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BEGIN:VEVENT
SUMMARY:Keping Huang (MSU)
DTSTART:20221019T183000Z
DTEND:20221019T193000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/1
DESCRIPTION:Title: A Tits alternative for endomorphisms of the projective lin
e\nby Keping Huang (MSU) as part of Carleton-Ottawa Number Theory semi
nar\n\n\nAbstract\nWe prove an analog of the Tits alternative for endomorp
hisms of $\\mathbb{P}^1$. In particular\, we show that if $S$ is a finite
ly generated semigroup of endomorphisms of $\\mathbb{P}^1$ over $\\mathbb{
C}$\, then either $S$ has polynomially bounded growth or $S$ contains a no
nabelian free semigroup. We also show that if $f$ and $g$ are polarizable
maps over any field of any characteristic and $\\mathrm{Prep}(f) \\neq \\
mathrm{Prep}(g)$\, then for all sufficiently large $j$\, the semigroup $\\
langle f^j\, g^j \\rangle$ is a free semigroup on two generators. This is
a joint work with Jason Bell\, Wayne Peng\, and Thomas Tucker.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pranabesh Das (Xavier University of Louisiana)
DTSTART:20221026T190000Z
DTEND:20221026T200000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/2
DESCRIPTION:Title: Perfect Powers in power sums\nby Pranabesh Das (Xavier
University of Louisiana) as part of Carleton-Ottawa Number Theory seminar
\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Logan (Govt. of Canada and Carleton U.)
DTSTART:20221102T183000Z
DTEND:20221102T193000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/3
DESCRIPTION:Title: A conjectural uniform construction of many rigid Calabi-Ya
u threefolds\nby Adam Logan (Govt. of Canada and Carleton U.) as part
of Carleton-Ottawa Number Theory seminar\n\n\nAbstract\nGiven a rational H
ecke eigenform f of weight 2\, Eichler-Shimura theory gives a construction
of an elliptic curve over Q whose associated modular form is f. Mazur\, v
an Straten\, and others have asked whether there is an analogous construct
ion for Hecke eigenforms f of weight k >2 that produces a variety for whic
h the Galois representation on its etale H^{k−1} (modulo classes of cycl
es if k is odd) is that of f. In weight 3 this is understood by work of El
kies and Schutt\, but in higher weight it remains mysterious\, despite man
y examples in weight 4. In this talk I will present a new construction bas
ed on families of K3 surfaces of Picard number 19 that recovers many exist
ing examples in weight 4 and produces almost 20 new ones.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soren Kleine (Universität der Bundeswehr München)
DTSTART:20221109T193000Z
DTEND:20221109T203000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/4
DESCRIPTION:Title: On the $\\mathfrak{M}_H(G)$-property\nby Soren Kleine
(Universität der Bundeswehr München) as part of Carleton-Ottawa Number T
heory seminar\n\n\nAbstract\nLet $p$ be any rational prime\, and let $E$ b
e an elliptic curve defined over $\\mathbb{Q}$ which has good ordinary red
uction at the prime $p$. We let $K$ be a number field\, which we assume to
be totally imaginary if ${p = 2}$. \n \n Let $K_\\infty$ be a $\\Z_p^2$
-extension of $K$ which contains the cyclotomic $\\Z_p$-extension $K_{cyc}
$ of $K$. The classical $\\mathfrak{M}_H(G)$-conjecture is a statement abo
ut the Pontryagin dual $X(E/K_\\infty)$ of the Selmer group of $E$ over $K
_\\infty$: if \n \\[ H_{cyc} = \\Gal(K_\\infty/K_{cyc}) \\subseteq \\Gal(
K_\\infty/K) =: G\, \\] \n then the quotient $X(E/K_\\infty)/X(E/K_\\inft
y)[p^\\infty]$ of $X(E/K_\\infty)$ by its $p$-torsion submodule\, which is
known to be finitely generated over $\\Z_p[[G]]$\, is conjectured to be a
ctually finitely generated as a $\\Z_p[[H_{cyc}]]$-module. \n \n In this
talk\, we discuss an analogous property for non-cyclotomic $\\Z_p$-extens
ions. To be more precise\, we let $\\mathcal{E}$ be the set of $\\Z_p$-ext
ensions ${L \\subseteq K_\\infty}$ of $K$. For each ${L \\in \\mathcal{E}}
$\, one can ask whether the quotient \n \\[ X(E/K_\\infty)/X(E/K_\\infty)
[p^\\infty] \\] \n is finitely generated as a $\\Z_p[[H]]$-module\, where
now ${H = \\Gal(K_\\infty/L)}$. We prove many equivalent criteria for the
validity of this $\\mathfrak{M}_H(G)$-property\, some of which generalise
previously known conditions for the special case ${H = H_{cyc}}$\, wherea
s several other conditions are completely new. The new conditions involve\
, for example\, the boundedness of $\\lambda$-invariants of the Pontryagin
duals $X(E/L)$ as one runs over the elements ${L \\in \\mathcal{E}}$. By
using the new conditions\, we can show that the $\\mathfrak{M}_H(G)$-prope
rty holds for all but finitely many ${L \\in \\mathcal{E}}$. \n \n Moreo
ver\, we also derive several applications. For example\, we can prove some
special cases of a conjecture of Mazur on the growth of Mordell-Weil rank
s along the $\\Z_p$-extensions in $\\mathcal{E}$. \n \n All of this is j
oint work with Ahmed Matar and Sujatha.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shilun Wang (Università degli Studi di Padova)
DTSTART:20221116T193000Z
DTEND:20221116T203000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/5
DESCRIPTION:Title: Explicit reciprocity law for finite slope modulalr forms\nby Shilun Wang (Università degli Studi di Padova) as part of Carleton
-Ottawa Number Theory seminar\n\n\nAbstract\nDarmon and Rotger constructed
the generalized diagonal cycles in the product of three\nKuga-Sato variet
ies\, which generalizes the modified diagonal cycle considered by Gross–
Kudla and Gross–Schoen. Recently\, Bertolini\, Seveso and Venerucci foun
d a different way to construct the diagonal cycles. They proved the p-adic
Gross–Zagier formula and the explicit reciprocity law relating to p-adi
c L-function attached to the Garrett–Rankin triple convolution of three
Hida families of modular forms. These formulae have wide range of applicat
ions\, such as Bloch–Kato conjecture and exceptional zero problem. Howe
ver\, we find that both constructions do not have any requirements on the
slope of modular form\, so it is possible to apply their constructions to
the other case that the modular forms are of finite slope. Combining with
the p-adic L-function for modular forms of finite slope constructed by And
reatta and Iovita recently\, we can try to generalize results to the tripl
e convolution of three Coleman families of modular forms.\nIn this talk\,
I will give a brief introduction to how to generalize Bertolini\, Seveso a
nd\nVenerucci’s results and if time permits\, I will try to talk about s
ome applications. All of this is from the work in progress.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Hu (U. Oslo)
DTSTART:20221123T193000Z
DTEND:20221123T203000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/6
DESCRIPTION:Title: An upper bound for polynomial log-volume growth of automor
phisms of zero entropy\nby Fei Hu (U. Oslo) as part of Carleton-Ottawa
Number Theory seminar\n\n\nAbstract\nLet f be an automorphism of zero ent
ropy of a smooth projective variety X. \nThe polynomial log-volume growth
$\\operatorname{plov(f)}$ of f is a natural analog of Gromov's log-volume
growth of automorphisms (of positive entropy)\, formally introduced by Can
tat and Paris-Romaskevich for slow dynamics in 2020. \nA surprising fact n
oticed by Lin\, Oguiso\, and Zhang in 2021 is that this dynamical invarian
t plov(f) essentially coincides with the Gelfand-Kirillov dimension of the
twisted homogeneous coordinate ring associated with (X\, f)\, introduced
by Artin\, Tate\, and Van den Bergh in the 1990s.\nIt was conjectured by t
hem that $\\operatorname{plov}(f)$ is bounded above by $d^2$\, where $d =
\\operatorname{dim} X$. \n\nWe prove an upper bound for $\\operatorname{pl
ov}(f)$ in terms of the dimension $d$ of $X$ and another fundamental invar
iant $k$ of $(X\, f)$ (i.e.\, the degree growth rate of iterates $f^n$ wit
h respect to an arbitrary ample divisor on $X$).\nAs a corollary\, we prov
e the above conjecture based on an earlier work of Dinh\, Lin\, Oguiso\, a
nd Zhang.\nThis is joint work with Chen Jiang.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Bharadwaj (Queen's U.)
DTSTART:20221130T193000Z
DTEND:20221130T203000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/7
DESCRIPTION:Title: On primitivity and vanishing of Dirichlet series\nby A
bhishek Bharadwaj (Queen's U.) as part of Carleton-Ottawa Number Theory se
minar\n\n\nAbstract\nFor a rational valued periodic function\, we associat
e a Dirichlet series and provide a new necessary and sufficient condition
for the vanishing of this Dirichlet series specialized at positive integer
s. This theme was initiated by Chowla and carried out by Okada for a parti
cular infinite sum. Our approach relies on the decomposition of the Dirich
let characters in terms of primitive characters. Using this\, we find some
new family of natural numbers for which a conjecture of Erd\\"{o}s holds.
\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katharina Mueller (Université Laval)
DTSTART:20230208T194500Z
DTEND:20230208T204500Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/8
DESCRIPTION:Title: Iwasawa main conjectures for graphs\nby Katharina Muel
ler (Université Laval) as part of Carleton-Ottawa Number Theory seminar\n
\nLecture held in STEM 664 UOttawa.\n\nAbstract\nWe will give a short intr
oduction to the Iwasawa theory of finite connected graphs. We will then ex
plain the Iwasawa main conjecture for $\\mathbb{Z}_p^l$ coverings. If time
permits we will also discuss work in progress on the non-abelian case.\n\
nThis is joint work with Sören Kleine.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (University of Manitoba)
DTSTART:20230301T194500Z
DTEND:20230301T204500Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/9
DESCRIPTION:Title: Diagonal restriction of Eisenstein series and Kudla-Millso
n theta lift\nby Romain Branchereau (University of Manitoba) as part o
f Carleton-Ottawa Number Theory seminar\n\nLecture held in STEM 664 UOttaw
a.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Dion (Université Laval)
DTSTART:20230308T194500Z
DTEND:20230308T204500Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/10
DESCRIPTION:Title: Distribution of Iwasawa invariants for complete graphs\nby Cédric Dion (Université Laval) as part of Carleton-Ottawa Number T
heory seminar\n\nLecture held in STEM 664 UOttawa.\n\nAbstract\nFix a prim
e number $p$. Let $X$ be a finite multigraph and ̈$\\cdots \\rightarrow X
_2\\rightarrow X_1\\rightarrow X$ be a sequence of coverings such that $\\
mathrm{Gal}(X_n/X)\\cong \\mathbb{Z}/p^n\\mathbb{Z}$. McGown–Vallières
and Gonet have shown that there exists invariants $\\mu\,\\lambda$ and $\\
nu$ such that the $p$-part of the number of spanning trees of $X_n$ is giv
en by $p^{\\mu p^n+\\lambda n+\\nu}$ for $n$ large enough. In this talk\,
we will study the distribution of these invariants when $X$ varies in the
family of complete graphs. This is joint work with Antonio Lei\, Anwesh Ra
y and Daniel Vallières.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiacheng Xia (Université Laval)
DTSTART:20230412T184500Z
DTEND:20230412T194500Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/11
DESCRIPTION:Title: The orthogonal Kudla conjecture over totally real fields<
/a>\nby Jiacheng Xia (Université Laval) as part of Carleton-Ottawa Number
Theory seminar\n\n\nAbstract\nOn a modular curve\, Gross--Kohnen--Zagier
proves that certain generating series of Heegner points are modular forms
of weight 3/2 with values in the Jacobian. Such a result has been extended
to orthogonal Shimura varieties over totally real fields by Yuan--Zhang--
Zhang for special Chow cycles assuming absolute convergence of the generat
ing series.\n\nBased on the method of Bruinier--Raum over the rationals\,
we plan to fill this gap of absolute convergence over totally real fields.
In this talk\, I will lay out the setting of the problem and explain some
of the new challenges that we face over totally real fields.\n\nThis is a
joint work in progress with Qiao He.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yukako Kezuka (Institut de Mathématiques de Jussieu)
DTSTART:20230215T194500Z
DTEND:20230215T204500Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/12
DESCRIPTION:Title: Non-vanishing theorems for central L-values\nby Yukak
o Kezuka (Institut de Mathématiques de Jussieu) as part of Carleton-Ottaw
a Number Theory seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bharathwaj Palvannan (Indian Institute of Science\, Bangalore)
DTSTART:20230315T140000Z
DTEND:20230315T150000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/13
DESCRIPTION:Title: An ergodic approach towards an equidistribution result of
Ferrero–Washington\nby Bharathwaj Palvannan (Indian Institute of Sc
ience\, Bangalore) as part of Carleton-Ottawa Number Theory seminar\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nike Vatsal (UBC)
DTSTART:20230320T170000Z
DTEND:20230320T180000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/14
DESCRIPTION:Title: Congruences for symmetric square and Rankin L-functions\nby Nike Vatsal (UBC) as part of Carleton-Ottawa Number Theory seminar\
n\nLecture held in STEM 464.\n\nAbstract\nWork of Coates\, Schmidt\, and H
ida dating back almost 40 years shows how to construct p-adic L-functions
for the symmetric square and Rankin-Selberg L-functions associated to modu
lar forms. There constructions work over Q\, and it has long been a folklo
re question as to whether or not their constructions work over integer rin
gs. In this talk we will show how to adapt their construction to give inte
gral results\, and to show that congruent modular forms have congruent p-a
dic L-functions.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabien Pazuki (University of Copenhagen)
DTSTART:20230329T184500Z
DTEND:20230329T194500Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/15
DESCRIPTION:Title: Isogeny volcanoes: an ordinary inverse problem\nby Fa
bien Pazuki (University of Copenhagen) as part of Carleton-Ottawa Number T
heory seminar\n\nLecture held in STEM-201.\n\nAbstract\nWe prove that any
abstract $\\ell$-volcano graph can be realized as a connected component of
the $\\ell$-isogeny graph of an ordinary elliptic curve defined over $\\m
athbb{F}_p$\, where $\\ell$ and $p$ are two different primes. This is join
t work with Henry Bambury and Francesco Campagna.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sash Zotine (Queen's U.)
DTSTART:20230405T184500Z
DTEND:20230405T194500Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/16
DESCRIPTION:Title: Kawaguchi-Silverman Conjecture for Projectivized Bundles
over Curves\nby Sash Zotine (Queen's U.) as part of Carleton-Ottawa Nu
mber Theory seminar\n\n\nAbstract\nThe Kawaguchi-Silverman Conjecture is a
recent conjecture equating two invariants of a dominant rational map betw
een projective varieties: the first dynamical degree and arithmetic degree
. The first dynamical degree measures the mixing of the map\, and the arit
hmetic degree measures how complicated rational points become after iterat
ion. Recently\, the conjecture was established for several classes of vari
eties\, including projectivized bundles over any non-elliptic curve. We wi
ll discuss my recent work with Brett Nasserden to resolve the elliptic cas
e\, hence proving KSC for all projectivized bundles over curves.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammad Manji (University of Warwick)
DTSTART:20231010T200000Z
DTEND:20231010T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/17
DESCRIPTION:Title: Iwasawa Theory for GU(2\,1) at inert primes\nby Muham
mad Manji (University of Warwick) as part of Carleton-Ottawa Number Theory
seminar\n\nLecture held in STEM-464.\n\nAbstract\nThe Iwasawa main conjec
ture was stated by Iwasawa in the 1960s\, linking the Riemann Zeta functio
n to certain ideals coming from class field theory\, and proved in 1984 by
Mazur and Wiles. This work was generalised to the setting of modular form
s\, predicting that analytic and algebraic constructions of the p-adic L-f
unction of a modular form agree\, proved by Kato (’04) and Skinner--Urba
n (’06) for ordinary modular forms. For the non-ordinary case there are
some modern approaches which use p-adic Hodge theory and rigid geometry to
formulate and prove cases of the conjecture. I will review these cases an
d discuss my work in the setting of automorphic representations of unitary
groups at non-split primes\, where a new approach uses the L-analytic reg
ulator map of Schneider—Venjakob. My aim is to state a version of the co
njecture which was previously unknown\, and discuss what is still needed t
o prove the conjecture in full.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erman Isik (University of Ottawa)
DTSTART:20231017T200000Z
DTEND:20231017T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/18
DESCRIPTION:Title: Modular approach to Diophantine equation $x^p+y^p=z^3$ ov
er some number fields\nby Erman Isik (University of Ottawa) as part of
Carleton-Ottawa Number Theory seminar\n\nLecture held in STEM-464.\n\nAbs
tract\nSolving Diophantine equations\, in particular\, Fermat-type equatio
ns is one of the oldest and most widely studied topics in mathematics. Aft
er Wiles’ proof of Fermat’s Last Theorem using his celebrated modulari
ty theorem\, several mathematicians have attempted to extend this approach
to various Diophantine equations and number fields over several number fi
elds.\n\n\nThe method used in the proof of this theorem is now called “m
odular approach”\, which makes use of the relation between modular forms
and elliptic curves. I will first briefly mention the main steps of the m
odular approach\, and then report our asymptotic result (joint work with {
\\"O}zman and Kara) on the solutions of the Fermat-type equation $x^p+y^p=
z^3$ over various number fields.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chatchai Noytaptim (University of Waterloo)
DTSTART:20231107T210000Z
DTEND:20231107T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/19
DESCRIPTION:Title: Arithmetic Dynamical Questions with Local Rationality
\nby Chatchai Noytaptim (University of Waterloo) as part of Carleton-Ottaw
a Number Theory seminar\n\n\nAbstract\nIn this talk\, we first introduce a
numerical criterion which bounds the degree of any algebraic integer in s
hort intervals (i.e.\, intervals of length less than 4). As an application
\, we classify all unicritical polynomials defined over the maximal totall
y real extension of the field of rational numbers. Using tools from comple
x and p-adic potential theory\, we also classify all quadratic unicritical
polynomials defined over the field of rational numbers in which they have
only finitely many totally real preperiodic points. In particular\, we ar
e able to explicitly compute totally real preperiodic points of some quadr
atic unicritical polynomials by applying the numerical tool and p-adic dyn
amics. This is based on joint work with Clay Petsche.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akash Sengupta (University of Waterloo)
DTSTART:20231121T210000Z
DTEND:20231121T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/20
DESCRIPTION:Title: Radical Sylvester-Gallai configurations\nby Akash Sen
gupta (University of Waterloo) as part of Carleton-Ottawa Number Theory se
minar\n\n\nAbstract\nIn 1893\, Sylvester asked a basic question in combina
torial geometry: given a finite set of distinct points v_1\,...\, v_m in R
^n such that the line joining any pair of distinct points v_i\,v_j contai
ns a third point v_k in the set\, must all points in the set be collinear?
\n\nThe classical Sylvester-Gallai (SG) theorem says that the answer to Sy
lvester’s question is yes\, i.e. such finite sets of points are all coll
inear. Generalizations of Sylvester's problem\, which are known as Sylvest
er-Gallai type problems have been widely studied by mathematicians\, have
found remarkable applications in algebraic complexity theory and coding th
eory. The underlying theme in all Sylvester-Gallai type questions is the f
ollowing:\n\nAre Sylvester-Gallai type configurations always low-dimension
al?\n\nIn this talk\, we will discuss a non-linear generalization of Sylve
ster's problem\, and its connections with the Stillman uniformity phenomen
on in Commutative Algebra. I’ll talk about an algebraic-geometric approa
ch towards studying such SG-configurations and a result showing that radic
al SG-configurations are indeed low dimensional as conjectured by Gupta in
2014. This is based on joint work with Rafael Oliveira.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Nguyen (Queen's University)
DTSTART:20231114T210000Z
DTEND:20231114T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/21
DESCRIPTION:Title: Variance over Z and moments of L-functions\nby David
Nguyen (Queen's University) as part of Carleton-Ottawa Number Theory semin
ar\n\n\nAbstract\nOne of the central problems in analytic number theory ha
s been to evaluate moments of the absolute value of L-functions on the cri
tical line. Bounds on these moments are approximations to the Lindelöf hy
pothesis and\, thus\, subconvexity bounds for these L-functions. Besides a
few low moments where rigorous results are known\, sharp bounds on higher
moments are wide open. Recently\, in 2018\, it has been discovered that t
here is a certain connection between asymptotics of moments of L-functions
and variance over the integers (the Keating--Rodgers--Roditty-Gershon--Ru
dnick--Soundararajan conjecture in arithmetic progressions). Certain analo
gues of this conjecture are completely known\, i.e.\, are theorems\, in th
e function field setting. In this lecture\, I plan to explain this new con
nection between asymptotics of variance over Z and those of moments\, and
discuss my work on confirming a smoothed version of this conjecture in a r
estricted range.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chelsea Walton (Rice University)
DTSTART:20231026T230000Z
DTEND:20231027T000000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/22
DESCRIPTION:Title: Fields-Carleton Distinguished Lecture (public lecture): M
odernizing Modern Algebra\, I: Category Theory is coming\, whether we like
it or not\nby Chelsea Walton (Rice University) as part of Carleton-Ot
tawa Number Theory seminar\n\nLecture held in 274\, 275 Teraanga Commons\,
Carleton University\, Ottawa.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harun Kir (Queen's University)
DTSTART:20231205T210000Z
DTEND:20231205T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/24
DESCRIPTION:Title: The refined Humbert invariant as an ingredient\nby Ha
run Kir (Queen's University) as part of Carleton-Ottawa Number Theory semi
nar\n\nLecture held in STEM-664.\n\nAbstract\nIn this talk\, I will adve
rtise the refined Humbert invariant\, which is the main ingredient of my
research. It was introduced by Ernst Kani(1994) upon observing that ever
y curve $C$ comes equipped with a canonically defined positive definite qu
adratic form $q_C$. This result can be used to define algebraically the (
usual) Humbert invariant (1899) and Humbert surfaces. \n\nThe beauty of th
e refined Humbert invariant is that it translates the geometric questions
into the arithmetic questions. Therefore\, it allows us to solve many int
eresting geometric problems regarding the nature of curves of genus $2$ in
cluding the automorphism groups and the elliptic subcovers of these curves
\, the intersection of the Humbert surfaces\, and the CM points on the Sh
imuracurves in this intersection. \n\nI will also give the classification
of this invariant in the CM case as these illustrations reveal how interes
ting the refined Humbert invariant is.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chelsea Walton (Rice University)
DTSTART:20231027T173000Z
DTEND:20231027T183000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/25
DESCRIPTION:Title: Fields-Carleton Distinguished Lecture (research lecture):
Modernizing Modern Algebra\, II: Category Theory is coming\, whether we l
ike it or not\nby Chelsea Walton (Rice University) as part of Carleton
-Ottawa Number Theory seminar\n\nLecture held in 4351 Herzberg Building\,
Macphail Room\, Carleton University\, Ottawa.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Baril Boudreau (U. Lethbridge)
DTSTART:20240305T210000Z
DTEND:20240305T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/27
DESCRIPTION:Title: The Distribution of Logarithmic Derivatives of Quadratic
L-functions in Positive Characteristic\nby Felix Baril Boudreau (U. Le
thbridge) as part of Carleton-Ottawa Number Theory seminar\n\nLecture held
in STEM-664.\n\nAbstract\nTo each square-free monic polynomial $D$ in a f
ixed polynomial ring $\\mathbb{F}_q[t]$\, we can associate a real quadrati
c character $\\chi_D$\, and then a Dirichlet $L$-function $L(s\,\\chi_D)$.
We compute the limiting distribution of the family of values $L'(1\,\\chi
_D)/L(1\,\\chi_D)$ as $D$ runs through the square-free monic polynomials o
f $\\mathbb{F}_q[t]$ and establish that this distribution has a smooth den
sity function. Time permitting\, we discuss connections of this result wit
h Euler-Kronecker constants and ideal class groups of quadratic extensions
. This is joint work with Amir Akbary.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fırtına Küçük (University College Dublin)
DTSTART:20240319T200000Z
DTEND:20240319T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/28
DESCRIPTION:Title: Factorization of algebraic p-adic L-functions of Rankin-S
elberg products\nby Fırtına Küçük (University College Dublin) as
part of Carleton-Ottawa Number Theory seminar\n\n\nAbstract\nIn the first
part of the talk\, I will give a brief review of Artin formalism and its p
-adic variant. Artin formalism gives a factorization of L-functions whenev
er the associated Galois representation decomposes. I will explain why the
p-adic Artin formalism is a non-trivial problem when there are no critica
l L-values. In particular\, I will focus on the case where the Galois repr
esentation arises from a self-Rankin-Selberg product of a newform\, and pr
esent the results in this direction including the one I obtained in my PhD
thesis.\n\nIn the last part of the talk\, I will discuss the case where t
he newform f in question has a theta-critical p-stabilization\, i.e. if f
is in the image of the theta operator. Unlike the ordinary and the non-cri
tical slope cases\, one cannot simply define the p-adic L-function of f in
terms of its interpolative properties. I will discuss technical difficult
ies paralleling this and explain the degenerate properties of the theta-cr
itical forms in terms of the algebro-geometric properties of the eigencurv
e.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Bharadwaj (Queen's U.)
DTSTART:20240409T200000Z
DTEND:20240409T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/29
DESCRIPTION:Title: Sufficient conditions for a problem of Polya\nby Abhi
shek Bharadwaj (Queen's U.) as part of Carleton-Ottawa Number Theory semin
ar\n\n\nAbstract\nThere is an old result attributed to Polya on identifyin
g algebraic integers by studying the power traces\; and a finite version o
f this result was proved by Bart de Smit. We study the generalisation of t
hese questions\, namely determining algebraic integers by imposing certain
constraints on the power sums. This is a joint work with V Kumar\, A Pal
and R Thangadurai. Time permitting\, we will also describe related results
in an ongoing project.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gary Walsh (Tutte Institute and University of Ottawa)
DTSTART:20240513T130000Z
DTEND:20240513T140000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/30
DESCRIPTION:Title: Solving problems of Erdos using elliptic curves and an el
liptic curve analogue of the Ankeny-Artin-Chowla Conjecture\nby Gary W
alsh (Tutte Institute and University of Ottawa) as part of Carleton-Ottawa
Number Theory seminar\n\n\nAbstract\nWe describe how the Mordell-Weil gro
up of rational points on a certain families of elliptic curves give rise t
o solutions to conjectures of Erdos on powerful numbers\, and state a rela
ted conjecture\, which can be viewed as an elliptic curve analogue of the
Ankeny-Artin-Chowla Conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arul Shankar (University of Toronto))
DTSTART:20240513T143000Z
DTEND:20240513T153000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/31
DESCRIPTION:Title: Conditional bounds on the 2\, 3\, 4\, and 5 torsion of th
e class groups of number fields\nby Arul Shankar (University of Toront
o)) as part of Carleton-Ottawa Number Theory seminar\n\n\nAbstract\nLet n
be a positive integer\, and let K be a degree n number field. It is believ
ed that the class group of K should be a cyclic group\, up to factors that
are negligible compared to the size of the discriminant of K. Another way
of phrasing this is to say that for any fixed m\, the m torsion subgroup
of the class group of K is negligible in size. This is only known for the
2 torsion subgroups of quadratic fields by work of Gauss.\n\nFor other pai
rs m and n\, it is a natural question to obtain nontrivial bounds for the
sizes of the m torsion in the class groups of degree n fields K.\nIn this
talk\, I will discuss joint work with Jacob Tsimerman\, in which we prove
such bounds\, conditional on some standard elliptic curve conjectures\, fo
r the cases m=2\, 3\, 4\, and 5 (and where n is allowed to be any positive
integer).\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammadreza Mohajer (University of Ottawa)
DTSTART:20240513T173000Z
DTEND:20240513T183000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/32
DESCRIPTION:Title: Exploring p-adic periods of 1-motive\nby Mohammadreza
Mohajer (University of Ottawa) as part of Carleton-Ottawa Number Theory s
eminar\n\n\nAbstract\nPeriod numbers and p-adic periods are crucial in num
ber theory\, offering insights into transcendence theory and arithmetic ge
ometry. Classical period numbers\, arising from integrals of algebraic dif
ferential forms\, serve as transcendental numbers\, encoding deep arithmet
ic information. Studying classical periods is well-explored in curtain cas
es however\, extending these concepts to their p-adic counterparts present
greater complexity. In this work\, we develop an integration theory for 1
-motives with good reduction\, serving as a generalization of Fontaine-Mes
sing p-adic integration. For 1-motive M with good reduction\, the p-adic n
umbers resulting from this integration are called Fontaine-Messing p-adic
periods of M. We identify a suitable p-adic Betti-like Q-structure inside
the crystalline realisation and we show that a p-adic version Kontsevich-Z
agier conjecture holds for M\, if one takes the Fontaine-Messing p-adic pe
riods of M relative to its p-adic Betti lattice. This theorem is the p-adi
c version of analytic subgroup theorem for 1-motives with good reduction.\
n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier (McGill U.)
DTSTART:20240513T200000Z
DTEND:20240513T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/33
DESCRIPTION:Title: Statistics of automorphic forms using endoscopy\nby M
athilde Gerbelli-Gauthier (McGill U.) as part of Carleton-Ottawa Number Th
eory seminar\n\n\nAbstract\nClassical questions about modular forms on SL_
2 have direct analogues on higher-rank groups: What is the dimension of sp
aces of forms of a given weight and level? How are the Hecke eigenvalues d
istributed? What is the sign of the functional equation of the associated
L-function? Though exact answers can be hard to obtain in general for grou
ps of higher rank\, I’ll describe some statistical results towards these
questions\, and outline how we obtain them using the stable trace formula
. This is joint work\, some of it in progress\, with Rahul Dalal.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raiza Corpuz (Waikato/Ottawa)
DTSTART:20240916T200000Z
DTEND:20240916T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/34
DESCRIPTION:Title: Equivalences of the Iwasawa main conjecture\nby Raiza
Corpuz (Waikato/Ottawa) as part of Carleton-Ottawa Number Theory seminar\
n\nLecture held in STEM-464.\n\nAbstract\nLet $p$ be an odd prime\, and su
ppose that $E_1$ and $E_2$ are two elliptic curves which are congruent mod
ulo $p$. Fix an Artin representation $\\tau: G_F \\to \\text{\\rm GL}_2(\\
mathbb{C})$ over a totally real field $F$\, induced from a Hecke character
over a CM-extension $K/F$. We compute the variation of the $\\mu$- and $\
\lambda$-invariants of the Iwasawa Main Conjecture\, as one switches betwe
en $\\tau$-twists of $E_1$ and $E_2$\, thereby establishing an analogue of
Greenberg and Vatsal's result. Moreover\, we show that provided an Euler
system exists\, IMC$(E_1\, \\tau)$ is true if and only if IMC$(E_2\, \\ta
u)$ is true. This is joint work with Daniel Delbourgo from University of W
aikato.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taiga Adachi (Kyushu/Ottawa)
DTSTART:20241007T200000Z
DTEND:20241007T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/35
DESCRIPTION:Title: Iwasawa theory for weighted graphs\nby Taiga Adachi (
Kyushu/Ottawa) as part of Carleton-Ottawa Number Theory seminar\n\nLecture
held in STEM-464.\n\nAbstract\nLet $p$ be a prime number and $d$ a positi
ve integer. In Iwasawa theory for graphs\, the asymptotic behavior of the
number of the spanning trees in $\\mathbb{Z}_p^d$-towers has been studied.
In this talk\, we generalize several results for graphs to weighted graph
s. We prove an analogue of Iwasawa’s class number formula and that of Ri
emann-Hurwitz formula for $\\mathbb{Z}_p^d$-towers of weighted graphs. Thi
s is a joint work with Kosuke Mizuno and Sohei Tateno.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chatchai Noytaptim (University of Waterloo)
DTSTART:20241118T210000Z
DTEND:20241118T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/36
DESCRIPTION:Title: A finiteness result of common zeros of iterated rational
functions\nby Chatchai Noytaptim (University of Waterloo) as part of C
arleton-Ottawa Number Theory seminar\n\nLecture held in STEM-664.\n\nAbstr
act\nIn 2017\, Hsia and Tucker proved—under compositional independence a
ssumptions—that there are only finitely many irreducible factors of the
greatest common divisors of two iterated polynomials with complex coeffici
ents. In the same paper\, Hsia and Tucker posed a question and asked wheth
er a finiteness result of common zeros holds true for iterated rational fu
nctions with complex coefficients. In joint work with Xiao Zhong (Waterloo
)\, we have recently answered the question in affirmative. In fact\, the q
uestion is true except for special families of rational functions of degre
e one.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nic Fellini (Queen's University)
DTSTART:20241028T190000Z
DTEND:20241028T200000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/37
DESCRIPTION:Title: Congruence relations of Ankeny--Artin--Chowla type for re
al quadratic fields\nby Nic Fellini (Queen's University) as part of Ca
rleton-Ottawa Number Theory seminar\n\nLecture held in STEM-464.\n\nAbstra
ct\nIn 1951\, Ankeny\, Artin\, and Chowla published a brief note containin
g four congruence relations involving the class number of Q(sqrt(d)) for p
ositive squarefree integers d = 1 (mod 4). Many of the ideas present in th
eir paper can be seen as the precursors to the now developed theory of cyc
lotomic fields. Curiously\, little attention has been paid to the cases of
d = 2\, 3 (mod 4) in the literature.\n\nIn this talk\, I will describe th
e present state of affairs for congruences of the type proven by Ankeny\,
Artin\, and Chowla\, indicating where possible\, the connection to p-adic
L-functions. Time permitting\, I will sketch how the so called "Ankeny--Ar
tin--Chowla conjecture" is related to special dihedral extensions of Q.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerry Wang (University of Waterloo)
DTSTART:20241104T210000Z
DTEND:20241104T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/38
DESCRIPTION:Title: On the squarefree values of $a^4 + b^3$\nby Jerry Wan
g (University of Waterloo) as part of Carleton-Ottawa Number Theory semina
r\n\n\nAbstract\nA classical question in analytic number theory is to dete
rmine the density of integers $a_1\, \\ldots\, a_n$ such that $P(a_1\, \\l
dots\, a_n)$ is squarefree\, where $P$ is a fixed integer polynomial. In t
his talk\, we consider the case $P(a\, b) = a^4 + b^3$. When the pairs $(a
\, b)$ are ordered by $\\max\\{|a|^{1/3}\, |b|^{1/4}\\}$\, we prove that t
his density equals the conjectured product of local densities. We combine
Bhargava's set up for counting integral orbits\, with the circle method an
d the Selberg sieve. This is joint work with Gian Sanjaya.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Earp-Lynch (Carleton University)
DTSTART:20241125T210000Z
DTEND:20241125T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/39
DESCRIPTION:Title: Simplest relative Thue equations and inequalities\nby
Ben Earp-Lynch (Carleton University) as part of Carleton-Ottawa Number Th
eory seminar\n\nLecture held in STEM-664.\n\nAbstract\nA Thue equation has
the form $F(X\,Y)=m$\, where $F\\in \\Z[X\,Y]$ is an irreducible binary f
orm of degree at least $3$\, and $m$ is an integer. In 1909\, Axel Thue s
howed that such equations have finitely many integer solutions. The so-ca
lled simplest Thue equations are those from which arise the simplest numbe
r fields\, which were first studied in a different context by Shanks in th
e 1970s. I will discuss recent work which solves a parametric family of s
implest quartic relative Thue inequalities over quadratic fields.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Pagano (Concordia University)
DTSTART:20241202T210000Z
DTEND:20241202T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/40
DESCRIPTION:Title: Hilbert 10 via additive combinatorics\nby Carlo Pagan
o (Concordia University) as part of Carleton-Ottawa Number Theory seminar\
n\nLecture held in STEM-664.\n\nAbstract\nIn 1970 Matiyasevich\, building
on earlier work of Davis--Putnam--Robinson\, proved that every enumerable
subset of Z is Diophantine\, thus showing that Hilbert's 10th problem is u
ndecidable for Z. The problem of extending this result to the ring of inte
gers of number fields (and more generally to finitely generated infinite r
ings) has attracted significant attention and\, thanks to the efforts of m
any mathematicians\, the task has been reduced to the problem of construct
ing\, for certain quadratic extensions of number fields L/K\, an elliptic
curve E/K with rk(E(L))=rk(E(K))>0. \nIn this talk I will explain joint wo
rk with Peter Koymans\, where we use Green--Tao to construct the desired e
lliptic curves\, settling Hilbert 10 for every finitely generated infinite
ring.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dong Quan Nguyen (University of Maryland College Park)
DTSTART:20241007T183000Z
DTEND:20241007T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/41
DESCRIPTION:Title: An analogue of the Kronecker-Weber theorem for rational f
unction fields over ultra-finite fields\nby Dong Quan Nguyen (Universi
ty of Maryland College Park) as part of Carleton-Ottawa Number Theory semi
nar\n\nLecture held in STEM-464.\n\nAbstract\nIn this talk\, I will talk a
bout my recent work that establishes a correspondence between Galois exten
sions of rational function fields over arbitrary fields F_s and Galois ext
ensions of the rational function field over the ultraproduct of the fields
F_s. As an application\, I will discuss an analogue of the Kronecker-Web
er theorem for rational function fields over ultraproducts of finite field
s. I will also describe an analogue of cyclotomic fields for these rationa
l function fields that generalizes the works of Carlitz from the 1930s\, a
nd Hayes in the 1970s. If time permits\, I will talk about how to use the
correspondence established in my work to study the inverse Galois problem
for rational function fields over finite fields.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hatley (Union College)
DTSTART:20241111T210000Z
DTEND:20241111T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/42
DESCRIPTION:Title: Recent Progress on Watkins's Conjecture\nby Jeff Hatl
ey (Union College) as part of Carleton-Ottawa Number Theory seminar\n\nLec
ture held in STEM-664.\n\nAbstract\nIt is now known that every elliptic cu
rve E/Q has a modular parameterization. From this parameterization\, one c
an define several arithmetic invariants for E\, such as its modular degree
. This geometrically-defined invariant is expected to have an important ar
ithmetic interpretation\; in particular\, Watkins's Conjecture predicts th
at the Mordell-Weil rank of E(Q) is bounded above by the 2-valuation of th
e modular degree. In this talk\, we will explain Watkins's Conjecture and
survey some of the progress that has been made on it\, focusing especially
on some recent work which is joint with Debanjana Kundu.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Royer (CNRS/CRM)
DTSTART:20241121T210000Z
DTEND:20241121T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/43
DESCRIPTION:Title: Differential algebras of quasi-Jacobi forms of index zero
\nby Emmanuel Royer (CNRS/CRM) as part of Carleton-Ottawa Number Theor
y seminar\n\nLecture held in STEM-464.\n\nAbstract\nAfter introducing the
concepts of singular Jacobi forms\, we will define quasi-Jacobi forms and
study their algebraic structure. We will focus in particular on their stab
ility under various derivations and construct sequences of bidifferential
operators with the aim of finding analogs of the well-known Rankin-Cohen b
rackets or transvectants on algebras of modular forms. This is a joint wor
k with François Dumas and François Martin from the University of Clermon
t Auvergne.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hatley (Union College)
DTSTART:20241113T210000Z
DTEND:20241113T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/44
DESCRIPTION:Title: Rational Points on Elliptic Curves over Infinite Extensio
ns\nby Jeff Hatley (Union College) as part of Carleton-Ottawa Number T
heory seminar\n\nLecture held in Stem 664.\n\nAbstract\nElliptic curves ar
e among the most-studied objects in modern number theory. The Mordell-Weil
theorem\nsays that if K/Q is an algebraic extension of finite degree\, th
en E(K)\, the K-rational points of E\, form a\nfinitely-generated abelian
group\, and much work continues to be done on classifying the groups that
can\narise in this way. It turns out that\, for many infinite extensions K
/Q\, the group E(K) remains finitely-\ngenerated\, and the same sorts of q
uestions can be asked (and sometimes answered) in this new setting.\nWe wi
ll give a survey of some of the active research being done in this area.\n
Tea\, coffee and goodies will be served at 3:30 in STM 664. This colloquiu
m is partially sponsored by the CRM.\n\nSpecial uOttawa Colloquium.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Martin (IMPA)
DTSTART:20250120T210000Z
DTEND:20250120T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/45
DESCRIPTION:Title: The Xiao conjecture for surfaces fibered by trigonal genu
s 5 curves\nby Olivier Martin (IMPA) as part of Carleton-Ottawa Number
Theory seminar\n\n\nAbstract\nThe Xiao conjecture predicts that the relat
ive irregularity\nq_f:=q(S)-g(B) of a fibered surface f: S--->B is at most
g/2+1\, where g\nis the genus of the general fiber. It was proven by Barj
a\,\nGonzález-Alonso\, and Naranjo when the general fiber has maximal Cli
fford\nindex. I will present a proof of the Xiao conjecture for surfaces\n
fibered by trigonal genus 5 curves\, which completes the proof of the\nXia
o conjecture for surfaces fibered by genus 5 curves.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhang Xiao (Peking University)
DTSTART:20250225T000000Z
DTEND:20250225T010000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/46
DESCRIPTION:Title: Diophantine Approximation on Surfaces and Distribution of
Integral Points\nby Zhang Xiao (Peking University) as part of Carleto
n-Ottawa Number Theory seminar\n\n\nAbstract\nAfter Mordell’s conjecture
for curves was proved by Faltings\, attentions turn to the distribution o
f rational and integral points on higher dimensional varieties\, which is
encoded in the celebrated Vojta’s conjecture. Along this line we proved
a subspace type inequality\, improving the result of Ru-Vojta\, on surface
s. Meanwhile\, we obtain a sharp criterion of when some certain surfaces a
dmit a non Zariski-dense set of integral points. Joint with Huang\, Levin.
\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stanley Xiao (UNBC)
DTSTART:20250304T223000Z
DTEND:20250304T233000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/47
DESCRIPTION:Title: Polynomials in two variables of degree at most 6 cannot r
epresent all positive integers without representing infinitely negative in
tegers\nby Stanley Xiao (UNBC) as part of Carleton-Ottawa Number Theor
y seminar\n\n\nAbstract\nIn 2010\, Bjorn Poonen asked a famous question on
MathOverflow with nearly 300 upvotes which sought an answer to the follow
ing: does there exist a polynomial $f \\in \\mathbb{Z}[x\,y]$ such that $f
(\\mathbb{Z} \\times \\mathbb{Z}) = \\mathbb{N}$? If we allow three or mor
e variables\, then the answer is yes\, by famous theorems of Lagrange and
Gauss who showed that the polynomials \n\n$\\mathcal{L}(x_1\, x_2\, x_3\,
x_4) = x_1^2 + x_2^2 + x_3^2 + x_4^2$ \n\nand\n\n$\\mathcal{G}(x_1\, x_2\,
x_3) = \\frac{x_1(x_1 - 1)}{2} + \\frac{x_2(x_2 - 1)}{2} + \\frac{x_3(x_3
- 1)}{2}$\n\nwork respectively. If we have only one variable\, then the a
nswer would obviously be "no". Thus\, the most interesting case is the two
-variable case.\n\nDespite significant apparent interest in the question\,
and a highly voted "answer" by Terry Tao\, the question remains unresolve
d. Recently\, in a joint paper with S. Yamagishi\, we have shown that it i
s not possible for quartic polynomials in two variables to satisfy Poonen'
s question. Later\, in a separate paper\, I showed that no such degree six
polynomials exist either.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Logan (Carleton University)
DTSTART:20250317T200000Z
DTEND:20250317T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/48
DESCRIPTION:Title: Kodaira dimension of Hilbert modular threefolds\nby A
dam Logan (Carleton University) as part of Carleton-Ottawa Number Theory s
eminar\n\nLecture held in STEM-664.\n\nAbstract\nFollowing a method introd
uced by Thomas-Vasquez and developed by Grundman\,\nwe prove that many Hil
bert modular threefolds of arithmetic\ngenus $0$ and $1$ are of general ty
pe\, and that some are of nonnegative\nKodaira dimension. The new ingredi
ent is a detailed study\nof the geometry and combinatorics of totally posi
tive integral elements\n$x$ of a fractional ideal $I$ in a totally real nu
mber field $K$ with\nthe property that tr $xy < $ min $I$ tr $y$ for some
$y \\gg 0 \\in K$.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammad Manji (Concordia University)
DTSTART:20250324T183000Z
DTEND:20250324T193000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/50
DESCRIPTION:Title: Iwasawa theory for \\mathbb{Q}_{p^2}-analytic distributio
ns\nby Muhammad Manji (Concordia University) as part of Carleton-Ottaw
a Number Theory seminar\n\nLecture held in STEM-664.\n\nAbstract\nThere ar
e many existing cases of Iwasawa theory of arithmetic objects in Z_p exten
sions\, starting from the original work of Iwasawa and later Mazur-Wiles f
or GL_1 studying the behaviour of class numbers up the cyclotomic tower. L
ater work (Kato\, Skinner-Urban) studied the Iwasawa theory of modular for
ms\, showing that certain Selmer groups can give us p-adic distributions w
hich interpolate L-values of ordinary cusp forms. This work has been gener
alised to many more settings where the Galois tower is larger but the loca
l extension remains a \\mathbb{Z}_p-extension. Recent development in the c
onstruction of a regulator map for Lubin—Tate Iwasawa cohomology allows
us to study a new setting where p is inert in the reflex field of our arit
hmetic data. We will go through two examples\; one of CM elliptic curves w
ith p inert in the CM field and one of unitary groups.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Earp-Lynch (Carleton University)
DTSTART:20250407T200000Z
DTEND:20250407T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/51
DESCRIPTION:Title: Variants of a Problem of Lucas and Schäffer\nby Simo
n Earp-Lynch (Carleton University) as part of Carleton-Ottawa Number Theor
y seminar\n\nLecture held in STEM-664.\n\nAbstract\nIn 1875\, Édouard Luc
as posited that the only pairs of integers x and y satisfying 1^k+2^k+...+
x^k=y^n with k=n=2 are (x\,y)=(1\,1) and (24\,70). Schäffer's Conjecture
(1956) broadened this to include all but a handful of exponents. Althoug
h the conjecture remains open\, progress towards it has provoked interest
in related Diophantine problems. I will discuss work concerning two varia
nts of the problem and the multifarious tools applied\, which include loca
l methods\, Lucas sequences\, linear forms in logarithms and the modular a
pproach over number fields.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihir Deo (University of Ottawa)
DTSTART:20250203T210000Z
DTEND:20250203T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/52
DESCRIPTION:Title: On $p$-adic $L$-functions of Bianchi modular forms\nb
y Mihir Deo (University of Ottawa) as part of Carleton-Ottawa Number Theor
y seminar\n\nLecture held in STEM-664.\n\nAbstract\nFor a prime $p$\, one
can think of $p$-adic $L$-functions as power series with coefficients in a
local field or the ring of integers of a local field\, which have certain
growth properties and interpolate special values of complex $L$-functions
. In this talk\, I will discuss the decomposition of $p$-adic $L$-function
s with unbounded coefficients\, attached to $p$-non-ordinary Bianchi modul
ar forms\, into signed $p$-adic $L$-functions with bounded coefficients in
two different scenarios. These results generalise works of Pollack\, Spru
ng\, and Lei-Loeffler-Zerbes on elliptic modular forms. The talk will begi
n with a review of Bianchi modular forms\, as well as complex and $p$-adic
$L$-functions associated with them.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anwesh Ray (Chennai Mathematical Institute)
DTSTART:20250623T200000Z
DTEND:20250623T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/53
DESCRIPTION:Title: Modular forms with large Selmer $p$-rank\nby Anwesh R
ay (Chennai Mathematical Institute) as part of Carleton-Ottawa Number Theo
ry seminar\n\n\nAbstract\nWe construct modular forms whose associated Galo
is representations have Bloch--Kato Selmer groups with arbitrarily large $
p$-torsion. While such phenomena were previously known only for small prim
es\, we extend these results to any fixed prime $p \\geq 5$. The method co
mbines Iwasawa theory with deformation theory of Galois representations. T
his is joint work with Eknath Ghate.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debanjana Kundu (University of Regina)
DTSTART:20250721T200000Z
DTEND:20250721T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/54
DESCRIPTION:Title: Iwasawa Theory of Elliptic Curves in Quadratic Twist Fami
lies\nby Debanjana Kundu (University of Regina) as part of Carleton-Ot
tawa Number Theory seminar\n\nLecture held in STEM-664.\n\nAbstract\nIn my
talk I will discuss the variation of Iwasawa invariants of rational ellip
tic curves in some quadratic twist families using two different approaches
. This is work in progress with Katharina Mueller.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brandon Hansson
DTSTART:20250922T130000Z
DTEND:20250922T140000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/55
DESCRIPTION:Title: Arithmetic combinatorics from high-dimensional probabilit
y\nby Brandon Hansson as part of Carleton-Ottawa Number Theory seminar
\n\nLecture held in 664.\n\nAbstract\nThe use of probability in combinator
ics was pioneered by Erdos\, rather famously. Recently\, techniques from h
igh-dimensional probability have proved fruitful in attacking problems whe
re sparsity is a prominent feature. I will highlight its role in work join
t with Rudnev\, Shkredov and Zhelezov on the sum-product problem\, and if
time permits\, newer results joint with Waterhouse convolutions in the boo
lean cube.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omer Avci (University of Ottawa)
DTSTART:20250929T130000Z
DTEND:20250929T140000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/56
DESCRIPTION:Title: Torsion of Rational Elliptic Curves over the Galois Exten
sions of $\\mathbb{Q}$\nby Omer Avci (University of Ottawa) as part of
Carleton-Ottawa Number Theory seminar\n\n\nAbstract\nMazur's celebrated t
heorem gives a complete classification of the torsion subgroups $E(\\mathb
b{Q})_{\\mathrm{tors}}$ for elliptic curves $E/\\mathbb{Q}$. This result i
nspired the broader problem of classifying $E(L)_{\\mathrm{tors}}$ for ell
iptic curves $E/L$\, where $L$ is a field of characteristic zero. In this
talk\, I will first review results from the literature and some variants o
f this problem. I will then focus on the case where $L/\\mathbb{Q}$ is a G
alois extension\, outlining our methods and presenting two families of res
ults: when $L = \\mathbb{Q}(\\zeta_p)$ for a prime $p$\, and when $L$ is a
$\\mathbb{Z}_p$-extension of a quadratic field $K$.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Sajadi (University of Toronto)
DTSTART:20251020T130000Z
DTEND:20251020T140000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/57
DESCRIPTION:Title: A Unified Finiteness Theorem For Curves\nby Sara Saja
di (University of Toronto) as part of Carleton-Ottawa Number Theory semina
r\n\nLecture held in 464.\n\nAbstract\nThis talk presents a unified framew
ork for finiteness results concerning arithmetic points on algebraic curve
s\, exploring the analogy between number fields and function fields. The n
umber field setting\, joint work with F. Janbazi\, generalizes and extends
classical results of Birch–Merriman\, Siegel\, and Faltings. We prove t
hat the set of Galois-conjugate points on a smooth projective curve with g
ood reduction outside a fixed finite set of places is finite\, when consid
ered up to the action of the automorphism group of a proper integral model
. Motivated by this\, we consider the function field analogue\, involving
a smooth and proper family of curves over an affine curve defined over a f
inite field. In this setting\, we show that for a fixed degree\, there are
only finitely many étale relative divisors over the base\, up to the act
ion of the family's automorphism group (and including the Frobenius in the
isotrivial case). Together\, these results illustrate both the parallels
and distinctions between the two arithmetic settings\, contributing to a b
roader unifying perspective on finiteness.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nic Banks (University of Waterloo)
DTSTART:20251006T130000Z
DTEND:20251006T140000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/58
DESCRIPTION:Title: Classification results for intersective polynomials with
no integral roots\nby Nic Banks (University of Waterloo) as part of Ca
rleton-Ottawa Number Theory seminar\n\n\nAbstract\nIn this talk\, I descri
be the contents of my recently-defended PhD thesis on strongly intersectiv
e polynomials. These are polynomials with no integer roots but with a root
modulo every positive integer\, thereby constituting a failure of the loc
al-global principle. We start by describing their relation to Hilbert's 10
th Problem and an algorithm of James Ax. These are fascinating objects whi
ch make contact with many areas of math\, including permutation group theo
ry\, splitting behaviour of prime ideals in number fields\, and Frobenius
elements from class field theory.\n\nIn particular\, we discuss constraint
s on the splitting behaviour of ramified primes in splitting fields of int
ersective polynomials\, building on the work of Berend-Bilu (1996) and Son
n (2008). We also explain the computation of a list of possible Galois gro
ups of such polynomials\, which includes many examples and which supports
some recent conjectures of Ellis & Harper (2024).\n\nTime permitting\, we
end by discussing future work\, including results from permutation group t
heory and from character theory.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlie Wu (University of Toronto)
DTSTART:20251027T130000Z
DTEND:20251027T140000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/59
DESCRIPTION:Title: Compactness and character varieties\nby Charlie Wu (U
niversity of Toronto) as part of Carleton-Ottawa Number Theory seminar\n\n
\nAbstract\nLet $X$ be an orientable genus $g$ surface with $n$ punctures.
Relative character varieties are spaces parametrizing isomorphism classes
of representations of $\\pi_1(X)$ satisfying some local conditions around
the punctures. When this space is a single point\, some remarkable work
of Katz shows that the unique representation in this space has interesting
arithmetic and complex geometric properties - namely that it is defined o
ver the ring of integers of a number field and it ``comes from geometry".
We discuss the geometry of this space when it is larger than a point\, and
we give a classification of their compact components. This is joint work
with Daniel Litt.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Baril Boudreau (CICMA)
DTSTART:20251103T140000Z
DTEND:20251103T150000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/60
DESCRIPTION:Title: Abelian varieties with homotheties\nby Felix Baril Bo
udreau (CICMA) as part of Carleton-Ottawa Number Theory seminar\n\n\nAbstr
act\nLet $A$ be an Abelian variety defined over a number field $K$. The ce
lebrated Bogomolov-Serre theorem states that\, for any prime $\\ell$\, the
image $G_\\ell$ of the $\\ell$-adic representation of the absolute Galois
group of $K$ contains all $c$-th power homotheties\, where $c$ is a posit
ive constant. If $K$ is a global function field\, the analogous statement
fails in general\, since Zahrin has shown the existence of ordinary Abelia
n varieties of positive dimensions defined over $K$\, for which $G_\\ell$
only contains finitely many homotheties. In this talk\, I will discuss my
ongoing joint work with Sebastian Petersen (University of Kassel)\, in whi
ch we prove\, under suitable additional assumptions\, an analogue of Bogom
olov--Serre Theorem when $K$ is a finitely generated field of positive cha
racteristic.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luochen Zhao (Morning Side Center)
DTSTART:20251110T140000Z
DTEND:20251110T150000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/61
DESCRIPTION:Title: On the arithmetic of Bernoulli--Hurwitz periods\nby L
uochen Zhao (Morning Side Center) as part of Carleton-Ottawa Number Theory
seminar\n\nLecture held in 664.\n\nAbstract\nLet E be an elliptic curve h
aving good ordinary reduction at a prime p. The values of the classical Ei
senstein series at E are algebraic and are called Bernoulli--Hurwitz numbe
rs\, and they admit a p-adic interpolation by specializing Katz's one-vari
able Eisenstein measure at E. We will explain that the periods of this p-a
dic measure are modular\, i.e.\, are special values of certain weight one
higher level Eisenstein series. Furthermore\, we explain a new proof of th
e interpolation by this modularity\, as well as how one can get a p-adic K
ronecker's first limit formula.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luochen Zhao (Morning Side Center)
DTSTART:20251117T140000Z
DTEND:20251117T150000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/62
DESCRIPTION:Title: On the structure of anticyclotomic Selmer groups of modul
ar forms\nby Luochen Zhao (Morning Side Center) as part of Carleton-Ot
tawa Number Theory seminar\n\nLecture held in 664.\n\nAbstract\nI will rep
ort the recent work with Antonio Lei and Luca Mastella\, in which we deter
mine the structure of the Selmer group of a modular form over the anticycl
otomic Zp extension\, assuming the imaginary quadratic field satisfies the
Heegner hypothesis\, that p splits in it and at which the form has good r
eduction\, and that the bottom generalized Heegner class is primitive. Her
e the last assumption springs from Gross's treatment of Kolyvagin's bound
on Shafarevich--Tate groups\, and was put in the Iwasawa theoretic context
by Matar--Nekovář and Matar for elliptic curves. This talk will focus o
n our use of the vanishing of BDP Selmer groups in proving the result\, wh
ich allows us to treat both ordinary and supersingular reduction types uni
formly.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Forras (University of Ottawa)
DTSTART:20251124T140000Z
DTEND:20251124T150000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/63
DESCRIPTION:Title: Graduated orders in equivariant Iwasawa theory\nby Be
n Forras (University of Ottawa) as part of Carleton-Ottawa Number Theory s
eminar\n\nLecture held in 664.\n\nAbstract\nWe describe graduated orders o
ver regular local rings of dimension at most two\, and explain how this ca
n be used to prove integrality results in equivariant Iwasawa theory.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luochen Zhao (Morning Side Center)
DTSTART:20251114T140000Z
DTEND:20251114T150000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/64
DESCRIPTION:Title: On the structure of anticyclotomic Selmer groups of a sup
ersingular elliptic curve\nby Luochen Zhao (Morning Side Center) as pa
rt of Carleton-Ottawa Number Theory seminar\n\nLecture held in 664.\n\nAbs
tract\nLet p be a fixed prime. The study of the variation of Selmer groups
attached to a given Galois representation over a Z_p-extension is a centr
al topic in Iwasawa theory. When the Galois representation is the Tate mod
ule of a rational elliptic curve having good supersingular reduction at p\
, the information of the Selmer groups becomes rather elusive due to the f
ailure of Mazur's control theorem. In this expository talk I'll explain a
strategy (due to Matar) to study the growth of Selmer groups of a supersin
gular elliptic curve over the anticyclotomic Z_p extension\, assuming the
indivisibility of the Heegner point. Along the way\, we will introduce Ko
bayashi's modification of Selmer groups (i.e.\, plus/minus Selmer groups)\
, and explain how they could be fitted together to yield information on th
e usual Selmer groups.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Grieve (Carleton University)
DTSTART:20251208T150000Z
DTEND:20251208T160000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/65
DESCRIPTION:Title: Complexity thresholds for divisors and explicit effective
Diophantine approximation of rational points\nby Nathan Grieve (Carle
ton University) as part of Carleton-Ottawa Number Theory seminar\n\nLectur
e held in Carleton University (Room HP 4351).\n\nAbstract\nI will survey r
ecent results which surround complexity thresholds for divisors\, includin
g measures of positivity and singularities thereof\, and explain how they
interplay with Diophantine approximation of algebraic points. A portion o
f these results include recent joint work C. Noytaptim. Further\, I will
place emphasis on explicit and effective results.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Fazzari (University of Genova)
DTSTART:20260224T150000Z
DTEND:20260224T160000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/66
DESCRIPTION:Title: On the third moment of log-zeta and a twisted pair correl
ation conjecture\nby Alessandro Fazzari (University of Genova) as part
of Carleton-Ottawa Number Theory seminar\n\nLecture held in 664.\n\nAbstr
act\nI will present joint work with Maxim Gerspach on lower-order terms in
Selberg's central limit theorem. In particular\, we compute precise asymp
totic formulas for the third moment of both the real and imaginary parts o
f the logarithm of the Riemann zeta function. Our results are conditional
on the Riemann Hypothesis\, Hejhal's triple correlation\, and a new conjec
ture describing the interaction between prime powers and Montgomery's pair
correlation function. To support this conjecture\, which we refer to as t
he "twisted" pair correlation conjecture\, we prove it unconditionally in
a limited range and under the Hardy-Littlewood conjecture in a larger rang
e.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ari Shnidman (Temple University)
DTSTART:20260305T210000Z
DTEND:20260305T220000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/67
DESCRIPTION:Title: On the geometric origin of rational points on modular cur
ves\nby Ari Shnidman (Temple University) as part of Carleton-Ottawa Nu
mber Theory seminar\n\nLecture held in 664.\n\nAbstract\nBuilding on recen
t work of Zywina\, we show that all known rational points on all modular c
urves are explained by geometry in a precise sense. Along the way\, we ref
ine Zywina's explicit (conditional) classification of the images of the Ga
lois representations of elliptic curves over Q\, which places all Galois i
mages in finitely many twist families of modular curves. I'll discuss how
these results fit into Mazur's Program B. This is joint work with Derickx\
, Hashimoto\, and Najman.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan-Pablo Llerena (University of Ottawa)
DTSTART:20260309T200000Z
DTEND:20260309T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/68
DESCRIPTION:Title: ***CANCELED*** Numerical study of refined conjectures of
the Birch--Swinnerton-Dyer type\nby Juan-Pablo Llerena (University of
Ottawa) as part of Carleton-Ottawa Number Theory seminar\n\nLecture held i
n 664.\n\nAbstract\nIn 1987\, Mazur and Tate stated conjectures which\, in
some cases\, resemble the classical Birch--Swinnerton-Dyer conjecture and
its p-adic analog. We will present some of these refined conjectures\, wh
ich we studied numerically using SageMath. Furthermore\, we will mention s
ome discrepancies that we found in the original statement of these conject
ures. Lastly\, we will talk about a slight modification of these conjectur
es that appear to hold numerically.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sunil Lakshmana Naik (Queen's University)
DTSTART:20260319T190000Z
DTEND:20260319T200000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/69
DESCRIPTION:Title: Arithmetic of Fourier coefficients of Hecke eigenforms in
short intervals\nby Sunil Lakshmana Naik (Queen's University) as part
of Carleton-Ottawa Number Theory seminar\n\nLecture held in 664.\n\nAbstr
act\nIn this talk\, we will discuss the largest prime factor of Fourier co
efficients of non-CM normalized cuspidal Hecke eigenforms in short interva
ls. This requires an explicit version of the Chebotarev density theorem in
an interval of length ${x \\over (\\log x)^A}$ for any $A > 0$\, modifyin
g an earlier work of Balog and Ono. Furthermore\, we present a strengtheni
ng of a work of Rouse and Thorner to establish a lower bound on the larges
t prime factor of Fourier coefficients in an interval of length $x^{{1 \\o
ver 2} + \\epsilon}$ for any $\\epsilon > 0$. This is a joint work with Sa
noli Gun.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Logan
DTSTART:20260323T200000Z
DTEND:20260323T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/70
DESCRIPTION:Title: The degree of irrationality of del Pezzo surfaces\nby
Adam Logan as part of Carleton-Ottawa Number Theory seminar\n\n\nAbstract
\nThe degree of irrationality of a variety is the smallest degree of a dom
inant map to a rational variety of the same dimension\, while del Pezzo su
rfaces are surfaces on which the anticanonical divisor is ample. Over an
algebraically closed field\, all del Pezzo surfaces are rational and there
fore have degree of irrationality equal to 1\, but over a general field th
is does not hold. We determine the possible degrees of irrationality of d
el Pezzo surfaces of all degrees over local fields\, number fields\, and a
rbitrary fields. This is joint work with Tony Várilly-Alvarado and David
Zureick-Brown.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (McGill University)
DTSTART:20260330T200000Z
DTEND:20260330T210000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/71
DESCRIPTION:Title: Generating series of modular symbols in SL_n\nby Roma
in Branchereau (McGill University) as part of Carleton-Ottawa Number Theor
y seminar\n\n\nAbstract\nIn the 1980s\, Kudla and Millson constructed modu
lar forms whose Fourier coefficients are intersection numbers between tota
lly geodesic cycles in orthogonal locally symmetric spaces. I will present
a similar construction for cycles in the symmetric space of SL_n\, incorp
orating the work of Kudla–Millson as well as recent work of Bergeron–C
harollois–Garcia. In the case where n=2\, I will explain how it relates
to the work of Li and of Borisov–Gunnells.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rylan Gajek-Leonard (Union College)
DTSTART:20260319T170000Z
DTEND:20260319T180000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/72
DESCRIPTION:Title: Mazur--Tate elements of non-ordinary modular forms with S
erre weight larger than two\nby Rylan Gajek-Leonard (Union College) as
part of Carleton-Ottawa Number Theory seminar\n\nLecture held in 464.\n\n
Abstract\nFix an odd prime p and let f be a non-ordinary eigen-cuspform of
weight k and level coprime to p. In this talk\, we describe asymptotic fo
rmulas for the Iwasawa invariants of the Mazur-Tate elements attached to f
of weight kDifferent approaches to Arakelov theory\nby Antoine S
edillot (University of Regensburg) as part of Carleton-Ottawa Number Theor
y seminar\n\nLecture held in 664.\n\nAbstract\nIn this talk\, I will intro
duce the philosophy of Arakelov geometry and present different approaches
that allow for transferring geometric observations into arithmetic informa
tion over various kinds of fields\, such as global fields\, finitely gener
ated extensions of the prime field\, and fields of complex meromorphic fun
ctions studied in Nevanlinna theory. More precisely\, we will introduce th
e modern formalism of adelic curves of Chen and Moriwaki and their topolog
ical counterpart\, aiming at interpreting Arakelov geometry via Zariski-Ri
emann type spaces.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artane Siad (Tsinghua University)
DTSTART:20260218T180000Z
DTEND:20260218T190000Z
DTSTAMP:20260404T094649Z
UID:CarletonOttawaNT/74
DESCRIPTION:Title: On anomalies in the class groups of monogenised and unit-
monogenised number fields\nby Artane Siad (Tsinghua University) as par
t of Carleton-Ottawa Number Theory seminar\n\nLecture held in STEM-664.\n\
nAbstract\nIn this talk\, I will detail developments in our understanding
of class group anomalies in monogenised and unit-monogenised fields and ou
tline a few concrete consequences in arithmetic statistics. Variously base
d on joint work with Shankar-Swaminathan\, Shnidman\, and Venkatesh.\n
LOCATION:https://stable.researchseminars.org/talk/CarletonOttawaNT/74/
END:VEVENT
END:VCALENDAR