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BEGIN:VEVENT
SUMMARY:Jishnu Ray (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20200423T210000Z
DTEND;VALUE=DATE-TIME:20200423T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/1
DESCRIPTION:Title: Conjectures in Iwasawa Theory of Selmer groups and Iwasawa Algebras\n
by Jishnu Ray (University of British Columbia) as part of UCSD number theo
ry seminar\n\n\nAbstract\nThe Iwasawa Theory of Selmer groups provides a n
atural way for p-adic approach to the celebrated Birch and Swinnerton Dyer
conjecture. Over a non-commutative p-adic Lie extension\, the (dual) Selm
er group becomes a module over a non-commutative Iwasawa algebra and its s
tructure can be understood by analyzing “(left) reflexive ideals” in t
he Iwasawa algebra. In this talk\, we will start by recalling several exis
ting conjectures in Iwasawa Theory and then we will give an explicit ring-
theoretic presentation\, by generators and relations\, of such Iwasawa alg
ebras and sketch its implications in understanding the (two-sides) reflexi
ve ideals. Generalizing Clozel’s work for SL(2)\, we will also show that
such an explicit presentation of Iwasawa algebras can be obtained for a m
uch 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 s
ome of my recent Iwasawa theoretic results joint with Sujatha Ramdorai.\n\
npretalk\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jize Yu (California Institute of Technology)
DTSTART;VALUE=DATE-TIME:20200430T210000Z
DTEND;VALUE=DATE-TIME:20200430T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/2
DESCRIPTION:Title: The integral geometric Satake equivalence in mixed characteristic\nby
Jize Yu (California Institute of Technology) as part of UCSD number theor
y seminar\n\nLecture held in APM 7321.\n\nAbstract\nThe geometric Satake e
quivalence establishes a link between two monoidal categories: the categor
y of perverse sheaves on the local Hecke stack and the category of finitel
y generated representations of the Langlands dual group. It has many impor
tant applications in the study of the geometric Langlands program and numb
er theory. In this talk\, I will discuss the integral coefficient geometri
c Satake equivalence in the mixed characteristic setting. It generalizes t
he previous results of Lusztig\, Ginzburg\, Mirkovic-Vilonen\, and Zhu. Ti
me permitting\, I will discuss an application of this result in constructi
ng a Jacquet-Langlands transfer.\n\nThere will be a pretalk.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Wang-Erickson (University of Pittsburgh)
DTSTART;VALUE=DATE-TIME:20200507T210000Z
DTEND;VALUE=DATE-TIME:20200507T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/3
DESCRIPTION:Title: The Eisenstein ideal with squarefree level\nby Carl Wang-Erickson (Un
iversity of Pittsburgh) as part of UCSD number theory seminar\n\nLecture h
eld in APM 7321.\n\nAbstract\nIn his landmark paper "Modular forms and the
Eisenstein ideal\," Mazur studied congruences modulo a prime p between th
e Hecke eigenvalues of an Eisenstein series and the Hecke eigenvalues of c
usp forms\, assuming these modular forms have weight 2 and prime level N.
He asked about generalizations to squarefree levels N. I will present some
work on such generalizations\, which is joint with Preston Wake and Cathe
rine Hsu.\n\nThere will be a pretalk.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jack Thorne (Cambridge University)
DTSTART;VALUE=DATE-TIME:20200521T210000Z
DTEND;VALUE=DATE-TIME:20200521T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/5
DESCRIPTION:Title: Symmetric power functoriality for holomorphic modular forms\nby Jack
Thorne (Cambridge University) as part of UCSD number theory seminar\n\nLec
ture held in APM 7321.\n\nAbstract\nLanglands’s functoriality conjecture
s predict the existence of “liftings” of automorphic representations a
long morphisms of L-groups. A basic case of interest comes from the irredu
cible algebraic representations of GL(2)\, thought of as the L-group of th
e reductive group GL(2) over Q. I will discuss the proof\, joint with Jame
s Newton\, of the existence of the corresponding functorial liftings for
a broad class of holomorphic modular forms\, including Ramanujan’s Delta
function.\n\nThere will be a pre-talk.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Fuchs (University of California\, Davis)
DTSTART;VALUE=DATE-TIME:20200528T210000Z
DTEND;VALUE=DATE-TIME:20200528T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/6
DESCRIPTION:Title: Prime components in integral circle packings\nby Elena Fuchs (Univers
ity of California\, Davis) as part of UCSD number theory seminar\n\nLectur
e held in APM 7321.\n\nAbstract\nCircle packings in which all circles have
integer curvature\, particularly Apollonian circle packings\, have in the
last decade become objects of great interest in number theory. In this ta
lk\, we explore some of their most fascinating arithmetic features\, from
local to global properties to prime components in the packings\, going fro
m theorems\, to widely believed conjectures\, to wild guesses as to what m
ight be true.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niccolo Ronchetti (University of California\, Los Angeles)
DTSTART;VALUE=DATE-TIME:20200604T210000Z
DTEND;VALUE=DATE-TIME:20200604T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/7
DESCRIPTION:Title: A derived Hecke action on the ordinary Hida tower\nby Niccolo Ronchet
ti (University of California\, Los Angeles) as part of UCSD number theory
seminar\n\nLecture held in APM 7321.\n\nAbstract\nWhen studying the cohomo
logy of Shimura varieties and arithmetic manifolds\, one encounters the fo
llowing phenomenon: the same Hecke eigensystem shows up in multiple degree
s around the middle dimension\, and its multiplicities in these degrees re
sembles that of an exterior algebra.\n\nIn a series of recent papers\, Ven
katesh and his collaborators provide an explanation: they construct graded
objects having a graded action on the cohomology\, and show that under go
od circumstances this action factors through that of an explicit exterior
algebra\, which in turn acts faithfully and generate the entire Hecke eige
nspace.\n\nIn this talk\, we discuss joint work with Khare where we invest
igate 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 ordinary H
ida tower and show that (under some technical assumptions)\, this action g
enerates the full Hecke eigenspace under its lowest nonzero degree. Then\,
we bring Galois representations into the picture\, and show that the deri
ved Hecke action constructed before is in fact related to the action of a
certain dual Selmer group.\n\nThere will be a pre-talk.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Pellarin (U. Jean Monnet\, Saint-Etienne\, France)
DTSTART;VALUE=DATE-TIME:20200514T170000Z
DTEND;VALUE=DATE-TIME:20200514T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/8
DESCRIPTION:Title: On Drinfeld modular forms in Tate algebras\nby Federico Pellarin (U.
Jean Monnet\, Saint-Etienne\, France) as part of UCSD number theory semina
r\n\nLecture held in APM 7321.\n\nAbstract\nIn this talk we will describe
some recent works on Drinfeld modular forms with values in Tate algebras (
in 'equal positive characteristic'). In particular\, we will discuss some
remarkable identities (proved or conjectural) for Eisenstein and Poincaré
series\, and the problem of analytically interpolate families of Drinfeld
modular forms for congruence subgroups at the infinity place.\n\nThe pre-
talk will begin 30 minutes prior (09:30 local time).\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Tong (University of California\, San Diego)
DTSTART;VALUE=DATE-TIME:20200514T210000Z
DTEND;VALUE=DATE-TIME:20200514T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/10
DESCRIPTION:Title: Towards a Hodge-Iwasawa theory\nby Xin Tong (University of Californi
a\, San Diego) as part of UCSD number theory seminar\n\n\nAbstract\nWith t
he motivation of generalizing the corresponding geometrization of Tamagawa
-Iwasawa theory after Kedlaya-Pottharst\, and with motivation of establish
ing the corresponding equivariant version of the relative p-adic Hodge the
ory after Kedlaya-Liu aiming at the deformation of representations of prof
inite fundamental groups and the family of étale local systems\, we initi
ate the corresponding Hodge-Iwasawa theory with deep point of view and phi
losophy in mind from early work of Kato and Fukaya-Kato. In this talk\, we
are going to discuss some foundational results on the Hodge-Iwasawa modul
es and Hodge-Iwasawa sheaves\, as well as some interesting investigation t
owards 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://researchseminars.org/talk/UCSD_NTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Organizational meeting (UCSD)
DTSTART;VALUE=DATE-TIME:20201001T210000Z
DTEND;VALUE=DATE-TIME:20201001T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/11
DESCRIPTION:Title: Organizational meeting\nby Organizational meeting (UCSD) as part of
UCSD number theory seminar\n\nLecture held in normally APM 7321\, currentl
y online.\n\nAbstract\nThis is an organizational meeting for the remainder
of the term. The seminar itself will begin one week later.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Pollack (UCSD)
DTSTART;VALUE=DATE-TIME:20201008T210000Z
DTEND;VALUE=DATE-TIME:20201008T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
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 APM 7321
\, currently online.\n\nAbstract\nThe exceptional group $E_{7\,3}$ has a s
ymmetric space with Hermitian tube structure. On it\, Henry Kim wrote dow
n low weight holomorphic modular forms that are "singular" in the sense th
at their Fourier expansion has many terms equal to zero. The symmetric sp
ace associated to the exceptional group $E_{8\,4}$ does not have a Hermiti
an structure\, but it has what might be the next best thing: a quaternioni
c structure and associated "modular forms". I will explain the constructio
n of singular modular forms on $E_{8\,4}$\, and the proof that these speci
al modular forms have rational Fourier expansions\, in a precise sense. T
his builds off of work of Wee Teck Gan and uses key input from Gordan Savi
n.\n\npre-talk at 1:30pm\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Mundy (Columbia)
DTSTART;VALUE=DATE-TIME:20201105T220000Z
DTEND;VALUE=DATE-TIME:20201105T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
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\nLectu
re held in normally APM 7321\, currently online.\n\nAbstract\nI will talk
about some recent work determining the archimedean components of certain E
isenstein 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 work in p
rogress on producing nonzero classes in symmetric cube Selmer groups.\n\np
re-talk at 1:30\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brandon Alberts (UCSD)
DTSTART;VALUE=DATE-TIME:20201029T210000Z
DTEND;VALUE=DATE-TIME:20201029T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/14
DESCRIPTION:Title: Modeling Malle's Conjecture with Random Groups\nby Brandon Alberts (
UCSD) as part of UCSD number theory seminar\n\nLecture held in normally AP
M 7321\, currently online.\n\nAbstract\nWe construct a random group with a
local structure that models the behavior of the absolute Galois group ${\
\rm Gal}(\\overline{K}/K)$\, and prove that this random group satisfies Ma
lle's conjecture for counting number fields ordered by discriminant with p
robability 1. This work is motivated by the use of random groups to model
class group statistics in families of number fields (and generalizations).
We take care to address the known counter-examples to Malle's conjecture
and how these may be incorporated into the random group.\n\npre-talk at 1:
30\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Upton (UCSD)
DTSTART;VALUE=DATE-TIME:20201112T220000Z
DTEND;VALUE=DATE-TIME:20201112T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/15
DESCRIPTION:Title: Newton Slopes in $\\mathbb{Z}_p$-Towers of Curves\nby James Upton (U
CSD) as part of UCSD number theory seminar\n\nLecture held in normally APM
7321\, currently online.\n\nAbstract\nLet $X/\\mathbb{F}_q$ be a smooth a
ffine 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-cov
ering $X_\\infty:\\cdots \\to X_1 \\to X_0 = X$ with total Galois group $\
\mathbb{Z}_p$. For certain ``monodromy stable'' coverings over an ordinary
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 $[0\,1]$\, confirming a
conjecture of Daqing Wan. We also prove a ``Riemann hypothesis'' for a fa
mily of Galois representations associated to $X_\\infty/X$\, analogous to
the Riemann hypothesis for equicharacteristic $L$-series as posed by Davi
d Goss. This is joint work with Joe Kramer-Miller.\n\npre-talk at 1:30\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yifeng Liu (Yale University)
DTSTART;VALUE=DATE-TIME:20201120T000000Z
DTEND;VALUE=DATE-TIME:20201120T010000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
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\nLect
ure held in normally APM 7321\, currently online.\n\nAbstract\nIn this tal
k\, 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 extensio
n\, whose global root number is -1. We show that\, under some restrictions
on the ramification of \\pi\, if the central derivative L'(1/2\,\\pi) is
nonvanishing\, then the \\pi-nearly isotypic localization of the Chow grou
p of a certain unitary Shimura variety over its reflex field does not vani
sh. This proves part of the Beilinson--Bloch conjecture for Chow groups an
d L-functions. Moreover\, assuming the modularity of Kudla's generating fu
nctions of special cycles\, we explicitly construct elements in a certain
\\pi-nearly isotypic subspace of the Chow group by arithmetic theta liftin
g\, 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 Chao Li.
\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Mornev (ETHZ)
DTSTART;VALUE=DATE-TIME:20201203T180000Z
DTEND;VALUE=DATE-TIME:20201203T190000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/17
DESCRIPTION:Title: Local monodromy of Drinfeld modules\nby Maxim Mornev (ETHZ) as part
of UCSD number theory seminar\n\nLecture held in normally APM 7321\, curre
ntly online.\n\nAbstract\nThe theory of Drinfeld modules is remarkably sim
ilar to the theory of abelian varieties\, but their local monodromy behave
s differently and is poorly understood. In this talk I will present a rese
arch program which aims to fully describe this monodromy. The cornerstone
of this program is a "z-adic" variant of Grothendieck's l-adic monodromy t
heorem.\n\nThe talk is aimed at a general audience of number theorists and
arithmetic geometers. No special knowledge of monodromy theory or Drinfel
d modules is assumed.\n\nThere will be a pre-talk introducing the theory o
f t-motives.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Popescu (UCSD)
DTSTART;VALUE=DATE-TIME:20201015T210000Z
DTEND;VALUE=DATE-TIME:20201015T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/18
DESCRIPTION:Title: An equivariant Tamagawa number formula for Drinfeld modules and beyond\nby Cristian Popescu (UCSD) as part of UCSD number theory seminar\n\nLe
cture held in normally APM 7321\, currently online.\n\nAbstract\nI will pr
esent a vast generalization of Taelman's 2012 celebrated class-number form
ula for Drinfeld modules to the setting of (rigid analytic) L-functions of
Drinfeld module motives with Galois equivariant coefficients. I will disc
uss applications and potential extensions of this formula to the category
of t-modules and t-motives. This is based on joint work with Ferrara\, Gre
en and Higgins\, and a result of meetings in the UCSD Drinfeld Module Semi
nar.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Van Koughnett (Purdue)
DTSTART;VALUE=DATE-TIME:20201022T210000Z
DTEND;VALUE=DATE-TIME:20201022T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/19
DESCRIPTION:Title: Topological modular forms for number theorists\nby Paul Van Koughnet
t (Purdue) as part of UCSD number theory seminar\n\nLecture held in normal
ly APM 7321\, currently online.\n\nAbstract\nThis will be a mainly exposit
ory talk about some recent applications of number theory to topology. The
crux of these applications is the construction of a cohomology theory call
ed topological modular forms (TMF) out of the moduli of elliptic curves. I
'll explain what TMF is\, what we have been doing with it\, and what we'd
still like to know\; I'll also discuss more recent attempts to extend the
theory using level structures\, higher-dimensional abelian varieties\, and
K3 surfaces. Time permitting\, I'll talk about my work with Dominic Culve
r on some partial number-theoretic interpretations of TMF co-operations.\n
\nI'll give a pre-talk.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Le Hung (Northwestern University)
DTSTART;VALUE=DATE-TIME:20201210T220000Z
DTEND;VALUE=DATE-TIME:20201210T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/20
DESCRIPTION:Title: Moduli of Fontaine-Laffaille modules and mod p local-global compatibilit
y.\nby Bao Le Hung (Northwestern University) as part of UCSD number th
eory seminar\n\nLecture held in normally APM 7321\, currently online.\n\nA
bstract\nThe mod p cohomology of locally symmetric spaces for definite uni
tary groups at infinite level is expected to realize the mod p local Langl
ands correspondence for GL_n. In particular\, one expects the (component a
t p) of the associated Galois representation to be determined by cohomolog
y as a smooth representation. I will describe how one can establish this e
xpectation in many cases when the local Galois representation is Fontaine-
Laffaille.\nThis is joint work with D. Le\, S. Morra\, C. Park and Z. Qian
.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Lam (Harvard University)
DTSTART;VALUE=DATE-TIME:20210107T220000Z
DTEND;VALUE=DATE-TIME:20210107T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/21
DESCRIPTION:Title: Calabi-Yau varieties and Shimura varieties\nby Joshua Lam (Harvard U
niversity) as part of UCSD number theory seminar\n\nLecture held in normal
ly APM 7321\, currently online.\n\nAbstract\nI will discuss the Attractor
Conjecture for Calabi-Yau varieties\, which was formulated by Moore in the
nineties\, highlighting the difference between Calabi-Yau varieties with
and without Shimura moduli. In the Shimura case\, I show that the conjectu
re holds and gives rise to an explicit parametrization of CM points on cer
tain Shimura varieties\; in the case without Shimura moduli\, I’ll prese
nt counterexamples to the conjecture using unlikely intersection theory. P
art of this is joint work with Arnav Tripathy.\n\nThere will be a 30 minut
e pre-talk.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aranya Lahiri (Indiana University)
DTSTART;VALUE=DATE-TIME:20210114T220000Z
DTEND;VALUE=DATE-TIME:20210114T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
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 number theo
ry seminar\n\nLecture held in normally APM 7321\, currently online.\n\nAbs
tract\nLocally analytic representations of $p$-adic analytic groups have p
layed a crucial role in many areas of arithmetic and representation theory
(including in $p$-adic local Langlands program) since their introduction
by Schneider and Teitelbaum. In this talk we will briefly review some asp
ects of the theory of locally analytic representations. Then\, for a loca
lly analytic representation $V$ of $GL_2(F)$ we will construct a coefficie
nt system attached to the Bruhat-Tits tree of $Gl_2(F)$. Finally we will u
se this coefficient system to construct a resolution for locally analytic
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 pre-talk.
\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naomi Sweeting (Harvard University)
DTSTART;VALUE=DATE-TIME:20210204T220000Z
DTEND;VALUE=DATE-TIME:20210204T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/23
DESCRIPTION:Title: Kolyvagin's conjecture and higher congruences of modular forms\nby N
aomi Sweeting (Harvard University) as part of UCSD number theory seminar\n
\nLecture held in normally APM 7321\, currently online.\n\nAbstract\nGiven
an elliptic curve E\, Kolyvagin used CM points on modular curves to cons
truct a system of classes valued in the Galois cohomology of the torsion p
oints of E. Under the conjecture that not all of these classes vanish\, h
e gave a description for the Selmer group of E. This talk will report on
recent work proving new cases of Kolyvagin's conjecture. The methods foll
ow in the footsteps of Wei Zhang\, who used congruences between modular fo
rms to prove Kolyvagin's conjecture under some technical hypotheses. We re
move many of these hypotheses by considering congruences modulo higher po
wers of p. The talk will explain the difficulties associated with higher
congruences of modular forms and how they can be overcome. I will also pro
vide an introduction to the conjecture and its consequences\, including a
'converse theorem': algebraic rank one implies analytic rank one.\n\npre-t
alk at 1:30\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kwun Angus Chung (University of Michigan)
DTSTART;VALUE=DATE-TIME:20210121T220000Z
DTEND;VALUE=DATE-TIME:20210121T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/24
DESCRIPTION:Title: $v$-adic convergence for exp and log in function fields and applications
to $v$-adic $L$-values\nby Kwun Angus Chung (University of Michigan)
as part of UCSD number theory seminar\n\nLecture held in normally APM 7321
\, currently online.\n\nAbstract\nClassically over the rational numbers\,
the exponential and logarithm series converge $p$-adically within some ope
n disc of $\\mathbb{C}_p$. For function fields\, exponential and logarithm
series arise naturally from Drinfeld modules\, which are objects construc
ted by Drinfeld in his thesis to prove the Langlands conjecture for $\\mat
hrm{GL}_2$ over function fields. For a "finite place" $v$ on such a curve\
, one can ask if the exp and log possess similar $v$-adic convergence prop
erties. 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 ell
iptic curves and a certain class of hyperelliptic curves. As an applicatio
n\, 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 formula
in the number field case.\n\npre-talk\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashwin Iyengar (King's College\, London)
DTSTART;VALUE=DATE-TIME:20210128T220000Z
DTEND;VALUE=DATE-TIME:20210128T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
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 seminar\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 famili
es over the extended eigencurve\, and how to formulate a two-variable Iwas
awa main conjecture. If time permits\, I will state some open questions ab
out this family of functions.\n\nI will give a pre-talk beforehand at 1:30
.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allechar Serrano Lopez (University of Utah)
DTSTART;VALUE=DATE-TIME:20210211T220000Z
DTEND;VALUE=DATE-TIME:20210211T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/26
DESCRIPTION:Title: Counting elliptic curves with prescribed torsion over imaginary quadrati
c fields\nby Allechar Serrano Lopez (University of Utah) as part of UC
SD number theory seminar\n\nLecture held in normally APM 7321\, currently
online.\n\nAbstract\nA generalization of Mazur's theorem states that 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 groups\, we
count the number of elliptic curves of bounded naive height whose torsion
subgroup is isomorphic to $G$ in the case of imaginary quadratic fields.\n
\npre-talk\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zuhair Mullath (University of Massachusetts\, Amherst)
DTSTART;VALUE=DATE-TIME:20210218T220000Z
DTEND;VALUE=DATE-TIME:20210218T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/27
DESCRIPTION:Title: Unobstructed Galois deformation problems associated to GSp(4)\nby Zu
hair Mullath (University of Massachusetts\, Amherst) as part of UCSD numbe
r theory seminar\n\nLecture held in normally APM 7321\, currently online.\
n\nAbstract\nTo a cuspidal automorphic representation of GSp(4) over $\\ma
thbb Q$\, one can associate a compatible system of Galois representations
$\\{\\rho_p\\}_{p \\\; \\mathrm{prime}}$. For $p$ sufficiently large\, the
deformation theory of the mod-$p$ reduction $\\overline \\rho_p$ is expec
ted to be unobstructed -- meaning the universal deformation ring is a powe
r series ring. The global obstructions to deforming $\\overline \\rho_p$ i
s controlled by certain adjoint Bloch-Kato Selmer groups\, which are expec
ted to be trivial for $p$ large enough.\n\nI will talk about some recent r
esults showing that there are no local obstructions to the deformation the
ory 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://researchseminars.org/talk/UCSD_NTS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Trudgian (UNSW Canberra at ADFA)
DTSTART;VALUE=DATE-TIME:20210225T220000Z
DTEND;VALUE=DATE-TIME:20210225T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/28
DESCRIPTION:Title: Verifying the Riemann hypothesis to a new height\nby Tim Trudgian (U
NSW Canberra at ADFA) as part of UCSD number theory seminar\n\nLecture hel
d in normally APM 7321\, currently online.\n\nAbstract\nSadly\, I won’t
have time to prove the Riemann hypothesis in this talk. However\, I do hop
e to outline recent work in a record partial-verification of RH. This is j
oint work with Dave Platt\, in Bristol\, UK.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soumya Sankar (The Ohio State University)
DTSTART;VALUE=DATE-TIME:20210304T220000Z
DTEND;VALUE=DATE-TIME:20210304T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/29
DESCRIPTION:Title: Counting elliptic curves with a rational $N$-isogeny\nby Soumya Sank
ar (The Ohio State University) as part of UCSD number theory seminar\n\nLe
cture held in normally APM 7321\, currently online.\n\nAbstract\nThe class
ical problem of counting elliptic curves with a rational N-isogeny can be
phrased in terms of counting rational points on certain moduli stacks of e
lliptic curves. Counting points on stacks poses various challenges\, and I
will discuss these along with a few ways to overcome them. I will also ta
lk about the theory of heights on stacks developed in recent work of Ellen
berg\, Satriano and Zureick-Brown and use it to count elliptic curves with
an $N$-isogeny for certain $N$. The talk assumes no prior knowledge of st
acks and is based on joint work with Brandon Boggess.\n\nThere will be a 3
0 minute pre-talk for graduate students and postdocs preceding the main ta
lk.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Organizational meeting (UCSD)
DTSTART;VALUE=DATE-TIME:20210311T220000Z
DTEND;VALUE=DATE-TIME:20210311T230000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/30
DESCRIPTION:Title: Organizational meeting\nby Organizational meeting (UCSD) as part of
UCSD number theory seminar\n\nLecture held in normally APM 7321\, currentl
y online.\n\nAbstract\nOrganizational meeting to plan for next quarter. No
talk.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Koymans (MPIM)
DTSTART;VALUE=DATE-TIME:20210401T180000Z
DTEND;VALUE=DATE-TIME:20210401T190000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
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 normally
APM 7321\, currently online.\n\nAbstract\nIn 2002 Malle conjectured an asy
mptotic formula for the number of $G$-extensions of a number field $K$ wit
h discriminant bounded by $X$. In this talk I will discuss recent joint wo
rk with Etienne Fouvry on this conjecture. Our main result proves Malle's
conjecture in the special case of nonic Heisenberg extensions.\n\npre-talk
\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahesh Kakde (IISc\, Bangalore)
DTSTART;VALUE=DATE-TIME:20210408T170000Z
DTEND;VALUE=DATE-TIME:20210408T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/32
DESCRIPTION:Title: On the Brumer-Stark conjecture and applications to Hilbert's 12th proble
m\nby Mahesh Kakde (IISc\, Bangalore) as part of UCSD number theory se
minar\n\nLecture held in normally APM 7321\, currently online.\n\nAbstract
\nI will report on my joint work with Samit Dasgupta on the Brumer-Stark c
onjecture proving existence of the Brumer-Stark units and on a conjecture
of Dasgupta giving a p-adic analytic formula for these units. I will prese
nt a sketch of our proof of the Brumer-Stark conjecture and also mention a
pplications to Hilbert's 12th problem\, or explicit class field theory.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lance Miller (University of Arkansas)
DTSTART;VALUE=DATE-TIME:20210415T210000Z
DTEND;VALUE=DATE-TIME:20210415T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/33
DESCRIPTION:Title: Finiteness of quasi-canonical lifts of elliptic curves\nby Lance Mil
ler (University of Arkansas) as part of UCSD number theory seminar\n\nLect
ure held in normally APM 7321\, currently online.\n\nAbstract\nFix a prime
integer $p$. Set $R$ the completed valuation ring of the maximal unramifi
ed extension of $\\mathbb{Q}_p$. For $X := X_1(N)$ the modular curve with
$N$ at least 4 and coprime to $p$\, Buium-Poonen in 2009 showed that the
locus of canonical lifts enjoys finite intersection with preimages of fini
te rank subgroups of $E(R)$ when $E$ is an elliptic curve with a surjectio
n from $X$. This is done using Buium's theory of arithmetic ODEs\, in part
icular interesting homomorphisms $E(R) \\to R$ which are arithmetic analog
ues of Manin maps. \n\nIn this talk\, I will review the general idea behin
d this result and other applications of arithmetic jet spaces to Diophanti
ne geometry and discuss a recent analogous result for quasi-canonical lift
s\, i.e.\, those curves with Serre-Tate parameter a root of unity. Here th
e ODE Manin maps are insufficient\, so we introduce a PDE version of Buium
's theory to provide the needed maps. All of this is joint work with A. Bu
ium.\n\npre-talk at 1:30\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Owen Barrett (University of Chicago)
DTSTART;VALUE=DATE-TIME:20210422T210000Z
DTEND;VALUE=DATE-TIME:20210422T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/34
DESCRIPTION:Title: The derived category of the abelian category of constructible sheaves\nby Owen Barrett (University of Chicago) as part of UCSD number theory s
eminar\n\nLecture held in normally APM 7321\, currently online.\n\nAbstrac
t\nNori proved in 2002 that given a complex algebraic variety $X$\, the bo
unded\nderived category of the abelian category of constructible sheaves o
n $X$ is\nequivalent to the usual triangulated category $D(X)$ of bounded\
nconstructible complexes on $X$.\nHe moreover showed that given any constr
uctible sheaf $\\mathcal F$ on\n$\\A^n$\, there is an injection $\\mathcal
F\\hookrightarrow\\mathcal G$ with\n$\\mathcal G$ constructible and $H^i(
\\A^n\,\\mathcal G)=0$ for $i>0$.\n\nIn this talk\, I'll discuss how to ex
tend Nori's theorem to the case of a\nvariety over an algebraically closed
field of positive characteristic\, with\nBetti constructible sheaves repl
aced by $\\ell$-adic sheaves.\nThis is the case $p=0$ of the general probl
em which asks whether the bounded\nderived category of $p$-perverse sheave
s is equivalent to $D(X)$\, resolved\naffirmatively for the middle pervers
ity by Beilinson.\n\npre-talk at 1:30pm\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Klevdal (University of Utah)
DTSTART;VALUE=DATE-TIME:20210429T210000Z
DTEND;VALUE=DATE-TIME:20210429T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/35
DESCRIPTION:Title: Integrality of G-local systems\nby Christian Klevdal (University of
Utah) as part of UCSD number theory seminar\n\nLecture held in normally AP
M 7321\, currently online.\n\nAbstract\nSimpson conjectured that for a red
uctive group $G$\, rigid $G$-local systems on a smooth projective complex
variety are integral. I will discuss a proof of integrality for cohomologi
cally rigid $G$-local systems. This generalizes and is inspired by work of
Esnault and Groechenig for $GL_n$. Surprisingly\, the main tools used 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 Drinfeld
on companions of $\\ell$-adic sheaves. The major differences between gener
al $G$ and $GL_n$ are first to make sense of companions for $G$-local syst
ems\, and second to show that the monodromy group of a rigid G-local syste
m is semisimple. All work is joint with Stefan Patrikis.\n\npre-talk\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Fox (University of Oregon)
DTSTART;VALUE=DATE-TIME:20210506T210000Z
DTEND;VALUE=DATE-TIME:20210506T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/36
DESCRIPTION:by Maria Fox (University of Oregon) as part of UCSD number the
ory seminar\n\nLecture held in normally APM 7321\, currently online.\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Howe (University of Utah)
DTSTART;VALUE=DATE-TIME:20210513T210000Z
DTEND;VALUE=DATE-TIME:20210513T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/37
DESCRIPTION:by Sean Howe (University of Utah) as part of UCSD number theor
y seminar\n\nLecture held in normally APM 7321\, currently online.\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nahid Walji (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20210520T210000Z
DTEND;VALUE=DATE-TIME:20210520T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/38
DESCRIPTION:by Nahid Walji (University of British Columbia) as part of UCS
D number theory seminar\n\nLecture held in normally APM 7321\, currently o
nline.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evan O'Dorney (Princeton University)
DTSTART;VALUE=DATE-TIME:20210527T210000Z
DTEND;VALUE=DATE-TIME:20210527T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/39
DESCRIPTION:by Evan O'Dorney (Princeton University) as part of UCSD number
theory seminar\n\nLecture held in normally APM 7321\, currently online.\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kelly Isham (University of California Irvine)
DTSTART;VALUE=DATE-TIME:20210603T210000Z
DTEND;VALUE=DATE-TIME:20210603T220000Z
DTSTAMP;VALUE=DATE-TIME:20210419T084808Z
UID:UCSD_NTS/40
DESCRIPTION:by Kelly Isham (University of California Irvine) as part of UC
SD number theory seminar\n\nLecture held in normally APM 7321\, currently
online.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/40/
END:VEVENT
END:VCALENDAR