge structure whose associate period m
ap is injective\, then the number of S-integral points on X of height at m
ost H grows more slowly than H^{\\epsilon}\, for any positive \\epsilon.
This is a sort of weak generalization of the Shafarevich conjecture\; it i
s a consequence of a point-counting theorem of Broberg\, and the largeness
of the fundamental group of X. Joint with Ellenberg and Venkatesh.\n\npr
e-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michelle Manes (U. Hawaii)
DTSTART:20220519T210000Z
DTEND:20220519T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/62
DESCRIPTION:Title: Iterating Backwards in Arithmetic Dynamics\nby Michelle Manes
(U. Hawaii) as part of UCSD number theory seminar\n\nLecture held in APM
6402 and online.\n\nAbstract\nIn classical real and complex dynamics\, one
studies topological and analytic properties of orbits of points under ite
ration of self-maps of $\\mathbb R$ or $\\mathbb C$ (or more generally sel
f-maps of a real or complex manifold). In arithmetic dynamics\, a more rec
ent subject\, one likewise studies properties of orbits of self-maps\, but
with a number theoretic flavor. Many of the motivating problems in arithm
etic dynamics come via analogy with classical problems in arithmetic geome
try: rational and integral points on varieties correspond to rational and
integral points in orbits\; torsion points on abelian varieties correspond
to periodic and preperiodic points of rational maps\; and abelian varieti
es with complex multiplication correspond to post-critically finite ration
al maps.\n\nThis analogy focuses on forward iteration\, but sometimes surp
rising and interesting results can be found by thinking instead about pre-
images of rational points under iteration. In this talk\, we will give som
e background and motivation for the field of arithmetic dynamics in order
to describe some of these "backwards iteration" results\, including unifor
m boundedness for rational pre-images and open image results for Galois re
presentations associated to dynamical systems.\n\nA pre-talk for graduate
students will describe some of the motivating results in arithmetic geomet
ry.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Koji Shimizu (UC Berkeley)
DTSTART:20220526T210000Z
DTEND:20220526T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/63
DESCRIPTION:Title: Robba site and Robba cohomology\nby Koji Shimizu (UC Berkeley
) as part of UCSD number theory seminar\n\nLecture held in APM 6402 and on
line.\n\nAbstract\nWe will discuss a $p$-adic cohomology theory for rigid
analytic varieties with overconvergent structure (dagger spaces) over a lo
cal field of characteristic $p$. After explaining the motivation\, we will
define a site (Robba site) and discuss its basic properties.\n\nThe main
talk will be preceded by a pre-talk.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hansen (MPIM)
DTSTART:20220407T210000Z
DTEND:20220407T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/64
DESCRIPTION:Title: Duality and the p-adic Jacquet-Langlands correspondence\nby D
avid Hansen (MPIM) as part of UCSD number theory seminar\n\nLecture held i
n APM 6402 and online.\n\nAbstract\nIn joint work with Lucas Mann\, we est
ablish several new properties of the p-adic Jacquet-Langlands functor defi
ned by Scholze in terms of the cohomology of the Lubin-Tate tower. In part
icular\, we prove a duality theorem\, establish bounds on Gelfand-Kirillov
dimension\, prove some non-vanishing results\, and show a kind of partial
Künneth formula. The key new tool is the six functor formalism with soli
d almost $\\mathcal{O}^+/p$-coefficients developed recently by Mann.\n\nPr
e-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Organizational meeting
DTSTART:20220331T210000Z
DTEND:20220331T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/65
DESCRIPTION:Title: Organizational meeting (Zoom only)\nby Organizational meeting
as part of UCSD number theory seminar\n\nLecture held in online.\nAbstrac
t: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Kling (U. Arizona)
DTSTART:20220421T210000Z
DTEND:20220421T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/66
DESCRIPTION:Title: Comparison of Integral Structures on the Space of Modular Forms o
f Full Level $N$\nby Anthony Kling (U. Arizona) as part of UCSD number
theory seminar\n\nLecture held in APM 6402 and online.\n\nAbstract\nLet $
N\\geq3$ and $r\\geq1$ be integers and $p\\geq2$ be a prime such that $p\\
nmid N$. One can consider two different integral structures on the space o
f modular forms over $\\mathbb{Q}$\, one coming from arithmetic via $q$-ex
pansions\, the other coming from geometry via integral models of modular c
urves. Both structures are stable under the Hecke operators\; furthermore\
, their quotient is finite torsion. Our goal is to investigate the exponen
t of the annihilator of the quotient. We will apply results due to Brian C
onrad to the situation of modular forms of even weight and level $\\Gamma(
Np^{r})$ over $\\mathbb{Q}_{p}(\\zeta_{Np^{r}})$ to obtain an upper bound
for the exponent. We also use Klein forms to construct explicit modular fo
rms of level $p^{r}$ whenever $p^{r}>3$\, allowing us to compute a lower b
ound which agrees with the upper bound. Hence we are able to compute the e
xponent precisely.\n\npre-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masahiro Nakahara (U. Washington)
DTSTART:20220505T210000Z
DTEND:20220505T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/67
DESCRIPTION:Title: Uniform potential density for rational points on algebraic groups
and elliptic K3 surfaces\nby Masahiro Nakahara (U. Washington) as par
t of UCSD number theory seminar\n\nLecture held in APM 6402 and online.\n\
nAbstract\nA variety satisfies potential density if it contains a dense su
bset of rational points after extending its ground field by a finite degre
e. A collection of varieties satisfies uniform potential density if that d
egree can be uniformly bounded. I will discuss this property for connected
algebraic groups of a fixed dimension and elliptic K3 surfaces. This is j
oint work with Kuan-Wen Lai.\n\npre-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gyujin Oh (Princeton)
DTSTART:20220512T210000Z
DTEND:20220512T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/68
DESCRIPTION:Title: A cohomological approach to harmonic Maass forms\nby Gyujin O
h (Princeton) as part of UCSD number theory seminar\n\nLecture held in APM
6402 and online.\n\nAbstract\nWe interpret a harmonic Maass form as a var
iant of a local cohomology class of the modular curve. This is not only am
enable to algebraic interpretation\, but also nicely generalized to other
Shimura varieties\, avoiding the barrier of Koecher's principle\, which co
uld be useful for developing a generalization of Borcherds lifts. In this
talk\, we will exhibit how the theory looks like in the case of Hilbert mo
dular varities.\n\npre-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Florea (UC Irvine)
DTSTART:20220602T210000Z
DTEND:20220602T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/69
DESCRIPTION:Title: Negative moments of the Riemann zeta function\nby Alexandra F
lorea (UC Irvine) as part of UCSD number theory seminar\n\nLecture held in
APM 6402 and online.\n\nAbstract\nI will talk about recent work towards a
conjecture of Gonek regarding negative shifted moments of the Riemann zet
a function. I will explain how to obtain asymptotic formulas when the shif
t in the Riemann zeta function is big enough\, and how we can obtain non-t
rivial upper bounds for smaller shifts. Joint work with H. Bui.\n\npre-tal
k at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Organizational meeting (UCSD)
DTSTART:20220929T210000Z
DTEND:20220929T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/70
DESCRIPTION:Title: Organizational meeting (APM 7321)\nby Organizational meeting
(UCSD) as part of UCSD number theory seminar\n\nLecture held in APM 6402 a
nd online.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Klevdal (UCSD)
DTSTART:20221006T210000Z
DTEND:20221006T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/71
DESCRIPTION:Title: Strong independence of $\\ell$ for Shimura varieties\nby Chri
stian Klevdal (UCSD) as part of UCSD number theory seminar\n\nLecture held
in APM 6402 and online.\n\nAbstract\n(Joint with Stefan Patrikis.) In thi
s talk\, we discuss a strong form of independence of $\\ell$ for canonical
$\\ell$-adic local systems on Shimura varieties\, and sketch a proof of t
his for Shimura varieties arising from adjoint groups whose simple factors
have real rank $\\geq 2$. Notably\, this includes all adjoint Shimura var
ieties which are not of abelian type. The key tools used are the existence
of companions for $\\ell$-adic local systems and the superrigidity theore
m of Margulis for lattices in Lie groups of real rank $\\geq 2$. \n\nThe
independence of $\\ell$ is motivated by a conjectural description of Shimu
ra varieties as moduli spaces of motives. For certain Shimura varieties th
at arise as a moduli space of abelian varieties\, the strong independence
of $\\ell$ is proven (at the level of Galois representations) by recent wo
rk of Kisin and Zhou\, refining the independence of $\\ell$ on the Tate mo
dule given by Deligne's work on the Weil conjectures.\n\npre-talk at 1:20p
m\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shishir Agrawal (UCSD)
DTSTART:20221013T210000Z
DTEND:20221013T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/72
DESCRIPTION:Title: From category $\\mathcal{O}^\\infty$ to locally analytic represen
tations\nby Shishir Agrawal (UCSD) as part of UCSD number theory semin
ar\n\nLecture held in APM 6402 and online.\n\nAbstract\nLet $G$ be a $p$-a
dic reductive group with $\\mathfrak{g} = \\mathrm{Lie}(G)$. I will summar
ize work with Matthias Strauch in which we construct an exact functor from
category $\\mathcal{O}^\\infty$\, the extension closure of the Bernstein-
Gelfand-Gelfand category $\\mathcal{O}$ inside the category of $U(\\mathfr
ak{g})$-modules\, into the category of admissible locally analytic represe
ntations of $G$. This expands on an earlier construction by Sascha Orlik a
nd Matthias Strauch. A key role in our new construction is played by $p$-a
dic logarithms on tori\, and representations in the image of this functor
are related to some that are known to arise in the context of the $p$-adic
Langlands program.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Aycock (UCSD)
DTSTART:20221020T210000Z
DTEND:20221020T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/73
DESCRIPTION:Title: Differential operators for overconvergent Hilbert modular forms\nby Jon Aycock (UCSD) as part of UCSD number theory seminar\n\nLecture
held in APM 6402 and online.\n\nAbstract\nIn 1978\, Katz gave a constructi
on of the $p$-adic $L$-function of a CM field by using a $p$-adic analog o
f the Maass--Shimura operators acting on $p$-adic Hilbert modular forms. H
owever\, this $p$-adic Maass--Shimura operator is only defined over the or
dinary locus\, which restricted Katz's choice of $p$ to one that splits in
the CM field. In 2021\, Andreatta and Iovita extended Katz's construction
to all $p$ for quadratic imaginary fields using overconvergent differenti
al operators constructed by Harron--Xiao and Urban\, which act on elliptic
modular forms. Here we give a construction of such overconvergent differe
ntial operators which act on Hilbert modular forms.\n\npre-talk at 1:20pm\
n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rusiru Gambheera Arachchige (UCSD)
DTSTART:20221027T210000Z
DTEND:20221027T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/74
DESCRIPTION:Title: An unconditional equivariant main conjecture in Iwasawa theory\nby Rusiru Gambheera Arachchige (UCSD) as part of UCSD number theory sem
inar\n\nLecture held in APM 6402 and online.\n\nAbstract\nIn 2015 Greither
and Popescu constructed a new class of Iwasawa modules\, which are the nu
mber field analogues of $p-$adic realizations of Picard 1- motives constru
cted by Deligne. They proved an equivariant main conjecture by computing t
he Fitting ideal of these new modules over the appropriate profinite group
ring. This is an integral\, equivariant refinement of Wiles' classical ma
in conjecture. As a consequence they proved a refinement of the Brumer-Sta
rk conjecture away from 2. All of the above was proved under the assumptio
n that the relevant prime $p$ is odd and that the appropriate classical Iw
asawa $\\mu$–invariants vanish. Recently\, Dasgupta and Kakde proved the
Brumer-Stark conjecture\, away from 2\, unconditionally\, using a general
ization of Ribet's method. We use the Dasgupta-Kakde results to prove an u
nconditional equivariant main conjecture\, which is a generalization of th
at of Greither and Popescu. As applications of our main theorem we prove a
generalization of a certain case of the main result of Dasgupta-Kakde and
we compute the Fitting ideal of a certain naturally arising Iwasawa modul
e. This is joint work with Cristian Popescu.\n\npre-talk at 1:20\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Finn McGlade (UCSD)
DTSTART:20221103T210000Z
DTEND:20221103T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/75
DESCRIPTION:Title: Fourier coefficients on quaternionic U(2\,n)\nby Finn McGlade
(UCSD) as part of UCSD number theory seminar\n\nLecture held in APM 6402
and online.\n\nAbstract\nLet $E/\\mathbb{Q}$ be an imaginary quadratic ext
ension and suppose $G$ is the unitary group attached to hermitian space ov
er $E$ of signature $(2\,n)$. The symmetric domain $X$ attached to $G$ is
a quaternionic Kahler manifold. In the late nineties N. Wallach studied ha
rmonic analysis on $X$ in the context of this quaternionic structure. He e
stablished a multiplicity one theorem for spaces of generalized Whittaker
periods appearing in the cohomology of certain $G$-bundles on $X$. \n\nWe
prove an analogous multiplicity one statement for some degenerate generali
zed Whittaker periods and give explicit formulas for these periods in term
s of modified K-Bessel functions. Our results give a refinement of the Fou
rier expansion of certain automorphic forms on $G$ which are quaternionic
discrete series at infinity. As an application\, we study the Fourier expa
nsion of cusp forms on $G$ which arise as theta lifts of holomorphic modul
ar forms on quasi-split $\\mathrm{U}(1\,1)$. We show that these cusp forms
can be normalized so that all their Fourier coefficients are algebraic nu
mbers. (joint with Anton Hilado and Pan Yan)\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kalyani Kansal (Johns Hopkins)
DTSTART:20221110T220000Z
DTEND:20221110T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/76
DESCRIPTION:Title: Intersections of components of Emerton-Gee stack for $\\mathrm{GL
}_2$\nby Kalyani Kansal (Johns Hopkins) as part of UCSD number theory
seminar\n\nLecture held in APM 6402 and online.\n\nAbstract\nThe Emerton-G
ee stack for $\\mathrm{GL}_2$ is a stack of $(\\varphi\, \\Gamma)$-modules
whose reduced part $\\mathcal{X}_{2\, \\mathrm{red}}$ can be viewed as a
moduli stack of mod $p$ representations of a $p$-adic Galois group. We com
pute criteria for codimension one intersections of the irreducible compone
nts of $\\mathcal{X}_{2\, \\mathrm{red}}$\, and interpret them in sheaf-th
eoretic terms. We also give a cohomological criterion for the number of to
p-dimensional components in a codimension one intersection.\n\npre-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romyar Sharifi (UCLA)
DTSTART:20221117T220000Z
DTEND:20221117T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/77
DESCRIPTION:Title: Cohomology of intermediate quotients\nby Romyar Sharifi (UCLA
) as part of UCSD number theory seminar\n\nLecture held in APM 6402 and on
line.\n\nAbstract\nWe will discuss Galois cohomology groups of “intermed
iate” quotients of an induced module\, which sit between Iwasawa cohomol
ogy up a tower and cohomology over the ground field. Special elements in I
wasawa cohomology that arise from Euler systems become divisible by a cert
ain Euler factor upon norming down to the ground field. In certain instanc
es\, there are reasons to wonder whether this divisibility can also hold f
or the image in intermediate cohomology. Using “intermediate” Coleman
maps\, we shall see that the situation locally at $p$ is as nice as one co
uld imagine.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Keyes (Emory)
DTSTART:20221201T220000Z
DTEND:20221201T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/78
DESCRIPTION:Title: Local solubility in families of superelliptic curves\nby Chri
stopher Keyes (Emory) as part of UCSD number theory seminar\n\nLecture hel
d in APM 6402 and online.\n\nAbstract\nIf we choose at random an integral
binary form $f(x\, z)$ of fixed degree $d$\, what is the probability that
the superelliptic curve with equation $C \\colon: y^m = f(x\, z)$ has a $
p$-adic point\, or better\, points everywhere locally? In joint work with
Lea Beneish\, we show that the proportion of forms $f(x\, z)$ for which $C
$ is everywhere locally soluble is positive\, given by a product of local
densities. By studying these local densities\, we produce bounds which are
suitable enough to pass to the large $d$ limit. In the specific case of c
urves of the form $y^3 = f(x\, z)$ for a binary form of degree 6\, we dete
rmine the probability of everywhere local solubility to be 96.94%\, with t
he exact value given by an explicit infinite product of rational function
expressions.\n\npre-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Marshall (Wisconsin)
DTSTART:20230209T220000Z
DTEND:20230209T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/79
DESCRIPTION:Title: Large values of eigenfunctions on hyperbolic manifolds\nby Si
mon Marshall (Wisconsin) as part of UCSD number theory seminar\n\nLecture
held in APM 6402 and online.\n\nAbstract\nIt is a folklore conjecture that
the sup norm of a Laplace eigenfunction on a compact hyperbolic surface g
rows more slowly than any positive power of the eigenvalue. In dimensions
three and higher\, this was shown to be false by Iwaniec-Sarnak and Donne
lly. I will present joint work with Farrell Brumley that strengthens thes
e results\, and extends them to locally symmetric spaces associated to $\\
mathrm{SO}(p\,q)$.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jef Laga (Cambridge)
DTSTART:20230309T220000Z
DTEND:20230309T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/80
DESCRIPTION:Title: Arithmetic statistics via graded Lie algebras\nby Jef Laga (C
ambridge) as part of UCSD number theory seminar\n\nLecture held in APM 640
2 and online.\n\nAbstract\nI will explain how various results in arithmeti
c statistics by Bhargava\, Gross\, Shankar and others on 2-Selmer groups o
f Jacobians of (hyper)elliptic curves can be organised and reproved using
the theory of graded Lie algebras\, following earlier work of Thorne. This
gives a uniform proof of these results and yields new theorems for certai
n families of non-hyperelliptic curves. I will also mention some applicati
ons to rational points on certain families of curves.\n\nThe talk will inv
olve a mixture of representation theory\, number theory and algebraic geom
etry and I will assume no familiarity with arithmetic statistics.\n\npre-t
alk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Longke Tang (Princeton)
DTSTART:20230119T220000Z
DTEND:20230119T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/81
DESCRIPTION:Title: Prismatic Poincaré duality\nby Longke Tang (Princeton) as pa
rt of UCSD number theory seminar\n\nLecture held in APM 6402 and online.\n
\nAbstract\nPrismatic cohomology is a new p-adic cohomology theory introdu
ced by Bhatt and Scholze that specializes to various well-known cohomology
theories such as étale\, de Rham and crystalline. I will roughly recall
the properties of this cohomology and explain how to prove its Poincaré d
uality.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nolan Wallach (UC San Diego)
DTSTART:20230126T220000Z
DTEND:20230126T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/82
DESCRIPTION:Title: The Whittaker Inversion Theorem and some applications\nby Nol
an Wallach (UC San Diego) as part of UCSD number theory seminar\n\nLecture
held in APM 6402 and online.\n\nAbstract\nThe Whittaker Plancherel theore
m appeared as Chapter 15 in my two volume book\, Real Reductive Groups. It
was meant to be an application of Harish-Chandra’s Plancherel Theorem.
As it turns out\, there are serious gaps in the proof given in the books.
At the same time as I was doing my research on the subject\, Harish-Chand
ra was also working on it. His approach was very different from mine and a
ppears as part of Volume 5 of his collected works\; which consists of thre
e pieces of research by Harish-Chandra that were incomplete at his death a
nd organized and edited by Gangolli and Varadarajan. Unfortunately\, it a
lso does not contain a proof of the theorem. There was a complication in t
he proof of this result that caused substantial difficulties which had to
do with the image of the analog of Harish-Chandra’s method of descent. I
n this lecture I will explain how one can complete the proof using a recen
t result of Raphael Beuzzart-Plessis. I will also give an application of t
he result to the Fourier transforms of automorphic functions at cusps.\n\n
(This seminar will be given remotely\, but there will still be a live audi
ence in the lecture room.)\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xu Gao (UC Santa Cruz)
DTSTART:20230316T210000Z
DTEND:20230316T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/83
DESCRIPTION:Title: $p$-adic representations and simplicial distance in Bruhat-Tits b
uildings\nby Xu Gao (UC Santa Cruz) as part of UCSD number theory semi
nar\n\nLecture held in APM 6402 and online.\n\nAbstract\n$p$-adic represen
tations are important objects in number theory\, and stable lattices serve
as a connection between the study of ordinary and modular representations
. These stable lattices can be understood as stable vertices in Bruhat-Tit
s buildings. From this viewpoint\, the study of fixed point sets in these
buildings can aid research on $p$-adic representations. The simplicial dis
tance holds an important role as it connects the combinatorics of lattices
and the geometry of root systems. In particularly\, the fixed-point sets
of Moy-Prasad subgroups are precisely the simplicial balls. In this talk\,
I'll explain those findings and compute their simplicial volume under cer
tain conditions.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sameera Vemulapalli (Princeton)
DTSTART:20230223T220000Z
DTEND:20230223T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/84
DESCRIPTION:Title: Counting low degree number fields with almost prescribed successi
ve minima\nby Sameera Vemulapalli (Princeton) as part of UCSD number t
heory seminar\n\nLecture held in APM 6402 and online.\n\nAbstract\nThe suc
cessive minima of an order in a degree n number field are n real numbers e
ncoding information about the Euclidean structure of the order. How many o
rders in degree n number fields are there with almost prescribed successiv
e minima\, fixed Galois group\, and bounded discriminant? In this talk\, I
will address this question for n = 3\, 4\, 5. The answers\, appropriately
interpreted\, turn out to be piecewise linear functions on certain convex
bodies. If time permits\, I will also discuss function field analogues of
this problem.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yujie Xu (MIT)
DTSTART:20230302T220000Z
DTEND:20230302T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/85
DESCRIPTION:Title: Hecke algebras for p-adic groups and the explicit Local Langlands
Correspondence for G_2\nby Yujie Xu (MIT) as part of UCSD number theo
ry seminar\n\nLecture held in APM 6402 and online.\n\nAbstract\nI will tal
k about my recent joint work with Aubert where we prove the Local Langland
s Conjecture for G_2 (explicitly). This uses our earlier results on Hecke
algebras attached to Bernstein components of reductive p-adic groups\, as
well as an expected property on cuspidal support\, along with a list of ch
aracterizing properties. In particular\, we obtain "mixed" L-packets conta
ining F-singular supercuspidals and non-supercuspidals.\n\npre-talk at 1:2
0pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arghya Sadhukhan (Maryland)
DTSTART:20230112T220000Z
DTEND:20230112T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/86
DESCRIPTION:Title: Understanding the dimension of some (union of) affine Deligne-Lus
ztig varieties via the quantum Bruhat graph\nby Arghya Sadhukhan (Mary
land) as part of UCSD number theory seminar\n\nLecture held in APM 6402 an
d online.\n\nAbstract\nThe study of affine Deligne-Lusztig varieties (ADLV
s) $X_w(b)$ and their certain union $X(\\mu\,b)$ has been crucial in under
standing mod-$p$ reduction of Shimura varieties\; for instance\, precise i
nformation about the connected components of ADLVs (in the hyperspecial le
vel) has proved to be useful in Kisin's proof of the Langlands-Rapoport co
njecture. On the other hand\, first introduced in the context of enumerati
ve geometry to describe the quantum cohomology ring of complex flag variet
ies\, quantum Bruhat graphs have found recent applications in solving cert
ain problems on the ADLVs. I will survey such developments and report on m
y work surrounding a dimension formula for $X(\\mu\,b)$ in the quasi-split
case\, as well as some partial description of the dimension and top-dimen
sional irreducible components in the non quasi-split case.\n\npre-talk at
1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Vallieres (CSU Chico/UC San Diego)
DTSTART:20230216T220000Z
DTEND:20230216T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/87
DESCRIPTION:Title: Iwasawa theory and graph theory\nby Daniel Vallieres (CSU Chi
co/UC San Diego) as part of UCSD number theory seminar\n\nLecture held in
APM 6402 and online.\n\nAbstract\nAnalogies between number theory and grap
h theory have been studied for quite some times now. During the past few
years\, it has been observed in particular that there is an analogy betwee
n classical Iwasawa theory and some phenomena in graph theory. In this ta
lk\, we will explain this analogy and present some of the results that hav
e been obtained so far in this area.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilyoung Cheong (UC Irvine)
DTSTART:20230202T220000Z
DTEND:20230202T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/88
DESCRIPTION:Title: Polynomial equations for matrices over integers modulo a prime po
wer and the cokernel of a random matrix\nby Gilyoung Cheong (UC Irvine
) as part of UCSD number theory seminar\n\nLecture held in APM 6402 and on
line.\n\nAbstract\nOver a commutative ring of finite cardinality\, how man
y $n \\times n$ matrices satisfy a polynomial equation? In this talk\, I w
ill explain how to solve this question when the ring is given by integers
modulo a prime power and the polynomial is square-free modulo the prime. T
hen I will discuss how this question is related to the distribution of the
cokernel of a random matrix and the Cohen--Lenstra heuristics. This is jo
int work with Yunqi Liang and Michael Strand\, as a result of a summer und
ergraduate research I mentored.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keegan Ryan (UC San Diego)
DTSTART:20230420T210000Z
DTEND:20230420T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/89
DESCRIPTION:Title: Fast Practical Lattice Reduction through Iterated Compression
\nby Keegan Ryan (UC San Diego) as part of UCSD number theory seminar\n\nL
ecture held in APM 6402 and online.\n\nAbstract\nWe introduce a new lattic
e basis reduction algorithm with approximation guarantees analogous to the
LLL algorithm and practical performance that far exceeds the current stat
e of the art. We achieve these results by iteratively applying precision m
anagement techniques within a recursive algorithm structure and show the s
tability of this approach. We analyze the asymptotic behavior of our algor
ithm\, and show that the heuristic running time is $O(n^{\\omega}(C+n)^{1+
\\varepsilon})$ for lattices of dimension $n$\, $\\omega\\in (2\,3]$ bound
ing the cost of size reduction\, matrix multiplication\, and QR factorizat
ion\, and $C$ bounding the log of the condition number of the input basis
$B$. This yields a running time of $O\\left(n^\\omega (p + n)^{1 + \\varep
silon}\\right)$ for precision $p = O(\\log \\|B\\|_{max})$ in common appli
cations. Our algorithm is fully practical\, and we have published our impl
ementation. We experimentally validate our heuristic\, give extensive benc
hmarks against numerous classes of cryptographic lattices\, and show that
our algorithm significantly outperforms existing implementations.\n\npre-t
alk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanlin Cai (Utah)
DTSTART:20230504T210000Z
DTEND:20230504T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/91
DESCRIPTION:Title: Perfectoid signature and local étale fundamental group\nby H
anlin Cai (Utah) as part of UCSD number theory seminar\n\nLecture held in
APM 6402 and online.\n\nAbstract\nIn this talk I'll talk about a (perfecto
id) mixed characteristic version of F-signature and Hilbert-Kunz multiplic
ity by utilizing the perfectoidization functor of Bhatt-Scholze and Faltin
gs' normalized length. These definitions coincide with the classical theor
y in equal characteristic. Moreover\, perfectoid signature detects BCM reg
ularity and transforms similarly to F-signature or normalized volume under
quasi-étale maps. As a consequence\, we can prove that BCM-regular rings
have finite local étale fundamental group and torsion part of their divi
sor class groups. This is joint work with Seungsu Lee\, Linquan Ma\, Karl
Schwede and Kevin Tucker.\n\npre-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Kobin (Emory)
DTSTART:20230518T210000Z
DTEND:20230518T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/92
DESCRIPTION:Title: Categorifying zeta and L-functions\nby Andrew Kobin (Emory) a
s part of UCSD number theory seminar\n\nLecture held in APM 6402 and onlin
e.\n\nAbstract\nZeta and L-functions are ubiquitous in modern number theor
y. While some work in the past has brought homotopical methods into the th
eory of zeta functions\, there is in fact a lesser-known zeta function tha
t is native to homotopy theory. Namely\, every suitably finite decompositi
on space (aka 2-Segal space) admits an abstract zeta function as an elemen
t of its incidence algebra. In this talk\, I will show how many 'classical
' zeta functions in number theory and algebraic geometry can be realized i
n this homotopical framework. I will also discuss work in progress towards
a categorification of motivic zeta and L-functions.\n\npre-talk at 1:20pm
\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samit Dasgupta (Duke)
DTSTART:20230511T210000Z
DTEND:20230511T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/93
DESCRIPTION:Title: Ribet’s Lemma\, the Brumer-Stark Conjecture\, and the Main Conj
ecture\nby Samit Dasgupta (Duke) as part of UCSD number theory seminar
\n\nLecture held in APM 6402 and online.\n\nAbstract\nIn 1976\, Ken Ribet
used modular techniques to prove an important relationship between class g
roups of cyclotomic fields and special values of the zeta function. Ribet
’s method was generalized to prove the Iwasawa Main Conjecture for odd p
rimes p by Mazur-Wiles over Q and by Wiles over arbitrary totally real fie
lds. \n\nCentral to Ribet’s technique is the construction of a nontrivi
al extension of one Galois character by another\, given a Galois represent
ation satisfying certain properties. Throughout the literature\, when wor
king integrally at p\, one finds the assumption that the two characters ar
e not congruent mod p. For instance\, in Wiles’ proof of the Main Conje
cture\, it is assumed that p is odd precisely because the relevant charact
ers might be congruent modulo 2\, though they are necessarily distinct mod
ulo any odd prime.\n\nIn this talk I will present a proof of Ribet’s Lem
ma in the case that the characters are residually indistinguishable. As a
rithmetic applications\, one obtains a proof of the Iwasawa Main Conjectur
e for totally real fields at p=2. Moreover\, we complete the proof of the
Brumer-Stark conjecture by handling the localization at p=2\, building on
joint work with Mahesh Kakde for odd p. Our results yield the full Equiv
ariant Tamagawa Number conjecture for the minus part of the Tate motive as
sociated to a CM abelian extension of a totally real field\, which has man
y important corollaries.\n\nThis is joint work with Mahesh Kakde\, Jesse S
illiman\, and Jiuya Wang.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nha Truong (Hawaii)
DTSTART:20230406T210000Z
DTEND:20230406T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/94
DESCRIPTION:Title: Slopes of modular forms and geometry of eigencurves\nby Nha T
ruong (Hawaii) as part of UCSD number theory seminar\n\nLecture held in AP
M 6402 and online.\n\nAbstract\nThe slopes of modular forms are the $p$-ad
ic valuations of the eigenvalues of the Hecke operators $T_p$. The study o
f slopes plays an important role in understanding the geometry of the eige
ncurves\, introduced by Coleman and Mazur. \n\nThe study of the slope bega
n in the 1990s when Gouvea and Mazur computed many numerical data and made
several interesting conjectures. Later\, Buzzard\, Calegari\, and other p
eople made more precise conjectures by studying the space of overconvergen
t modular forms. Recently\, Bergdall and Pollack introduced the ghost conj
ecture that unifies the previous conjectures in most cases. The ghost conj
ecture states that the slope can be predicted by an explicitly defined pow
er series. We prove the ghost conjecture under a certain mild technical co
ndition. In the pre-talk\, I will explain an example in the quaternionic s
etting which was used as a testing ground for the proof. \nThis is joint w
ork with Ruochuan Liu\, Liang Xiao\, and Bin Zhao.\n\npre-talk at 1:30pm (
note unusual time)\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Somnath Jha (IIT Kanpur)
DTSTART:20230427T210000Z
DTEND:20230427T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/95
DESCRIPTION:Title: Rational cube sum problem\nby Somnath Jha (IIT Kanpur) as par
t of UCSD number theory seminar\n\nLecture held in APM 6402 and online.\n\
nAbstract\nThe classical Diophantine problem of determining which integer
s can be written as a sum of two rational cubes has a long history\; it in
cludes works of Sylvester\, Selmer\, Satgé\, Leiman and the recent work
of Alpöge-Bhargava-Shnidman-Burungale-Skinner. In this talk\, we will
use Selmer groups of elliptic curves and integral binary cubic forms to s
tudy some cases of the rational cube sum problem. This talk is based on
joint works with D. Majumdar\, P. Shingavekar and B. Sury.\n\npre-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Bucur (UC San Diego)
DTSTART:20230413T210000Z
DTEND:20230413T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/96
DESCRIPTION:Title: Counting $D_4$ quartic extensions of a number field ordered by di
scriminant\nby Alina Bucur (UC San Diego) as part of UCSD number theor
y seminar\n\nLecture held in APM 6402 and online.\n\nAbstract\nA guiding q
uestion in number theory\, specifically in arithmetic statistics\, is coun
ting number fields of fixed degree and Galois group as their discriminants
grow to infinity. We will discuss the history of this question and take
a closer look at the story in the case of quartic fields. In joint work wi
th Florea\, Serrano Lopez\, and Varma\, we extend and make explicit the co
unts of extensions of an arbitrary number field that was done over the ra
tionals by Cohen\, Diaz y Diaz\, and Olivier.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Hsu (Swarthmore College)
DTSTART:20230601T210000Z
DTEND:20230601T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/97
DESCRIPTION:Title: Explicit non-Gorenstein R=T via rank bounds\nby Catherine Hsu
(Swarthmore College) as part of UCSD number theory seminar\n\nLecture hel
d in APM 6402 and online.\n\nAbstract\nIn his seminal work on modular curv
es and the Eisenstein ideal\, Mazur studied the existence of congruences b
etween certain Eisenstein series and newforms\, proving that Eisenstein id
eals associated to weight 2 cusp forms of prime level are locally principa
l. In this talk\, we'll explore generalizations of Mazur's result to squar
efree level\, focusing on recent work\, joint with P. Wake and C. Wang-Eri
ckson\, about a non-optimal level N that is the product of two distinct pr
imes and where the Galois deformation ring is not expected to be Gorenstei
n. First\, we will outline a Galois-theoretic criterion for the deformatio
n ring to be as small as possible\, and when this criterion is satisfied\,
deduce an R=T theorem. Then we'll discuss some of the techniques required
to computationally verify the criterion.\n\nPre-talk\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Organizational meeting
DTSTART:20230928T210000Z
DTEND:20230928T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/98
DESCRIPTION:Title: Organizational meeting (no Zoom)\nby Organizational meeting a
s part of UCSD number theory seminar\n\nLecture held in APM 6402 and onlin
e.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Pollack (UC San Diego)
DTSTART:20231005T210000Z
DTEND:20231005T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/99
DESCRIPTION:Title: Arithmeticity of quaternionic modular forms on G_2\nby Aaron
Pollack (UC San Diego) as part of UCSD number theory seminar\n\nLecture he
ld in APM 6402 and online.\n\nAbstract\nQuaternionic modular forms (QMFs)
on the split exceptional group G_2 are a special class of automorphic func
tions on this group\, whose origin goes back to work of Gross-Wallach and
Gan-Gross-Savin. While the group G_2 does not possess any holomorphic mod
ular forms\, the quaternionic modular forms seem to be able to be a good s
ubstitute. In particular\, QMFs on G_2 possess a semi-classical Fourier e
xpansion and Fourier coefficients\, just like holomorphic modular forms on
Shimura varieties. I will explain the proof that the cuspidal QMFs of ev
en weight at least 6 admit an arithmetic structure: there is a basis of th
e space of all such cusp forms\, for which every Fourier coefficient of ev
ery element of this basis lies in the cyclotomic extension of Q.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (UC Berkeley)
DTSTART:20231116T220000Z
DTEND:20231116T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/100
DESCRIPTION:Title: Mirror symmetry and the Breuil-Mezard Conjecture\nby Tony Fe
ng (UC Berkeley) as part of UCSD number theory seminar\n\n\nAbstract\nThe
Breuil-Mezard Conjecture predicts the existence of hypothetical "Breuil-Me
zard cycles" that should govern congruences between mod p automorphic form
s on a reductive group G. Most of the progress thus far has been concentra
ted on the case G = GL_2\, which has several special features. I will talk
about joint work with Bao Le Hung on a new approach to the Breuil-Mezard
Conjecture\, which applies for arbitrary groups (and in particular\, in ar
bitrary rank). It is based on the intuition that the Breuil-Mezard conject
ure is analogous to homological mirror symmetry.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shou-Wu Zhang (Princeton)
DTSTART:20231109T220000Z
DTEND:20231109T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/101
DESCRIPTION:Title: Triple product L-series and Gross–Kudla–Schoen cycles\nb
y Shou-Wu Zhang (Princeton) as part of UCSD number theory seminar\n\nLectu
re held in APM 6402 and online.\n\nAbstract\nIn this talk\, we consider a
conjecture by Gross and Kudla that relates the derivatives of triple-produ
ct L-functions \nfor three modular forms and the height pairing of the Gro
ss—Schoen cycles on Shimura curves.\nThen\, we sketch a proof of a gener
alization of this conjecture for Hilbert modular forms in the spherical ca
se. This is a report of work in progress with Xinyi Yuan and Wei Zhang\, w
ith help from Yifeng Liu.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Zhang (MIT)
DTSTART:20231109T204000Z
DTEND:20231109T214000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/102
DESCRIPTION:Title: Harris–Venkatesh plus Stark\nby Robin Zhang (MIT) as part
of UCSD number theory seminar\n\nLecture held in APM 6402 and online.\n\nA
bstract\nThe class number formula describes the behavior of the Dedekind z
eta function at s = 0 and s = 1. The Stark and Gross conjectures extend th
e class number formula\, describing the behavior of Artin L-functions and
p-adic L-functions at s = 0 and s = 1 in terms of units. The Harris–Venk
atesh conjecture describes the residue of Stark units modulo p\, giving a
modular analogue to the Stark and Gross conjectures while also serving as
the first verifiable part of the broader conjectures of Venkatesh\, Prasan
na\, and Galatius. In this talk\, I will draw an introductory picture\, fo
rmulate a unified conjecture combining Harris–Venkatesh and Stark for we
ight one modular forms\, and describe the proof of this in the imaginary d
ihedral case.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiran Kedlaya (UC San Diego)
DTSTART:20231102T210000Z
DTEND:20231102T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/103
DESCRIPTION:Title: The affine cone of a Fargues-Fontaine curve\nby Kiran Kedlay
a (UC San Diego) as part of UCSD number theory seminar\n\nLecture held in
APM 6402 and online.\n\nAbstract\nThe Fargues-Fontaine curve associated to
an algebraically closed nonarchimedean field of characteristic $p$ is a f
undamental geometric object in $p$-adic Hodge theory. Via the tilting equi
valence it is related to the Galois theory of finite extensions of Q_p\; i
t also occurs in Fargues's program to geometrize the local Langlands corre
spondence for such fields.\n\nRecently\, Peter Dillery and Alex Youcis hav
e proposed using a related object\, the "affine cone" over the aforementio
ned curve\, to incorporate some recent insights of Kaletha into Fargues's
program. I will summarize what we do and do not yet know\, particularly ab
out vector bundles on this and some related spaces (all joint work in prog
ress with Dillery and Youcis).\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Aycock (UC San Diego)
DTSTART:20231207T220000Z
DTEND:20231207T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/104
DESCRIPTION:Title: A p-adic Family of Quaternionic Modular Forms on a Group of Type
G_2\nby Jon Aycock (UC San Diego) as part of UCSD number theory semin
ar\n\nLecture held in APM 7218.\n\nAbstract\nThe concept of p-adic familie
s of automorphic forms has far reaching applications in number theory. In
this talk\, we will discuss one of the first examples of such a family\, b
uilt from the Eisenstein series\, before allowing this to inform a constru
ction of a family on an exceptional group of type G_2.\n\npre-talk at 1:20
pm in APM 6402\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Klevdal (UC San Diego)
DTSTART:20231019T210000Z
DTEND:20231019T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/105
DESCRIPTION:Title: p-adic periods of admissible pairs\nby Christian Klevdal (UC
San Diego) as part of UCSD number theory seminar\n\nLecture held in APM 6
402 and online.\n\nAbstract\nIn this talk\, we study a Tannakian category
of admissible pairs\, which arise naturally when one is comparing etale an
d de Rham cohomology of p-adic formal schemes. Admissible pairs are parame
terized by local Shimura varieties and their non-minuscule generalizations
\, which admit period mappings to de Rham affine Grassmannians. After revi
ewing this theory\, we will state a result characterizing the basic admiss
ible pairs that admit CM in terms of transcendence of their periods. This
result can be seen as a p-adic analogue of a theorem of Cohen and Shiga-Wo
lfhart characterizing CM abelian varieties in terms of transcendence of th
eir periods. All work is joint with Sean Howe.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Finley McGlade (UC San Diego)
DTSTART:20231130T220000Z
DTEND:20231130T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/106
DESCRIPTION:Title: A Level 1 Maass Spezialschar for Modular Forms on $\\mathrm{SO}_
8$\nby Finley McGlade (UC San Diego) as part of UCSD number theory sem
inar\n\nLecture held in APM 7218 and online.\n\nAbstract\nThe classical Sp
ezialschar is the subspace of the space of\nholomorphic modular forms on
$\\mathrm{Sp}_4(\\mathbb{Z})$ whose\nFourier coefficients satisfy a partic
ular system of linear equations. An\nequivalent characterization of the Sp
ezialschar can be obtained by\ncombining work of Maass\, Andrianov\, and Z
agier\, whose work identifies\nthe Spezialschar in terms of a theta-lift f
rom\n$\\widetilde{\\mathrm{SL}_2}$. Inspired by work of Gan-Gross-Savin\,\
nWeissman and Pollack have developed a theory of modular forms on the\nspl
it adjoint group of type D_4. In this setting we describe an analogue\nof
the classical Spezialschar\, in which Fourier coefficients are used to\nch
aracterize those modular forms which arise as theta lifts from\nholomorphi
c forms on $\\mathrm{Sp}_4(\\mathbb{Z})$.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Rosu (Leiden)
DTSTART:20240118T220000Z
DTEND:20240118T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/107
DESCRIPTION:Title: A higher degree Weierstrass function\nby Eugenia Rosu (Leide
n) as part of UCSD number theory seminar\n\nLecture held in APM 7321.\n\nA
bstract\nI will discuss recent developments and ongoing work for algebraic
and p-adic aspects of L-functions. Interest in p-adic properties of value
s of L-functions originated with Kummer’s study of congruences between v
alues of the Riemann zeta function at negative odd integers\, as part of h
is attempt to understand class numbers of cyclotomic extensions. After pre
senting an approach to studying analogous congruences for more general cla
sses of L-functions\, I will conclude by introducing ongoing joint work of
G. Rosso\, S. Shah\, and myself (concerning Spin L-functions for GSp_6).
I will explain how this work fits into the context of earlier developments
\, while also indicating where new technical challenges arise. All who are
curious about this topic are welcome at this talk\, even without prior ex
perience with p-adic L-functions or Spin L-functions.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shahed Sharif (CSU San Marcos)
DTSTART:20240215T220000Z
DTEND:20240215T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/108
DESCRIPTION:Title: Number theory and quantum computing: Algorithmists\, Assemble!\nby Shahed Sharif (CSU San Marcos) as part of UCSD number theory semina
r\n\nLecture held in APM 7321.\n\nAbstract\nQuantum computing made its nam
e by solving a problem in number theory\; namely\, determining if factorin
g could be accomplished efficiently. Since then\, there has been immense p
rogress in development of quantum algorithms related to number theory. I'l
l give a perhaps idiosyncratic overview of the computational tools quantum
computers bring to the table\, with the goal of inspiring the audience to
find new problems that quantum computers can solve.\n\npre-talk at 1:20pm
\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Yin (Wisconsin)
DTSTART:20240125T220000Z
DTEND:20240125T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/109
DESCRIPTION:Title: A Chebotarev Density Theorem over Local Fields\nby John Yin
(Wisconsin) as part of UCSD number theory seminar\n\nLecture held in APM 7
321.\n\nAbstract\nI will present an analog of the Chebotarev Density Theor
em which works over local fields. As an application\, I will use it to pro
ve a conjecture of Bhargava\, Cremona\, Fisher\, and Gajović. This is joi
nt work with Asvin G and Yifan Wei.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jessica Fintzen (Bonn)
DTSTART:20240112T220000Z
DTEND:20240112T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/111
DESCRIPTION:Title: Representations of p-adic groups and Hecke algebras\nby Jess
ica Fintzen (Bonn) as part of UCSD number theory seminar\n\nLecture held i
n APM 7321.\n\nAbstract\nAn explicit understanding of the category of all
(smooth\, complex)\nrepresentations of p-adic groups provides an important
tool in the\nconstruction of an explicit and a categorical local Langland
s\ncorrespondence and also has applications to the study of automorphic\nf
orms. The category of representations of p-adic groups decomposes into\nsu
bcategories\, called Bernstein blocks\, which are indexed by equivalence\n
classes of so called supercuspidal representations of Levi subgroups. In\n
this talk\, I will give an overview of what we know about an explicit\ncon
struction of supercuspidal representations and about the structure of\nthe
Bernstein blocks. In particular\, I will discuss a joint project in\nprog
ress with Jeffrey Adler\, Manish Mishra and Kazuma Ohara in which we\nshow
that general Bernstein blocks are equivalent to much better\nunderstood d
epth-zero Bernstein blocks. This is achieved via an\nisomorphism of Hecke
algebras and allows to reduce a lot of problems\nabout the (category of) r
epresentations of p-adic groups to problems\nabout representations of fini
te groups of Lie type\, where answers are\noften already known or easier t
o achieve.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aranya Lahiri (UC San Diego)
DTSTART:20240229T220000Z
DTEND:20240229T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/112
DESCRIPTION:Title: Dagger groups and $p$-adic distribution algebras\nby Aranya
Lahiri (UC San Diego) as part of UCSD number theory seminar\n\nLecture hel
d in APM 7321.\n\nAbstract\nLocally analytic representations were introduc
ed by Peter Schneider and Jeremy Teitelbaum as a tool to understand $p$-ad
ic Langlands program. From the very beginning the theory of $p$-valued gro
ups played an instrumental role in the study of locally analytic represent
ations. In a previous work we attached a rigid analytic group to a $\\tex
tit{$p$-saturated group}$ (a class of $p$-valued groups that contains unif
orm pro-$p$ groups and pro-$p$ Iwahori subgroups as examples). In this tal
k I will outline how to elevate the rigid group to a $\\textit{dagger grou
p}$\, a group object in the category of dagger spaces as introduced by Elm
ar Grosse-Klönne. I will further introduce the space of $\\textit{overcon
vergent functions}$ and its strong dual the $\\textit{overconvergent distr
ibution algebra}$ on such a group. Finally I will show that in analogy to
the locally analytic distribution algebra of compact $p$-adic groups\, in
the case of uniform pro-$p$ groups the overconvergent distribution algebra
is a Fr´echet-Stein algebra\, i.e.\, it is equipped with a desirable alg
ebraic structure. This is joint work with Claus Sorensen and Matthias Stra
uch.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Eischen (Oregon)
DTSTART:20240530T210000Z
DTEND:20240530T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/113
DESCRIPTION:Title: Algebraic and p-adic aspects of L-functions\, with a view toward
Spin L-functions for GSp_6\nby Ellen Eischen (Oregon) as part of UCSD
number theory seminar\n\nLecture held in APM 6402 and online.\n\nAbstract
\nI will discuss recent developments and ongoing work for\nalgebraic and p
-adic aspects of L-functions. Interest in p-adic\nproperties of values of
L-functions originated with Kummer’s study of\ncongruences between value
s of the Riemann zeta function at negative odd\nintegers\, as part of his
attempt to understand class numbers of\ncyclotomic extensions. After prese
nting an approach to studying\nanalogous congruences for more general clas
ses of L-functions\, I will\nconclude by introducing ongoing joint work of
G. Rosso\, S. Shah\, and\nmyself (concerning Spin L-functions for GSp_6).
I will explain how this\nwork fits into the context of earlier developmen
ts\, while also\nindicating where new technical challenges arise. All who
are curious\nabout this topic are welcome at this talk\, even without prio
r experience\nwith p-adic L-functions or Spin L-functions.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mckenzie West (Wisconsin-Eau Claire)
DTSTART:20240208T220000Z
DTEND:20240208T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/114
DESCRIPTION:Title: A Robust Implementation of an Algorithm to Solve the $S$-Unit Eq
uation\nby Mckenzie West (Wisconsin-Eau Claire) as part of UCSD number
theory seminar\n\nLecture held in APM 7321 and online.\n\nAbstract\nThe $
S$-unit equation has vast applications in number theory. We will discuss
an implementation of an algorithm to solve the $S$-unit equation in the ma
thematical software Sage. The mathematical foundation for this implementa
tion and some applications will be outlined\, including an asymptotic vers
ion of Fermat's Last Theorem for totally real cubic number fields with bou
nded discriminant in which 2 is totally ramified. We will conclude with a
discussion on current and future work toward improving the existing Sage f
unctionality.\n\npre-talk at 1:20\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:René Schoof (Rome 3)
DTSTART:20240307T220000Z
DTEND:20240307T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/115
DESCRIPTION:Title: Greenberg’s $\\lambda=0$ conjecture\nby René Schoof (Rome
3) as part of UCSD number theory seminar\n\nLecture held in APM 7321.\n\n
Abstract\nRecent and not so recent computations by Mercuri and Paoluzi\nha
ve verified Greenberg’s $\\lambda=0$ conjecture in Iwasawa theory\nin ma
ny cases. We discuss the conjecture and the computations.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Organizational meeting
DTSTART:20240404T210000Z
DTEND:20240404T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/116
DESCRIPTION:Title: Organizational meeting\nby Organizational meeting as part of
UCSD number theory seminar\n\nLecture held in APM 6402 and online.\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Aycock (UC San Diego)
DTSTART:20240425T210000Z
DTEND:20240425T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/117
DESCRIPTION:Title: Congruences Between Automorphic Forms\nby Jon Aycock (UC San
Diego) as part of UCSD number theory seminar\n\nLecture held in APM 6402
and online.\n\nAbstract\nWe will introduce an analytic notion of automorph
ic forms. These automorphic forms encode arithmetic data by way of their F
ourier theory\, and we will explore two different families of automorphic
forms which have interesting congruences between their Fourier coefficient
s.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Yin (UC San Diego)
DTSTART:20240502T210000Z
DTEND:20240502T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/118
DESCRIPTION:Title: Higher Coates-Sinnott Conjectures for CM-Fields\nby Wei Yin
(UC San Diego) as part of UCSD number theory seminar\n\nLecture held in AP
M 6402 and online.\n\nAbstract\nThe classical Coates-Sinnott Conjecture an
d its refinements predict the deep relationship between the special values
of L-functions and the structure of the étale cohomology groups attached
to number fields. In this talk\, we aim to delve deeper along this direct
ion to propose what we call the “Higher Coates-Sinnott Conjectures" whic
h reveal more information about these two types of important arithmetic ob
jects. We introduce the conjectures we formulate and our work towards them
. This is joint work with C. Popescu.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nandagopal Ramachandran (UC San Diego)
DTSTART:20240509T210000Z
DTEND:20240509T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/119
DESCRIPTION:Title: Euler factors in Drinfeld modules\nby Nandagopal Ramachandra
n (UC San Diego) as part of UCSD number theory seminar\n\nLecture held in
APM 6402 and online.\n\nAbstract\nIn this talk\, I'll first give a quick i
ntroduction to the theory of Drinfeld modules and talk about an equivarian
t $L$-function associated to Drinfeld modules as defined by Ferrara-Higgin
s-Green-Popescu in their work on the ETNC. As is usual\, these $L$-functio
ns are defined as an infinite product of Euler factors\, and the main focu
s of this talk is a result relating these Euler factors to a certain quoti
ent of Fitting ideals of some algebraically relevant modules. This is join
t work with Cristian Popescu.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryan Hu (UC San Diego)
DTSTART:20240516T210000Z
DTEND:20240516T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/120
DESCRIPTION:Title: Critical values of the adjoint L-function of U(2\,1) in the quat
ernionic case\nby Bryan Hu (UC San Diego) as part of UCSD number theor
y seminar\n\nLecture held in APM 6402 and online.\n\nAbstract\nWe will dis
cuss questions surrounding automorphic L-functions\, particularly Deligne
’s conjecture about critical values of motivic L-functions. In particula
r\, we study the adjoint L-function of U(2\,1). Hundley showed that a cert
ain integral\, involving an Eisenstein series on the exceptional group G_2
\, computes this L-function at unramified places. We discuss the computati
on of this integral at the archimedean place for quaternionic modular form
s\, and how this relates to Deligne's conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Klevdal (UC San Diego)
DTSTART:20240523T210000Z
DTEND:20240523T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/121
DESCRIPTION:Title: Local systems on Shimura varieties\nby Christian Klevdal (UC
San Diego) as part of UCSD number theory seminar\n\nLecture held in APM 6
402 and online.\n\nAbstract\nA large area of modern number theory (the Lan
glands program) studies a deep correspondence between the representation t
heory of Galois groups\, algebraic varieties and certain analytic objects
(automorphic forms). Many spectacular theorems have come from this area\,
for example the key insight in Wiles' proof of Fermat's last theorem was a
connection between elliptic curves\, modular forms and Galois representat
ions. \n\nThe goal of this talk is to explain how geometric constructions\
, particularly related to Shimura varieties\, arise naturally in the Langl
ands program. I will then talk about joint work with Stefan Patrikis\, sta
ting that Galois representations arising from certain Shimura varieties sa
tisfy the properties predicted by the correspondence introduced above.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claus Sorensen (UC San Diego)
DTSTART:20240411T210000Z
DTEND:20240411T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/122
DESCRIPTION:Title: Projective smooth representations mod $p$\nby Claus Sorensen
(UC San Diego) as part of UCSD number theory seminar\n\nLecture held in A
PM 6402 and online.\n\nAbstract\nThis talk will be colloquial and geared t
owards people from other fields. I will talk about smooth mod $p$ represen
tations of $p$-adic Lie groups. In stark contrast to the complex case\, th
ese categories typically do not have any (nonzero) projective objects. For
reductive groups this is a byproduct of a stronger result on the derived
functors of smooth induction. The talk is based on joint work with Peter S
chneider.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aranya Lahiri (UC San Diego)
DTSTART:20240418T210000Z
DTEND:20240418T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/123
DESCRIPTION:Title: Distribution algebras of p-adic groups\nby Aranya Lahiri (UC
San Diego) as part of UCSD number theory seminar\n\nLecture held in APM 6
402 and online.\n\nAbstract\nMy goal will be to motivate why looking at di
stribution algebras associated to p-adic lie groups is natural in the cont
ext of number theory. More specifically I will try to briefly outline thei
r importance in the p-adic Langlands program. And then I will give a simpl
e example of an overconvergent distribution algebra of certain kinds of p
-adic groups with an eye towards illuminating techniques used in my work D
agger groups and p-adic distribution algebras (joint w/ Matthias Strauch a
nd Claus Sorensen).\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Xu (UC San Diego)
DTSTART:20240606T210000Z
DTEND:20240606T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/124
DESCRIPTION:Title: Rational points on modular curves via the moduli interpretation<
/a>\nby Chris Xu (UC San Diego) as part of UCSD number theory seminar\n\nL
ecture held in APM 6402 and online.\n\nAbstract\nIn theory\, Chabauty-Cole
man provides an explicit method to obtain rational points on any curve\, s
o long as its genus exceeds its Mordell-Weil rank. In practice\, when appl
ied to modular curves\, we often encounter difficulties in finding a suita
ble plane model\, which only worsens as the genus increases. In this talk
we describe how to skip this step and instead work directly with the coars
e moduli space. This is joint work with Steve Huang and Jun Bo Lau.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Organizational meeting
DTSTART:20241002T230000Z
DTEND:20241003T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/126
DESCRIPTION:Title: Organizational meeting\nby Organizational meeting as part of
UCSD number theory seminar\n\nLecture held in APM 7321 and online.\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Johnson-Leung (University of Idaho)
DTSTART:20241023T230000Z
DTEND:20241024T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/127
DESCRIPTION:Title: Rationality of certain power series attached to paramodular Sieg
el modular forms\nby Jennifer Johnson-Leung (University of Idaho) as p
art of UCSD number theory seminar\n\nLecture held in APM 7321 and online.\
n\nAbstract\nThe Euler product expression of the Dirichlet series of Fouri
er coefficients of an elliptic modular eigenform follows from a formal ide
ntity in the Hecke algebra for GL(2) with full level. In the case of Siege
l modular forms of degree two with paramodular level\, the situation is mo
re delicate. In this talk\, I will present two rationality results. The fi
rst concerns the Dirichlet series of radial Fourier coefficients for an ei
genform of paramodular level divisible by the square of a prime. This resu
lt is an application of the theory of stable Klingen vectors (joint work w
ith Brooks Roberts and Ralf Schmidt). While we are able to calculate the
action of certain Hecke operators on eigenforms\, the structure of the Hec
ke algebra of deep level is not known in general. However\, in the case of
prime level\, there is a robust description of the local Hecke algebra wh
ich yields a rationality result for a formal power series of Hecke operato
rs (joint work with Joshua Parker and Brooks Roberts). In both cases\, we
obtain the expected local L-factor as the denominator of the rational func
tion.\n\npre-talk at 3:00pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brandon Alberts (Eastern Michigan)
DTSTART:20241107T000000Z
DTEND:20241107T010000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/128
DESCRIPTION:Title: Inductive methods for counting number fields\nby Brandon Alb
erts (Eastern Michigan) as part of UCSD number theory seminar\n\nLecture h
eld in APM 7321 and online.\n\nAbstract\nWe will discuss an inductive appr
oach to determining the asymptotic number of G-extensions of a number fiel
d with bounded discriminant\, and outline the proof of Malle's conjecture
in numerous new cases. This talk will include discussions of several examp
les demonstrating the method.\n\npre-talk at 3pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linli Shi (Connecticut)
DTSTART:20241121T000000Z
DTEND:20241121T010000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/129
DESCRIPTION:Title: On higher regulators of Picard modular surfaces\nby Linli Sh
i (Connecticut) as part of UCSD number theory seminar\n\nLecture held in A
PM 7321 and online.\n\nAbstract\nThe Birch and Swinnerton-Dyer conjecture
relates the leading coefficient of the L-function of an elliptic curve at
its central critical point to global arithmetic invariants of the elliptic
curve. Beilinson’s conjectures generalize the BSD conjecture to formula
s for values of motivic L-functions at non-critical points. In this talk\,
I will relate motivic cohomology classes\, with non-trivial coefficients\
, of Picard modular surfaces to a non-critical value of the motivic L-func
tion of certain automorphic representations of the group GU(2\,1).\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Xu (UC San Diego)
DTSTART:20241114T000000Z
DTEND:20241114T010000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/130
DESCRIPTION:Title: Special cycles on $G_2$\nby Chris Xu (UC San Diego) as part
of UCSD number theory seminar\n\nLecture held in APM 7321 and online.\n\nA
bstract\nOn the symmetric space for $G_2$\, there exist various submanifol
ds $G_D$ corresponding to the stabilizer of a norm $D$ vector. We show tha
t when a suitable automorphic form is integrated against the $G_D$\, the r
esulting numbers assemble to give a half-integral weight classical modular
form. Although this is already implied by a result of Kudla-Millson\, we
give a simpler proof that avoids the complications in their paper.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Fu (Caltech)
DTSTART:20241205T000000Z
DTEND:20241205T010000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/131
DESCRIPTION:Title: The p-adic analog of the Hecke orbit conjecture and density theo
rems toward the p-adic monodromy\nby Yu Fu (Caltech) as part of UCSD n
umber theory seminar\n\nLecture held in APM 7321 and online.\n\nAbstract\n
The Hecke orbit conjecture predicts that Hecke symmetries characterize the
central foliation on Shimura varieties over an algebraically closed field
$k$ of characteristic $p$. The conjecture predicts that on the mod $p$ re
duction of a Shimura variety\, any prime-to-p Hecke orbit is dense in the
central leaf containing it\, and was recently proved by a series of nice p
apers.\nHowever\, the behavior of Hecke correspondences induced by isogeni
es between abelian varieties in characteristic $p$ and $p$-adically is sig
nificantly different from the behavior in characteristic zero and under th
e topology induced by Archimedean valuations. In this talk\, we will form
ulate a $p$-adic analog of the Hecke orbit conjecture and investigate the
$p$-adic monodromy of $p$-adic Galois representations attached to points o
f Shimura varieties of Hodge type. We prove a density theorem for the locu
s of formal neighborhood associated to the mod $p$ points of the Shimura v
ariety whose monodromy is large and use it to deduce the non-where density
of Hecke orbits under certain circumstances.\n\npre-talk at 3:00pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Aycock (UC San Diego)
DTSTART:20241016T230000Z
DTEND:20241017T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/132
DESCRIPTION:Title: Jacobians of Graphs via Edges and Iwasawa Theory\nby Jon Ayc
ock (UC San Diego) as part of UCSD number theory seminar\n\nLecture held i
n APM 7321 and online.\n\nAbstract\nThe Jacobian (or sandpile group) is an
algebraic invariant of a graph that plays a similar role to the class gro
up in classical number theory. There are multiple recent results controlli
ng the sizes of these groups in Galois towers of graphs that mimic the cla
ssical results in Iwasawa theory\, though the connection to the values of
the Ihara zeta function often requires some adjustment. In this talk we wi
ll give a new way to view the Jacobian of a graph that more directly cente
rs the edges of the graph\, construct a module over the relevant Iwasawa a
lgebra that nearly corresponds to the interpolated zeta function\, and dis
cuss where the discrepancy comes from.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengyang Bao (UCLA)
DTSTART:20241030T230000Z
DTEND:20241031T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/133
DESCRIPTION:Title: Computing crystalline deformation rings via the Taylor-Wiles-Kis
in patching method\nby Chengyang Bao (UCLA) as part of UCSD number the
ory seminar\n\nLecture held in APM 7321 and online.\n\nAbstract\nCrystalli
ne deformation rings play an important role in Kisin's proof of the Fontai
ne-Mazur conjecture for GL2 in most cases. One crucial step in the proof i
s to prove the Breuil-Mezard conjecture on the Hilbert-Samuel multiplicity
of the special fiber of the crystalline deformation ring. In pursuit of f
ormulating a horizontal version of the Breuil-Mezard conjecture\, we devel
op an algorithm to compute arbitrarily close approximations of crystalline
deformation rings. Our approach\, based on reverse-engineering the Taylor
-Wiles-Kisin patching method\, aims to provide detailed insights into thes
e rings and their structural properties\, at least conjecturally.\n\npre-t
alk at 3pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Voight (Sydney)
DTSTART:20250123T000000Z
DTEND:20250123T010000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/134
DESCRIPTION:Title: Hilbert modular forms obtained from orthogonal modular forms on
quaternary lattices\nby John Voight (Sydney) as part of UCSD number th
eory seminar\n\nLecture held in APM 7321 and online.\n\nAbstract\nWe make
explicit the relationship between Hilbert modular forms and orthogonal mod
ular forms arising from positive definite quaternary lattices over the rin
g of integers of a totally real number field. Our work uses the Clifford
algebra\, and it generalizes that of Ponomarev\, Bocherer--Schulze-Pillot\
, and others by allowing for general discriminant\, weight\, and class gro
up of the base ring. This is joint work with Eran Assaf\, Dan Fretwell\,
Colin Ingalls\, Adam Logan\, and Spencer Secord.\n\npre-talk at 3pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masato Wakayama (Kyushu)
DTSTART:20250130T000000Z
DTEND:20250130T010000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/135
DESCRIPTION:Title: Quantum interactions and number theory\nby Masato Wakayama (
Kyushu) as part of UCSD number theory seminar\n\nLecture held in APM 7321
and online.\n\nAbstract\nQuantum interaction models discussed here are the
(asymmetric) quantum Rabi\nmodel (QRM) and non-commutative harmonic oscil
lator (NCHO). The QRM is the most fun-\ndamental model describing the inte
raction between a photon and two-level atoms. The NCHO\ncan be considered
as a covering model of the QRM\, and recently\, the eigenvalue problems of
\nNCHO and two-photon QRM (2pQRM) are shown to be equivalent. Spectral deg
eneracy can\noccur in models\, but correspondingly there is a hidden symme
try relates geometrical nature\ndescribed by hyperelliptic curves. In addi
tion\, the analytical formula for the heat kernel (prop-\nagator)/partitio
n function of the QRM is described as a discrete path integral and gives t
he\nmeromorphic continuation of its spectral zeta function (SZF). This dis
crete path integral can\nbe interpreted to the irreducible decomposition o
f the infinite symmetric group $\\mathfrak{S}_\\infty$ naturally acting on
$\\mathbb{F}_2^\\infty$\, $\\mathbb{F}_2$ being the binary field. Moreove
r\, from the special values of the SZF of NCHO\, an analogue of the Apéry
numbers is naturally appearing\, and their generating functions are\, e.g
.\, given by modular forms\, Eichler integrals of a congruence subgroup. T
he talk overviews those above and present questions which are open.\n\npre
-talk at 3pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Raghuram (Fordham)
DTSTART:20250206T000000Z
DTEND:20250206T010000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/136
DESCRIPTION:Title: Congruences and the special values of L-functions\nby A. Rag
huram (Fordham) as part of UCSD number theory seminar\n\nLecture held in A
PM 7321 and online.\n\nAbstract\nThere is an idea in number theory that if
two objects are congruent modulo a prime p\, then the congruence can also
be seen for the special values of L-functions attached to the objects. He
re is a context explicating this idea: Suppose f and f' are holomorphic cu
spidal eigenforms of weight k and level N\, and suppose f is congruent to
f' modulo p\; suppose g is another cuspidal eigenform of weight l\; if the
difference k - l is large then the Rankin-Selberg L-function L(s\, f x g)
has enough critical points\; same for L(s\, f' x g)\; one expects then th
at there is a congruence modulo p between the algebraic parts of L(m\, f x
g) and L(m\, f' x g) for any critical point m. In this talk\, after elabo
rating on this idea\, I will describe the results of some computational ex
periments where one sees such congruences for ratios of critical values fo
r Rankin-Selberg L-functions. Towards the end of my talk\, time-permitting
\, I will sketch a framework involving Eisenstein cohomology for GL(4) ove
r Q which will permit us to prove such congruences. This is joint work wit
h my student P. Narayanan.\n\npre-talk at 3pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Santiago Arango-Piñeros (Emory)
DTSTART:20250213T000000Z
DTEND:20250213T010000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/137
DESCRIPTION:Title: Counting 5-isogenies of elliptic curves over the rationals\n
by Santiago Arango-Piñeros (Emory) as part of UCSD number theory seminar\
n\nLecture held in APM 7321 and online.\n\nAbstract\nIn collaboration with
Han\, Padurariu\, and Park\, we show that the number of $5$-isogenies of
elliptic curves defined over $\\mathbb{Q}$ with naive height bounded by $H
> 0$ is asymptotic to $C_5\\cdot H^{1/6} (\\log H)^2$ for some explicitly
computable constant $C_5 > 0$. This settles the asymptotic count of ratio
nal points on the genus zero modular curves $X_0(m)$. We leverage an expli
cit $\\mathbb{Q}$-isomorphism between the stack $\\mathscr{X}_0(5)$ and th
e generalized Fermat equation $x^2 + y^2 = z^4$ with $\\mathbb{G}_m$ actio
n of weights $(4\, 4\, 2)$.\n\nPretalk: I will explain how to count isomor
phism classes of elliptic curves over the rationals. On the way\, I will i
ntroduce some basic stacky notions: torsors\, quotient stacks\, weighted p
rojective stacks\, and canonical rings.\n\npre-talk at 3pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marie-France Vigneras (Jussieu)
DTSTART:20250313T210000Z
DTEND:20250313T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/139
DESCRIPTION:Title: Asymptotics of $p$-adic groups\, mostly $SL_2$ [Colloquium]\
nby Marie-France Vigneras (Jussieu) as part of UCSD number theory seminar\
n\nLecture held in APM 6402.\n\nAbstract\nLet $p$ be a prime number and $
Q_p$ the field of $p$-adic numbers.\n The representations of a cousin
of the Galois group of an algebraic closure of $ Q_p$ are related (the
{\\bf Langlands's bridge}) to the representations of reductive $p$-adic g
roups\, for instance $SL_2(Q_p)\, GL_n(Q_p) $. The irreducible repr
esentations $\\pi$ of reductive $p$-adic groups are easier to study than
those of the Galois groups but they are rarely finite dimensional. Their
classification is very involved but \n their behaviour around the iden
tity\, that we call the ``asymptotics'' of $\\pi$\, are expected to be mor
e uniform. We shall survey what is known (joint work with Guy Henniart)\,
and what it suggests.\n\nColloquium\, no livestream\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Koji Shimizu and Gyujin Oh (Tsinghua/Columbia)
DTSTART:20250206T220000Z
DTEND:20250206T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/140
DESCRIPTION:Title: Moduli stack of isocrystals and counting local systems\nby K
oji Shimizu and Gyujin Oh (Tsinghua/Columbia) as part of UCSD number theor
y seminar\n\nLecture held in APM 6402 and online.\n\nAbstract\nTo a smooth
projective curve over a finite field\, we associate rigid-analytic moduli
stacks of isocrystals together with the Verschiebung endomorphism. We dev
elop relevant foundations of rigid-analytic stacks\, and discuss the examp
les and properties of such moduli stacks. We also illustrate how such modu
li can be used to count p-adic coefficient objects on the curve of rank on
e.\n\nThe main talk will be given by Oh. In the pre-talk\, Shimizu will in
troduce integrable connections and isocrystals\, which will be the key obj
ects in the main talk.\n\npre-talk at 1pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zeyu Liu (UC Berkeley)
DTSTART:20250220T000000Z
DTEND:20250220T010000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/141
DESCRIPTION:Title: A stacky approach to prismatic crystals\nby Zeyu Liu (UC Ber
keley) as part of UCSD number theory seminar\n\nLecture held in APM 7321 a
nd online.\n\nAbstract\nNowadays prismatic crystals are gathering an incre
asing interest as they unify various coefficients in $p$-adic cohomology t
heories. Recently\, attached to any $p$-adic formal scheme $X$\, Drinfeld
and Bhatt-Lurie constructed certain ring stacks\, including the prismatiza
tion of $X$\, on which quasi-coherent complexes correspond to various crys
tals on the prismatic site of $X$. While such a stacky approach sheds some
new light on studying prismatic crystals\, little is known outside of the
Hodge-Tate locus. In this talk\, we will introduce our recent work on stu
dying quasi-coherent complexes on the prismatization of $X$ via various ch
arts.\n\npre-talk at 3pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arijit Chakraborty (UC San Diego)
DTSTART:20250116T000000Z
DTEND:20250116T010000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/142
DESCRIPTION:Title: A Power-Saving Error Term in Counting C2 ≀ H Number Fields
\nby Arijit Chakraborty (UC San Diego) as part of UCSD number theory semin
ar\n\nLecture held in APM 7321 and online.\n\nAbstract\nOne of the central
problems in Arithmetic Statistics is counting number field extensions of
a fixed degree with a given Galois group\, parameterized by discriminants.
This talk focuses on C2 ≀ H extensions over an arbitrary base field. Wh
ile Jürgen Klüners has established the main term in this setting\, we pr
esent an alternative approach that provides improved power-saving error te
rms for the counting function.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keegan Ryan (UC San Diego)
DTSTART:20250306T000000Z
DTEND:20250306T010000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/143
DESCRIPTION:Title: Solving Multivariate Coppersmith Problems with Known Moduli\
nby Keegan Ryan (UC San Diego) as part of UCSD number theory seminar\n\nLe
cture held in APM 7321 and online.\n\nAbstract\nA central problem in crypt
analysis involves computing the set of solutions within a bounded region t
o systems of modular multivariate polynomials. Typical approaches to this
problem involve identifying shift polynomials\, or polynomial combinations
of input polynomials\, with good computational properties. In particular\
, we care about the size of the support of the shift polynomials\, the deg
ree of each monomial in the support\, and the magnitude of coefficients. W
hile shift polynomials for systems of a single modular univariate polynomi
al have been well understood since Coppersmith's original 1996 work\, mult
ivariate systems have been more difficult to analyze. Most analyses of shi
ft polynomials only apply to specific problem instances\, and it has long
been a goal to find a general method for constructing shift polynomials fo
r any system of modular multivariate polynomials. In recent work\, we have
made progress toward this goal by applying Groebner bases\, graph optimiz
ation algorithms\, and Ehrhart's theory of polytopes to this problem. This
talk focuses on these mathematical aspects as they relate to our work\, a
s well as open conjectures about the asymptotic performance of our strateg
ies.\n\npre-talk at 3pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jake Huryn (Ohio State)
DTSTART:20250402T230000Z
DTEND:20250403T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/144
DESCRIPTION:Title: Geometric properties of the "tautological" local systems on Shim
ura varieties\nby Jake Huryn (Ohio State) as part of UCSD number theor
y seminar\n\nLecture held in APM 7321 and online.\n\nAbstract\nSome Shimur
a varieties are moduli spaces of Abelian varieties with extra structure.\n
The Tate module of a universal Abelian variety is a natural source of $\\e
ll$-adic local systems on such Shimura varieties. Remarkably\, the theory
allows one to build these local systems intrinsically from the Shimura var
iety in an essentially tautological way\, and this construction can be car
ried out in exactly the same way for Shimura varieties whose moduli interp
retation remains conjectural.\n\nThis suggests the following program: Show
that these tautological local systems "look as if" they were arising from
the cohomology of geometric objects. In this talk\, I will describe some
recent progress. It is based on joint work with Kiran Kedlaya\, Christian
Klevdal\, and Stefan Patrikis\, as well as joint work with Yifei Zhang.\n\
npre-talk at 3pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Kramer-Miller (Lehigh)
DTSTART:20250521T230000Z
DTEND:20250522T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/145
DESCRIPTION:Title: On the diagonal and Hadamard grades of hypergeometric functions<
/a>\nby Joe Kramer-Miller (Lehigh) as part of UCSD number theory seminar\n
\nLecture held in APM 7321 and online.\n\nAbstract\nDiagonals of multivari
ate rational functions are an important class of functions arising in numb
er theory\, algebraic geometry\, combinatorics\, and physics. For instance
\, many hypergeometric functions are diagonals as well as the generating f
unction for Apery's sequence. A natural question is to determine the diago
nal grade of a function\, i.e.\, the minimum number of variables one needs
to express a given function as a diagonal. The diagonal grade gives the r
ing of diagonals a filtration. In this talk we study the notion of diagona
l grade and the related notion of Hadamard grade (writing functions as the
Hadamard product of algebraic functions)\, resolving questions of Allouch
e-Mendes France\, Melczer\, and proving half of a conjecture recently pose
d by a group of physicists. This work is joint with Andrew Harder.\n\npre-
talk at 3pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin Lauter (Meta)
DTSTART:20250430T220000Z
DTEND:20250430T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/146
DESCRIPTION:Title: Using machine learning to solve hard math problems in practice (
AWM colloquium)\nby Kristin Lauter (Meta) as part of UCSD number theor
y seminar\n\nLecture held in APM 6402.\n\nAbstract\nAI is taking off and w
e could say we are living in “the AI Era”. Progress in AI today is ba
sed on mathematics and statistics under the covers of machine learning mod
els. This talk will explain recent work on AI4Crypto\, where we train AI
models to attack Post Quantum Cryptography (PQC) schemes based on lattices
. I will use this work as a case study in training ML models to solve hard
math problems in practice. Our AI4Crypto project has developed AI models
capable of recovering secrets in post-quantum cryptosystems (PQC). The s
tandardized PQC systems were designed to be secure against a quantum compu
ter\, but are not necessarily safe against advanced AI! \n\nUnderstanding
the concrete security of these standardized PQC schemes is important for
the future of e-commerce and internet security. So instead of saying that
we are living in a “Post-Quantum” era\, we should say that we are liv
ing in a “Post-AI” era!\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (UC Berkeley)
DTSTART:20250516T230000Z
DTEND:20250517T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/147
DESCRIPTION:Title: Moduli spaces of curves with polynomial point count (AG seminar)
\nby Hannah Larson (UC Berkeley) as part of UCSD number theory seminar
\n\nLecture held in APM 7321.\n\nAbstract\nHow many isomorphism classes of
genus g curves are there over a finite field $\\mathbb{F}_q$? In joint wo
rk with Samir Canning\, Sam Payne\, and Thomas Willwacher\, we prove that
the answer is a polynomial in q if and only if g is at most 8. One of the
key ingredients is our recent progress on understanding low-degree odd coh
omology of moduli spaces of stable curves with marked points.\n\npre-talk
at 3:30pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jize Yu (Rice)
DTSTART:20251105T220000Z
DTEND:20251105T230000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/148
DESCRIPTION:Title: Towards a tamely ramified local geometric Langlands corresponden
ce for p-adic groups\nby Jize Yu (Rice) as part of UCSD number theory
seminar\n\nLecture held in APM 7321.\n\nAbstract\nFor a reductive $p$-adic
group $G$\, Kazhdan-Lusztig prove an isomorphism of the the extended affi
ne Hecke algebra and the $G^\\vee$-equivariant $K$-group of the Steinberg
variety of the Langlands dual group $G^\\vee$. It has a profound applicati
on of proving an important case of the local Langlands correspondence whic
h is known as the Deligne-Langlands conjecture. For $G$ being a reductive
group over an equal-characteristic local field\, Bezrukavnikov upgrades Ka
zhdan-Lusztig's isomorphism to an equivalence of monoidal categories and p
roves the tamely ramified local geometric Langlands correspondence. In thi
s talk\, we discuss an ongoing project with João Lourenço on proving a t
amely ramified local geometric Langlands correspondence for reductive $p$-
adic groups. Time permitting\, I will mention an interesting variant of Be
zrukavnikov's equivalence in Ben-Zvi-Sakellaridis-Venkatesh's framework of
the relative Langlands program based on a joint work in preparation with
Milton Lin and Toan Pham.\n\npre-talk at 1:20pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jasmine Camero (Emory)
DTSTART:20251029T210000Z
DTEND:20251029T220000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/150
DESCRIPTION:Title: Classifying Possible Density Degree Sets of Hyperelliptic Curves
\nby Jasmine Camero (Emory) as part of UCSD number theory seminar\n\nL
ecture held in APM 7321.\n\nAbstract\nLet $C$ be a smooth\, projective\, g
eometrically integral hyperelliptic curve of genus $g \\geq 2$ over a numb
er field $k$. To study the distribution of degree $d$ points on $C$\, we i
ntroduce the notion of $\\mathbb{P}^1$- and AV-parameterized points\, whic
h arise from natural geometric constructions. These provide a framework fo
r classifying density degree sets\, an important invariant of a curve that
records the degrees $d$ for which the set of degree $d$ points on $C$ is
Zariski dense. Zariski density has two geometric sources: If $C$ is a degr
ee $d$ cover of $\\mathbb{P}^1$ or an elliptic curve $E$ of positive rank\
, then pulling back rational points on $\\mathbb{P}^1$ or $E$ give an infi
nite family of degree $d$ points on $C$. Building on this perspective\, we
give a classification of the possible density degree sets of hyperellipti
c curves.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Yao (U. Chicago)
DTSTART:20260401T230000Z
DTEND:20260402T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/151
DESCRIPTION:Title: $p$-adic height pairing using $K_2$-class field theory and Galoi
s-valued heights\nby Wei Yao (U. Chicago) as part of UCSD number theor
y seminar\n\nLecture held in APM 7321.\n\nAbstract\nIn this talk\, I will
construct a $p$-adic height pairing for curves with split degenerate stabl
e reduction over a prime $p$ using the higher class field theory of Kato-S
aito. This pairing can be shown to coincide with the standard Coleman-Gros
s height pairing when extended to the semistable reduction case using meth
ods by Besser and Vologodsky. At the end\, I will briefly mention how this
new method inspires the definition of a height pairing valued in certain
Galois groups related to the function field of the original curve.\n\npre-
talk at 3pm\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Church (Stanford)
DTSTART:20260603T230000Z
DTEND:20260604T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/152
DESCRIPTION:by Ben Church (Stanford) as part of UCSD number theory seminar
\n\nLecture held in APM 7321.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Everett Howe (unaffiliated)
DTSTART:20260506T230000Z
DTEND:20260507T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/153
DESCRIPTION:Title: Curves of genus 2 with maps of every degree to a fixed elliptic
curve\nby Everett Howe (unaffiliated) as part of UCSD number theory se
minar\n\nLecture held in APM 7321.\n\nAbstract\nWe show that up to isomorp
hism there are exactly twenty pairs $(C\, E)$\, where $C$ is a genus-2 cur
ve over the complex numbers\, where $E$ is an elliptic curve over the comp
lex numbers\, and where for every integer $n > 1$ there is a map of degree
$n$ from $C$ to $E$. For example\, if $C$ is the curve $y^2 = x^5 + 5 x^3
+ 5 x$\, and if $E$ is an elliptic curve with CM by the order of discrimi
nant -20\, then $(C\, E)$ is such a pair.\n\nOn the other hand\, we produc
e some finite sets $S$ of integers such that if $C$ is a genus-2 curve in
characteristic 0\, and if for every $n$ in $S$ there is an elliptic curve
$E_n$ and a degree-$n$ map $\\phi_n$ from $C$ to $E_n$\, then for at least
one of these $n$\, the map $\\phi_n$ factors through a nontrivial isogeny
.\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Balakrishnan (Boston U.)
DTSTART:20260512T230000Z
DTEND:20260513T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/154
DESCRIPTION:by Jennifer Balakrishnan (Boston U.) as part of UCSD number th
eory seminar\n\nLecture held in APM 7321.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brandon Alberts (Eastern Michigan U.)
DTSTART:20260520T230000Z
DTEND:20260521T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/155
DESCRIPTION:by Brandon Alberts (Eastern Michigan U.) as part of UCSD numbe
r theory seminar\n\nLecture held in APM 7321.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolas Castro (UC San Diego)
DTSTART:20260527T230000Z
DTEND:20260528T000000Z
DTSTAMP:20260424T235212Z
UID:UCSD_NTS/156
DESCRIPTION:by Nikolas Castro (UC San Diego) as part of UCSD number theory
seminar\n\nLecture held in APM 7321.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UCSD_NTS/156/
END:VEVENT
END:VCALENDAR