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BEGIN:VEVENT
SUMMARY:Keping Huang (MSU)
DTSTART:20221019T183000Z
DTEND:20221019T193000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/1
DESCRIPTION:Title: A Tits alternative for endomorphisms of the projective line\n
by Keping Huang (MSU) as part of Carleton-Ottawa Number Theory seminar\n\n
\nAbstract\nWe prove an analog of the Tits alternative for endomorphisms o
f $\\mathbb{P}^1$. In particular\, we show that if $S$ is a finitely gene
rated semigroup of endomorphisms of $\\mathbb{P}^1$ over $\\mathbb{C}$\, t
hen either $S$ has polynomially bounded growth or $S$ contains a nonabelia
n free semigroup. We also show that if $f$ and $g$ are polarizable maps o
ver 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://researchseminars.org/talk/CarletonOttawaNT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pranabesh Das (Xavier University of Louisiana)
DTSTART:20221026T190000Z
DTEND:20221026T200000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/2
DESCRIPTION:Title: Perfect Powers in power sums\nby Pranabesh Das (Xavier Univer
sity of Louisiana) as part of Carleton-Ottawa Number Theory seminar\n\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Logan (Govt. of Canada and Carleton U.)
DTSTART:20221102T183000Z
DTEND:20221102T193000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/3
DESCRIPTION:Title: A conjectural uniform construction of many rigid Calabi-Yau three
folds\nby Adam Logan (Govt. of Canada and Carleton U.) as part of Carl
eton-Ottawa Number Theory seminar\n\n\nAbstract\nGiven a rational Hecke ei
genform f of weight 2\, Eichler-Shimura theory gives a construction of an
elliptic curve over Q whose associated modular form is f. Mazur\, van Stra
ten\, and others have asked whether there is an analogous construction for
Hecke eigenforms f of weight k >2 that produces a variety for which the G
alois representation on its etale H^{k−1} (modulo classes of cycles if k
is odd) is that of f. In weight 3 this is understood by work of Elkies an
d Schutt\, but in higher weight it remains mysterious\, despite many examp
les in weight 4. In this talk I will present a new construction based on f
amilies of K3 surfaces of Picard number 19 that recovers many existing exa
mples in weight 4 and produces almost 20 new ones.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soren Kleine (Universität der Bundeswehr München)
DTSTART:20221109T193000Z
DTEND:20221109T203000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/4
DESCRIPTION:Title: On the $\\mathfrak{M}_H(G)$-property\nby Soren Kleine (Univer
sität der Bundeswehr München) as part of Carleton-Ottawa Number Theory s
eminar\n\n\nAbstract\nLet $p$ be any rational prime\, and let $E$ be an el
liptic curve defined over $\\mathbb{Q}$ which has good ordinary reduction
at the prime $p$. We let $K$ be a number field\, which we assume to be tot
ally imaginary if ${p = 2}$. \n \n Let $K_\\infty$ be a $\\Z_p^2$-extens
ion of $K$ which contains the cyclotomic $\\Z_p$-extension $K_{cyc}$ of $K
$. The classical $\\mathfrak{M}_H(G)$-conjecture is a statement about the
Pontryagin dual $X(E/K_\\infty)$ of the Selmer group of $E$ over $K_\\inft
y$: if \n \\[ H_{cyc} = \\Gal(K_\\infty/K_{cyc}) \\subseteq \\Gal(K_\\inf
ty/K) =: G\, \\] \n then the quotient $X(E/K_\\infty)/X(E/K_\\infty)[p^\\
infty]$ 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 actually
finitely generated as a $\\Z_p[[H_{cyc}]]$-module. \n \n In this talk\,
we discuss an analogous property for non-cyclotomic $\\Z_p$-extensions. T
o be more precise\, we let $\\mathcal{E}$ be the set of $\\Z_p$-extensions
${L \\subseteq K_\\infty}$ of $K$. For each ${L \\in \\mathcal{E}}$\, one
can ask whether the quotient \n \\[ X(E/K_\\infty)/X(E/K_\\infty)[p^\\in
fty] \\] \n is finitely generated as a $\\Z_p[[H]]$-module\, where now ${
H = \\Gal(K_\\infty/L)}$. We prove many equivalent criteria for the validi
ty of this $\\mathfrak{M}_H(G)$-property\, some of which generalise previo
usly known conditions for the special case ${H = H_{cyc}}$\, whereas sever
al other conditions are completely new. The new conditions involve\, for e
xample\, the boundedness of $\\lambda$-invariants of the Pontryagin duals
$X(E/L)$ as one runs over the elements ${L \\in \\mathcal{E}}$. By using t
he new conditions\, we can show that the $\\mathfrak{M}_H(G)$-property hol
ds for all but finitely many ${L \\in \\mathcal{E}}$. \n \n Moreover\, w
e also derive several applications. For example\, we can prove some specia
l cases of a conjecture of Mazur on the growth of Mordell-Weil ranks along
the $\\Z_p$-extensions in $\\mathcal{E}$. \n \n All of this is joint wo
rk with Ahmed Matar and Sujatha.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shilun Wang (Università degli Studi di Padova)
DTSTART:20221116T193000Z
DTEND:20221116T203000Z
DTSTAMP:20260422T143609Z
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 ge
neralized diagonal cycles in the product of three\nKuga-Sato varieties\, w
hich generalizes the modified diagonal cycle considered by Gross–Kudla a
nd Gross–Schoen. Recently\, Bertolini\, Seveso and Venerucci found a dif
ferent way to construct the diagonal cycles. They proved the p-adic Gross
–Zagier formula and the explicit reciprocity law relating to p-adic L-fu
nction attached to the Garrett–Rankin triple convolution of three Hida f
amilies of modular forms. These formulae have wide range of applications\,
such as Bloch–Kato conjecture and exceptional zero problem. However\,
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 ot
her case that the modular forms are of finite slope. Combining with the p-
adic L-function for modular forms of finite slope constructed by Andreatta
and Iovita recently\, we can try to generalize results to the triple conv
olution of three Coleman families of modular forms.\nIn this talk\, I will
give a brief introduction to how to generalize Bertolini\, Seveso and\nVe
nerucci’s results and if time permits\, I will try to talk about some ap
plications. All of this is from the work in progress.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Hu (U. Oslo)
DTSTART:20221123T193000Z
DTEND:20221123T203000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/6
DESCRIPTION:Title: An upper bound for polynomial log-volume growth of automorphisms
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 entropy of
a smooth projective variety X. \nThe polynomial log-volume growth $\\oper
atorname{plov(f)}$ of f is a natural analog of Gromov's log-volume growth
of automorphisms (of positive entropy)\, formally introduced by Cantat and
Paris-Romaskevich for slow dynamics in 2020. \nA surprising fact noticed
by Lin\, Oguiso\, and Zhang in 2021 is that this dynamical invariant plov(
f) essentially coincides with the Gelfand-Kirillov dimension of the twiste
d homogeneous coordinate ring associated with (X\, f)\, introduced by Arti
n\, Tate\, and Van den Bergh in the 1990s.\nIt was conjectured by them tha
t $\\operatorname{plov}(f)$ is bounded above by $d^2$\, where $d = \\opera
torname{dim} X$. \n\nWe prove an upper bound for $\\operatorname{plov}(f)$
in terms of the dimension $d$ of $X$ and another fundamental invariant $k
$ of $(X\, f)$ (i.e.\, the degree growth rate of iterates $f^n$ with respe
ct to an arbitrary ample divisor on $X$).\nAs a corollary\, we prove the a
bove conjecture based on an earlier work of Dinh\, Lin\, Oguiso\, and Zhan
g.\nThis is joint work with Chen Jiang.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Bharadwaj (Queen's U.)
DTSTART:20221130T193000Z
DTEND:20221130T203000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/7
DESCRIPTION:Title: On primitivity and vanishing of Dirichlet series\nby Abhishek
Bharadwaj (Queen's U.) as part of Carleton-Ottawa Number Theory seminar\n
\n\nAbstract\nFor a rational valued periodic function\, we associate a Dir
ichlet series and provide a new necessary and sufficient condition for the
vanishing of this Dirichlet series specialized at positive integers. This
theme was initiated by Chowla and carried out by Okada for a particular i
nfinite sum. Our approach relies on the decomposition of the Dirichlet cha
racters in terms of primitive characters. Using this\, we find some new fa
mily of natural numbers for which a conjecture of Erd\\"{o}s holds.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katharina Mueller (Université Laval)
DTSTART:20230208T194500Z
DTEND:20230208T204500Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/8
DESCRIPTION:Title: Iwasawa main conjectures for graphs\nby Katharina Mueller (Un
iversité Laval) as part of Carleton-Ottawa Number Theory seminar\n\nLectu
re held in STEM 664 UOttawa.\n\nAbstract\nWe will give a short introductio
n to the Iwasawa theory of finite connected graphs. We will then explain t
he Iwasawa main conjecture for $\\mathbb{Z}_p^l$ coverings. If time permit
s we will also discuss work in progress on the non-abelian case.\n\nThis i
s joint work with Sören Kleine.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (University of Manitoba)
DTSTART:20230301T194500Z
DTEND:20230301T204500Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/9
DESCRIPTION:Title: Diagonal restriction of Eisenstein series and Kudla-Millson theta
lift\nby Romain Branchereau (University of Manitoba) as part of Carle
ton-Ottawa Number Theory seminar\n\nLecture held in STEM 664 UOttawa.\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Dion (Université Laval)
DTSTART:20230308T194500Z
DTEND:20230308T204500Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/10
DESCRIPTION:Title: Distribution of Iwasawa invariants for complete graphs\nby C
édric Dion (Université Laval) as part of Carleton-Ottawa Number Theory s
eminar\n\nLecture held in STEM 664 UOttawa.\n\nAbstract\nFix a prime numbe
r $p$. Let $X$ be a finite multigraph and ̈$\\cdots \\rightarrow X_2\\rig
htarrow X_1\\rightarrow X$ be a sequence of coverings such that $\\mathrm{
Gal}(X_n/X)\\cong \\mathbb{Z}/p^n\\mathbb{Z}$. McGown–Vallières and Gon
et have shown that there exists invariants $\\mu\,\\lambda$ and $\\nu$ suc
h that the $p$-part of the number of spanning trees of $X_n$ is given 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 Ray and D
aniel Vallières.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiacheng Xia (Université Laval)
DTSTART:20230412T184500Z
DTEND:20230412T194500Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/11
DESCRIPTION:Title: The orthogonal Kudla conjecture over totally real fields\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 weig
ht 3/2 with values in the Jacobian. Such a result has been extended to ort
hogonal Shimura varieties over totally real fields by Yuan--Zhang--Zhang f
or special Chow cycles assuming absolute convergence of the generating ser
ies.\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 thi
s 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://researchseminars.org/talk/CarletonOttawaNT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yukako Kezuka (Institut de Mathématiques de Jussieu)
DTSTART:20230215T194500Z
DTEND:20230215T204500Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/12
DESCRIPTION:Title: Non-vanishing theorems for central L-values\nby Yukako Kezuk
a (Institut de Mathématiques de Jussieu) as part of Carleton-Ottawa Numbe
r Theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bharathwaj Palvannan (Indian Institute of Science\, Bangalore)
DTSTART:20230315T140000Z
DTEND:20230315T150000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/13
DESCRIPTION:Title: An ergodic approach towards an equidistribution result of Ferrer
o–Washington\nby Bharathwaj Palvannan (Indian Institute of Science\,
Bangalore) as part of Carleton-Ottawa Number Theory seminar\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nike Vatsal (UBC)
DTSTART:20230320T170000Z
DTEND:20230320T180000Z
DTSTAMP:20260422T143609Z
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\nLect
ure held in STEM 464.\n\nAbstract\nWork of Coates\, Schmidt\, and Hida dat
ing back almost 40 years shows how to construct p-adic L-functions for the
symmetric square and Rankin-Selberg L-functions associated to modular for
ms. There constructions work over Q\, and it has long been a folklore ques
tion as to whether or not their constructions work over integer rings. In
this talk we will show how to adapt their construction to give integral re
sults\, and to show that congruent modular forms have congruent p-adic L-f
unctions.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabien Pazuki (University of Copenhagen)
DTSTART:20230329T184500Z
DTEND:20230329T194500Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/15
DESCRIPTION:Title: Isogeny volcanoes: an ordinary inverse problem\nby Fabien Pa
zuki (University of Copenhagen) as part of Carleton-Ottawa Number Theory s
eminar\n\nLecture held in STEM-201.\n\nAbstract\nWe prove that any abstrac
t $\\ell$-volcano graph can be realized as a connected component of the $\
\ell$-isogeny graph of an ordinary elliptic curve defined over $\\mathbb{F
}_p$\, where $\\ell$ and $p$ are two different primes. This is joint work
with Henry Bambury and Francesco Campagna.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sash Zotine (Queen's U.)
DTSTART:20230405T184500Z
DTEND:20230405T194500Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/16
DESCRIPTION:Title: Kawaguchi-Silverman Conjecture for Projectivized Bundles over Cu
rves\nby Sash Zotine (Queen's U.) as part of Carleton-Ottawa Number Th
eory seminar\n\n\nAbstract\nThe Kawaguchi-Silverman Conjecture is a recent
conjecture equating two invariants of a dominant rational map between pro
jective varieties: the first dynamical degree and arithmetic degree. The f
irst dynamical degree measures the mixing of the map\, and the arithmetic
degree measures how complicated rational points become after iteration. Re
cently\, the conjecture was established for several classes of varieties\,
including projectivized bundles over any non-elliptic curve. We will disc
uss my recent work with Brett Nasserden to resolve the elliptic case\, hen
ce proving KSC for all projectivized bundles over curves.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammad Manji (University of Warwick)
DTSTART:20231010T200000Z
DTEND:20231010T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/17
DESCRIPTION:Title: Iwasawa Theory for GU(2\,1) at inert primes\nby Muhammad Man
ji (University of Warwick) as part of Carleton-Ottawa Number Theory semina
r\n\nLecture held in STEM-464.\n\nAbstract\nThe Iwasawa main conjecture wa
s stated by Iwasawa in the 1960s\, linking the Riemann Zeta function to ce
rtain ideals coming from class field theory\, and proved in 1984 by Mazur
and Wiles. This work was generalised to the setting of modular forms\, pre
dicting that analytic and algebraic constructions of the p-adic L-function
of a modular form agree\, proved by Kato (’04) and Skinner--Urban (’0
6) for ordinary modular forms. For the non-ordinary case there are some mo
dern approaches which use p-adic Hodge theory and rigid geometry to formul
ate and prove cases of the conjecture. I will review these cases and discu
ss my work in the setting of automorphic representations of unitary groups
at non-split primes\, where a new approach uses the L-analytic regulator
map of Schneider—Venjakob. My aim is to state a version of the conjectur
e which was previously unknown\, and discuss what is still needed to prove
the conjecture in full.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erman Isik (University of Ottawa)
DTSTART:20231017T200000Z
DTEND:20231017T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/18
DESCRIPTION:Title: Modular approach to Diophantine equation $x^p+y^p=z^3$ over some
number fields\nby Erman Isik (University of Ottawa) as part of Carlet
on-Ottawa Number Theory seminar\n\nLecture held in STEM-464.\n\nAbstract\n
Solving Diophantine equations\, in particular\, Fermat-type equations is o
ne of the oldest and most widely studied topics in mathematics. After Wile
s’ proof of Fermat’s Last Theorem using his celebrated modularity theo
rem\, several mathematicians have attempted to extend this approach to var
ious Diophantine equations and number fields over several number fields.\n
\n\nThe method used in the proof of this theorem is now called “modular
approach”\, which makes use of the relation between modular forms and el
liptic curves. I will first briefly mention the main steps of the modular
approach\, and then report our asymptotic result (joint work with {\\"O}zm
an and Kara) on the solutions of the Fermat-type equation $x^p+y^p=z^3$ ov
er various number fields.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chatchai Noytaptim (University of Waterloo)
DTSTART:20231107T210000Z
DTEND:20231107T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/19
DESCRIPTION:Title: Arithmetic Dynamical Questions with Local Rationality\nby Ch
atchai Noytaptim (University of Waterloo) as part of Carleton-Ottawa Numbe
r Theory seminar\n\n\nAbstract\nIn this talk\, we first introduce a numeri
cal criterion which bounds the degree of any algebraic integer in short in
tervals (i.e.\, intervals of length less than 4). As an application\, we c
lassify all unicritical polynomials defined over the maximal totally real
extension of the field of rational numbers. Using tools from complex and p
-adic potential theory\, we also classify all quadratic unicritical polyno
mials defined over the field of rational numbers in which they have only f
initely many totally real preperiodic points. In particular\, we are able
to explicitly compute totally real preperiodic points of some quadratic un
icritical polynomials by applying the numerical tool and p-adic dynamics.
This is based on joint work with Clay Petsche.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akash Sengupta (University of Waterloo)
DTSTART:20231121T210000Z
DTEND:20231121T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/20
DESCRIPTION:Title: Radical Sylvester-Gallai configurations\nby Akash Sengupta (
University of Waterloo) as part of Carleton-Ottawa Number Theory seminar\n
\n\nAbstract\nIn 1893\, Sylvester asked a basic question in combinatorial
geometry: given a finite set of distinct points v_1\,...\, v_m in R^n suc
h that the line joining any pair of distinct points v_i\,v_j contains a th
ird 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 Sylvester
’s question is yes\, i.e. such finite sets of points are all collinear.
Generalizations of Sylvester's problem\, which are known as Sylvester-Gall
ai type problems have been widely studied by mathematicians\, have found r
emarkable applications in algebraic complexity theory and coding theory. T
he underlying theme in all Sylvester-Gallai type questions is the followin
g:\n\nAre Sylvester-Gallai type configurations always low-dimensional?\n\n
In this talk\, we will discuss a non-linear generalization of Sylvester's
problem\, and its connections with the Stillman uniformity phenomenon in C
ommutative Algebra. I’ll talk about an algebraic-geometric approach towa
rds studying such SG-configurations and a result showing that radical SG-c
onfigurations are indeed low dimensional as conjectured by Gupta in 2014.
This is based on joint work with Rafael Oliveira.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Nguyen (Queen's University)
DTSTART:20231114T210000Z
DTEND:20231114T220000Z
DTSTAMP:20260422T143609Z
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 seminar\n\n\
nAbstract\nOne of the central problems in analytic number theory has been
to evaluate moments of the absolute value of L-functions on the critical l
ine. Bounds on these moments are approximations to the Lindelöf hypothesi
s and\, thus\, subconvexity bounds for these L-functions. Besides a few lo
w moments where rigorous results are known\, sharp bounds on higher moment
s are wide open. Recently\, in 2018\, it has been discovered that there is
a certain connection between asymptotics of moments of L-functions and va
riance over the integers (the Keating--Rodgers--Roditty-Gershon--Rudnick--
Soundararajan conjecture in arithmetic progressions). Certain analogues of
this conjecture are completely known\, i.e.\, are theorems\, in the funct
ion field setting. In this lecture\, I plan to explain this new connection
between asymptotics of variance over Z and those of moments\, and discuss
my work on confirming a smoothed version of this conjecture in a restrict
ed range.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chelsea Walton (Rice University)
DTSTART:20231026T230000Z
DTEND:20231027T000000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/22
DESCRIPTION:Title: Fields-Carleton Distinguished Lecture (public lecture): Moderniz
ing Modern Algebra\, I: Category Theory is coming\, whether we like it or
not\nby Chelsea Walton (Rice University) as part of Carleton-Ottawa Nu
mber Theory seminar\n\nLecture held in 274\, 275 Teraanga Commons\, Carlet
on University\, Ottawa.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harun Kir (Queen's University)
DTSTART:20231205T210000Z
DTEND:20231205T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/24
DESCRIPTION:Title: The refined Humbert invariant as an ingredient\nby Harun Kir
(Queen's University) as part of Carleton-Ottawa Number Theory seminar\n\n
Lecture held in STEM-664.\n\nAbstract\nIn this talk\, I will advertise t
he refined Humbert invariant\, which is the main ingredient of my resear
ch. It was introduced by Ernst Kani(1994) upon observing that every curve
$C$ comes equipped with a canonically defined positive definite quadratic
form $q_C$. This result can be used to define algebraically the (usual)
Humbert invariant (1899) and Humbert surfaces. \n\nThe beauty of the refin
ed Humbert invariant is that it translates the geometric questions into th
e arithmetic questions. Therefore\, it allows us to solve many interestin
g geometric problems regarding the nature of curves of genus $2$ including
the automorphism groups and the elliptic subcovers of these curves\, the
intersection of the Humbert surfaces\, and the CM points on the Shimuracu
rves in this intersection. \n\nI will also give the classification of this
invariant in the CM case as these illustrations reveal how interesting th
e refined Humbert invariant is.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chelsea Walton (Rice University)
DTSTART:20231027T173000Z
DTEND:20231027T183000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/25
DESCRIPTION:Title: Fields-Carleton Distinguished Lecture (research lecture): Modern
izing Modern Algebra\, II: Category Theory is coming\, whether we like it
or not\nby Chelsea Walton (Rice University) as part of Carleton-Ottawa
Number Theory seminar\n\nLecture held in 4351 Herzberg Building\, Macphai
l Room\, Carleton University\, Ottawa.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Baril Boudreau (U. Lethbridge)
DTSTART:20240305T210000Z
DTEND:20240305T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/27
DESCRIPTION:Title: The Distribution of Logarithmic Derivatives of Quadratic L-funct
ions in Positive Characteristic\nby Felix Baril Boudreau (U. Lethbridg
e) as part of Carleton-Ottawa Number Theory seminar\n\nLecture held in STE
M-664.\n\nAbstract\nTo each square-free monic polynomial $D$ in a fixed po
lynomial ring $\\mathbb{F}_q[t]$\, we can associate a real quadratic chara
cter $\\chi_D$\, and then a Dirichlet $L$-function $L(s\,\\chi_D)$. We com
pute 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 of $\\ma
thbb{F}_q[t]$ and establish that this distribution has a smooth density fu
nction. Time permitting\, we discuss connections of this result with Euler
-Kronecker constants and ideal class groups of quadratic extensions. This
is joint work with Amir Akbary.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fırtına Küçük (University College Dublin)
DTSTART:20240319T200000Z
DTEND:20240319T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/28
DESCRIPTION:Title: Factorization of algebraic p-adic L-functions of Rankin-Selberg
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 v
ariant. Artin formalism gives a factorization of L-functions whenever the
associated Galois representation decomposes. I will explain why the p-adic
Artin formalism is a non-trivial problem when there are no critical L-val
ues. In particular\, I will focus on the case where the Galois representat
ion arises from a self-Rankin-Selberg product of a newform\, and present t
he 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 the newf
orm f in question has a theta-critical p-stabilization\, i.e. if f is in t
he image of the theta operator. Unlike the ordinary and the non-critical s
lope cases\, one cannot simply define the p-adic L-function of f in terms
of its interpolative properties. I will discuss technical difficulties par
alleling this and explain the degenerate properties of the theta-critical
forms in terms of the algebro-geometric properties of the eigencurve.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Bharadwaj (Queen's U.)
DTSTART:20240409T200000Z
DTEND:20240409T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/29
DESCRIPTION:Title: Sufficient conditions for a problem of Polya\nby Abhishek Bh
aradwaj (Queen's U.) as part of Carleton-Ottawa Number Theory seminar\n\n\
nAbstract\nThere is an old result attributed to Polya on identifying algeb
raic integers by studying the power traces\; and a finite version of this
result was proved by Bart de Smit. We study the generalisation of these qu
estions\, namely determining algebraic integers by imposing certain constr
aints on the power sums. This is a joint work with V Kumar\, A Pal and R T
hangadurai. Time permitting\, we will also describe related results in an
ongoing project.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gary Walsh (Tutte Institute and University of Ottawa)
DTSTART:20240513T130000Z
DTEND:20240513T140000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/30
DESCRIPTION:Title: Solving problems of Erdos using elliptic curves and an elliptic
curve analogue of the Ankeny-Artin-Chowla Conjecture\nby Gary Walsh (T
utte Institute and University of Ottawa) as part of Carleton-Ottawa Number
Theory seminar\n\n\nAbstract\nWe describe how the Mordell-Weil group of r
ational points on a certain families of elliptic curves give rise to solut
ions to conjectures of Erdos on powerful numbers\, and state a related con
jecture\, which can be viewed as an elliptic curve analogue of the Ankeny-
Artin-Chowla Conjecture.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arul Shankar (University of Toronto))
DTSTART:20240513T143000Z
DTEND:20240513T153000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/31
DESCRIPTION:Title: Conditional bounds on the 2\, 3\, 4\, and 5 torsion of the class
groups of number fields\nby Arul Shankar (University of Toronto)) as
part of Carleton-Ottawa Number Theory seminar\n\n\nAbstract\nLet n be a po
sitive integer\, and let K be a degree n number field. It is believed that
the class group of K should be a cyclic group\, up to factors that are ne
gligible compared to the size of the discriminant of K. Another way of phr
asing 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 torsi
on subgroups of quadratic fields by work of Gauss.\n\nFor other pairs m an
d n\, it is a natural question to obtain nontrivial bounds for the sizes o
f 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 bo
unds\, conditional on some standard elliptic curve conjectures\, for the c
ases m=2\, 3\, 4\, and 5 (and where n is allowed to be any positive intege
r).\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammadreza Mohajer (University of Ottawa)
DTSTART:20240513T173000Z
DTEND:20240513T183000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/32
DESCRIPTION:Title: Exploring p-adic periods of 1-motive\nby Mohammadreza Mohaje
r (University of Ottawa) as part of Carleton-Ottawa Number Theory seminar\
n\n\nAbstract\nPeriod numbers and p-adic periods are crucial in number the
ory\, offering insights into transcendence theory and arithmetic geometry.
Classical period numbers\, arising from integrals of algebraic differenti
al forms\, serve as transcendental numbers\, encoding deep arithmetic info
rmation. Studying classical periods is well-explored in curtain cases howe
ver\, extending these concepts to their p-adic counterparts present greate
r complexity. In this work\, we develop an integration theory for 1-motive
s with good reduction\, serving as a generalization of Fontaine-Messing p-
adic integration. For 1-motive M with good reduction\, the p-adic numbers
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 cry
stalline realisation and we show that a p-adic version Kontsevich-Zagier c
onjecture holds for M\, if one takes the Fontaine-Messing p-adic periods o
f M relative to its p-adic Betti lattice. This theorem is the p-adic versi
on of analytic subgroup theorem for 1-motives with good reduction.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier (McGill U.)
DTSTART:20240513T200000Z
DTEND:20240513T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/33
DESCRIPTION:Title: Statistics of automorphic forms using endoscopy\nby Mathilde
Gerbelli-Gauthier (McGill U.) as part of Carleton-Ottawa Number Theory se
minar\n\n\nAbstract\nClassical questions about modular forms on SL_2 have
direct analogues on higher-rank groups: What is the dimension of spaces of
forms of a given weight and level? How are the Hecke eigenvalues distribu
ted? What is the sign of the functional equation of the associated L-funct
ion? Though exact answers can be hard to obtain in general for groups of h
igher rank\, I’ll describe some statistical results towards these questi
ons\, 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://researchseminars.org/talk/CarletonOttawaNT/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raiza Corpuz (Waikato/Ottawa)
DTSTART:20240916T200000Z
DTEND:20240916T210000Z
DTSTAMP:20260422T143609Z
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\nLect
ure held in STEM-464.\n\nAbstract\nLet $p$ be an odd prime\, and suppose t
hat $E_1$ and $E_2$ are two elliptic curves which are congruent modulo $p$
. 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 between $\\t
au$-twists of $E_1$ and $E_2$\, thereby establishing an analogue of Greenb
erg and Vatsal's result. Moreover\, we show that provided an Euler system
exists\, IMC$(E_1\, \\tau)$ is true if and only if IMC$(E_2\, \\tau)$ is
true. This is joint work with Daniel Delbourgo from University of Waikato.
\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taiga Adachi (Kyushu/Ottawa)
DTSTART:20241007T200000Z
DTEND:20241007T210000Z
DTSTAMP:20260422T143609Z
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 i
n STEM-464.\n\nAbstract\nLet $p$ be a prime number and $d$ a positive inte
ger. 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 thi
s talk\, we generalize several results for graphs to weighted graphs. We p
rove an analogue of Iwasawa’s class number formula and that of Riemann-H
urwitz formula for $\\mathbb{Z}_p^d$-towers of weighted graphs. This is a
joint work with Kosuke Mizuno and Sohei Tateno.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chatchai Noytaptim (University of Waterloo)
DTSTART:20241118T210000Z
DTEND:20241118T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/36
DESCRIPTION:Title: A finiteness result of common zeros of iterated rational functio
ns\nby Chatchai Noytaptim (University of Waterloo) as part of Carleton
-Ottawa Number Theory seminar\n\nLecture held in STEM-664.\n\nAbstract\nIn
2017\, Hsia and Tucker proved—under compositional independence assumpti
ons—that there are only finitely many irreducible factors of the greates
t common divisors of two iterated polynomials with complex coefficients. I
n the same paper\, Hsia and Tucker posed a question and asked whether a fi
niteness result of common zeros holds true for iterated rational functions
with complex coefficients. In joint work with Xiao Zhong (Waterloo)\, we
have recently answered the question in affirmative. In fact\, the question
is true except for special families of rational functions of degree one.\
n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nic Fellini (Queen's University)
DTSTART:20241028T190000Z
DTEND:20241028T200000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/37
DESCRIPTION:Title: Congruence relations of Ankeny--Artin--Chowla type for real quad
ratic fields\nby Nic Fellini (Queen's University) as part of Carleton-
Ottawa Number Theory seminar\n\nLecture held in STEM-464.\n\nAbstract\nIn
1951\, Ankeny\, Artin\, and Chowla published a brief note containing four
congruence relations involving the class number of Q(sqrt(d)) for positive
squarefree integers d = 1 (mod 4). Many of the ideas present in their pap
er can be seen as the precursors to the now developed theory of cyclotomic
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 the prese
nt state of affairs for congruences of the type proven by Ankeny\, Artin\,
and Chowla\, indicating where possible\, the connection to p-adic L-funct
ions. Time permitting\, I will sketch how the so called "Ankeny--Artin--Ch
owla conjecture" is related to special dihedral extensions of Q.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerry Wang (University of Waterloo)
DTSTART:20241104T210000Z
DTEND:20241104T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/38
DESCRIPTION:Title: On the squarefree values of $a^4 + b^3$\nby Jerry Wang (Univ
ersity of Waterloo) as part of Carleton-Ottawa Number Theory seminar\n\n\n
Abstract\nA classical question in analytic number theory is to determine t
he density of integers $a_1\, \\ldots\, a_n$ such that $P(a_1\, \\ldots\,
a_n)$ is squarefree\, where $P$ is a fixed integer polynomial. In this tal
k\, 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 this den
sity equals the conjectured product of local densities. We combine Bhargav
a's set up for counting integral orbits\, with the circle method and the S
elberg sieve. This is joint work with Gian Sanjaya.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Earp-Lynch (Carleton University)
DTSTART:20241125T210000Z
DTEND:20241125T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/39
DESCRIPTION:Title: Simplest relative Thue equations and inequalities\nby Ben Ea
rp-Lynch (Carleton University) as part of Carleton-Ottawa Number Theory se
minar\n\nLecture held in STEM-664.\n\nAbstract\nA Thue equation has the fo
rm $F(X\,Y)=m$\, where $F\\in \\Z[X\,Y]$ is an irreducible binary form of
degree at least $3$\, and $m$ is an integer. In 1909\, Axel Thue showed t
hat such equations have finitely many integer solutions. The so-called si
mplest Thue equations are those from which arise the simplest number field
s\, which were first studied in a different context by Shanks in the 1970s
. I will discuss recent work which solves a parametric family of simplest
quartic relative Thue inequalities over quadratic fields.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Pagano (Concordia University)
DTSTART:20241202T210000Z
DTEND:20241202T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/40
DESCRIPTION:Title: Hilbert 10 via additive combinatorics\nby Carlo Pagano (Conc
ordia University) as part of Carleton-Ottawa Number Theory seminar\n\nLect
ure held in STEM-664.\n\nAbstract\nIn 1970 Matiyasevich\, building on earl
ier work of Davis--Putnam--Robinson\, proved that every enumerable subset
of Z is Diophantine\, thus showing that Hilbert's 10th problem is undecida
ble for Z. The problem of extending this result to the ring of integers of
number fields (and more generally to finitely generated infinite rings) h
as attracted significant attention and\, thanks to the efforts of many mat
hematicians\, the task has been reduced to the problem of constructing\, f
or 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 work with
Peter Koymans\, where we use Green--Tao to construct the desired elliptic
curves\, settling Hilbert 10 for every finitely generated infinite ring.\
n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dong Quan Nguyen (University of Maryland College Park)
DTSTART:20241007T183000Z
DTEND:20241007T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/41
DESCRIPTION:Title: An analogue of the Kronecker-Weber theorem for rational function
fields over ultra-finite fields\nby Dong Quan Nguyen (University of M
aryland College Park) as part of Carleton-Ottawa Number Theory seminar\n\n
Lecture held in STEM-464.\n\nAbstract\nIn this talk\, I will talk about my
recent work that establishes a correspondence between Galois extensions o
f rational function fields over arbitrary fields F_s and Galois extensions
of the rational function field over the ultraproduct of the fields F_s.
As an application\, I will discuss an analogue of the Kronecker-Weber theo
rem for rational function fields over ultraproducts of finite fields. I wi
ll also describe an analogue of cyclotomic fields for these rational funct
ion fields that generalizes the works of Carlitz from the 1930s\, and Haye
s in the 1970s. If time permits\, I will talk about how to use the corresp
ondence established in my work to study the inverse Galois problem for rat
ional function fields over finite fields.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hatley (Union College)
DTSTART:20241111T210000Z
DTEND:20241111T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/42
DESCRIPTION:Title: Recent Progress on Watkins's Conjecture\nby Jeff Hatley (Uni
on College) as part of Carleton-Ottawa Number Theory seminar\n\nLecture he
ld in STEM-664.\n\nAbstract\nIt is now known that every elliptic curve E/Q
has a modular parameterization. From this parameterization\, one can defi
ne several arithmetic invariants for E\, such as its modular degree. This
geometrically-defined invariant is expected to have an important arithmeti
c interpretation\; in particular\, Watkins's Conjecture predicts that the
Mordell-Weil rank of E(Q) is bounded above by the 2-valuation of the modul
ar 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 som
e recent work which is joint with Debanjana Kundu.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Royer (CNRS/CRM)
DTSTART:20241121T210000Z
DTEND:20241121T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/43
DESCRIPTION:Title: Differential algebras of quasi-Jacobi forms of index zero\nb
y Emmanuel Royer (CNRS/CRM) as part of Carleton-Ottawa Number Theory semin
ar\n\nLecture held in STEM-464.\n\nAbstract\nAfter introducing the concept
s of singular Jacobi forms\, we will define quasi-Jacobi forms and study t
heir algebraic structure. We will focus in particular on their stability u
nder various derivations and construct sequences of bidifferential operato
rs with the aim of finding analogs of the well-known Rankin-Cohen brackets
or transvectants on algebras of modular forms. This is a joint work with
François Dumas and François Martin from the University of Clermont Auver
gne.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hatley (Union College)
DTSTART:20241113T210000Z
DTEND:20241113T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/44
DESCRIPTION:Title: Rational Points on Elliptic Curves over Infinite Extensions\
nby Jeff Hatley (Union College) as part of Carleton-Ottawa Number Theory s
eminar\n\nLecture held in Stem 664.\n\nAbstract\nElliptic curves are among
the most-studied objects in modern number theory. The Mordell-Weil theore
m\nsays that if K/Q is an algebraic extension of finite degree\, then 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\nar
ise in this way. It turns out that\, for many infinite extensions K/Q\, th
e group E(K) remains finitely-\ngenerated\, and the same sorts of question
s can be asked (and sometimes answered) in this new setting.\nWe will give
a survey of some of the active research being done in this area.\nTea\, c
offee and goodies will be served at 3:30 in STM 664. This colloquium is pa
rtially sponsored by the CRM.\n\nSpecial uOttawa Colloquium.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Martin (IMPA)
DTSTART:20250120T210000Z
DTEND:20250120T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/45
DESCRIPTION:Title: The Xiao conjecture for surfaces fibered by trigonal genus 5 cur
ves\nby Olivier Martin (IMPA) as part of Carleton-Ottawa Number Theory
seminar\n\n\nAbstract\nThe Xiao conjecture predicts that the relative irr
egularity\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 Barja\,\nGo
nzález-Alonso\, and Naranjo when the general fiber has maximal Clifford\n
index. I will present a proof of the Xiao conjecture for surfaces\nfibered
by trigonal genus 5 curves\, which completes the proof of the\nXiao conje
cture for surfaces fibered by genus 5 curves.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhang Xiao (Peking University)
DTSTART:20250225T000000Z
DTEND:20250225T010000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/46
DESCRIPTION:Title: Diophantine Approximation on Surfaces and Distribution of Integr
al Points\nby Zhang Xiao (Peking University) as part of Carleton-Ottaw
a Number Theory seminar\n\n\nAbstract\nAfter Mordell’s conjecture for cu
rves was proved by Faltings\, attentions turn to the distribution of ratio
nal and integral points on higher dimensional varieties\, which is encoded
in the celebrated Vojta’s conjecture. Along this line we proved a subsp
ace type inequality\, improving the result of Ru-Vojta\, on surfaces. Mean
while\, we obtain a sharp criterion of when some certain surfaces admit a
non Zariski-dense set of integral points. Joint with Huang\, Levin.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stanley Xiao (UNBC)
DTSTART:20250304T223000Z
DTEND:20250304T233000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/47
DESCRIPTION:Title: Polynomials in two variables of degree at most 6 cannot represen
t all positive integers without representing infinitely negative integers<
/a>\nby Stanley Xiao (UNBC) as part of Carleton-Ottawa Number Theory semin
ar\n\n\nAbstract\nIn 2010\, Bjorn Poonen asked a famous question on MathOv
erflow with nearly 300 upvotes which sought an answer to the following: do
es there exist a polynomial $f \\in \\mathbb{Z}[x\,y]$ such that $f(\\math
bb{Z} \\times \\mathbb{Z}) = \\mathbb{N}$? If we allow three or more varia
bles\, then the answer is yes\, by famous theorems of Lagrange and Gauss w
ho 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 answer w
ould obviously be "no". Thus\, the most interesting case is the two-variab
le case.\n\nDespite significant apparent interest in the question\, and a
highly voted "answer" by Terry Tao\, the question remains unresolved. Rece
ntly\, in a joint paper with S. Yamagishi\, we have shown that it is not p
ossible for quartic polynomials in two variables to satisfy Poonen's quest
ion. Later\, in a separate paper\, I showed that no such degree six polyno
mials exist either.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Logan (Carleton University)
DTSTART:20250317T200000Z
DTEND:20250317T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/48
DESCRIPTION:Title: Kodaira dimension of Hilbert modular threefolds\nby Adam Log
an (Carleton University) as part of Carleton-Ottawa Number Theory seminar\
n\nLecture held in STEM-664.\n\nAbstract\nFollowing a method introduced by
Thomas-Vasquez and developed by Grundman\,\nwe prove that many Hilbert mo
dular threefolds of arithmetic\ngenus $0$ and $1$ are of general type\, an
d that some are of nonnegative\nKodaira dimension. The new ingredient is
a detailed study\nof the geometry and combinatorics of totally positive in
tegral elements\n$x$ of a fractional ideal $I$ in a totally real number fi
eld $K$ with\nthe property that tr $xy < $ min $I$ tr $y$ for some $y \\gg
0 \\in K$.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammad Manji (Concordia University)
DTSTART:20250324T183000Z
DTEND:20250324T193000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/50
DESCRIPTION:Title: Iwasawa theory for \\mathbb{Q}_{p^2}-analytic distributions\
nby Muhammad Manji (Concordia University) as part of Carleton-Ottawa Numbe
r Theory seminar\n\nLecture held in STEM-664.\n\nAbstract\nThere are many
existing cases of Iwasawa theory of arithmetic objects in Z_p extensions\,
starting from the original work of Iwasawa and later Mazur-Wiles for GL_1
studying the behaviour of class numbers up the cyclotomic tower. Later wo
rk (Kato\, Skinner-Urban) studied the Iwasawa theory of modular forms\, sh
owing that certain Selmer groups can give us p-adic distributions which in
terpolate L-values of ordinary cusp forms. This work has been generalised
to many more settings where the Galois tower is larger but the local exten
sion remains a \\mathbb{Z}_p-extension. Recent development in the construc
tion of a regulator map for Lubin—Tate Iwasawa cohomology allows us to s
tudy a new setting where p is inert in the reflex field of our arithmetic
data. We will go through two examples\; one of CM elliptic curves with p i
nert in the CM field and one of unitary groups.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Earp-Lynch (Carleton University)
DTSTART:20250407T200000Z
DTEND:20250407T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/51
DESCRIPTION:Title: Variants of a Problem of Lucas and Schäffer\nby Simon Earp-
Lynch (Carleton University) as part of Carleton-Ottawa Number Theory semin
ar\n\nLecture held in STEM-664.\n\nAbstract\nIn 1875\, Édouard Lucas posi
ted 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. Although the c
onjecture remains open\, progress towards it has provoked interest in rela
ted Diophantine problems. I will discuss work concerning two variants of
the problem and the multifarious tools applied\, which include local metho
ds\, Lucas sequences\, linear forms in logarithms and the modular approach
over number fields.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihir Deo (University of Ottawa)
DTSTART:20250203T210000Z
DTEND:20250203T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/52
DESCRIPTION:Title: On $p$-adic $L$-functions of Bianchi modular forms\nby Mihir
Deo (University of Ottawa) as part of Carleton-Ottawa Number Theory semin
ar\n\nLecture held in STEM-664.\n\nAbstract\nFor a prime $p$\, one can thi
nk 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 th
is talk\, I will discuss the decomposition of $p$-adic $L$-functions with
unbounded coefficients\, attached to $p$-non-ordinary Bianchi modular form
s\, into signed $p$-adic $L$-functions with bounded coefficients in two di
fferent scenarios. These results generalise works of Pollack\, Sprung\, an
d Lei-Loeffler-Zerbes on elliptic modular forms. The talk will begin with
a review of Bianchi modular forms\, as well as complex and $p$-adic $L$-fu
nctions associated with them.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anwesh Ray (Chennai Mathematical Institute)
DTSTART:20250623T200000Z
DTEND:20250623T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/53
DESCRIPTION:Title: Modular forms with large Selmer $p$-rank\nby Anwesh Ray (Che
nnai Mathematical Institute) as part of Carleton-Ottawa Number Theory semi
nar\n\n\nAbstract\nWe construct modular forms whose associated Galois repr
esentations have Bloch--Kato Selmer groups with arbitrarily large $p$-tors
ion. While such phenomena were previously known only for small primes\, we
extend these results to any fixed prime $p \\geq 5$. The method combines
Iwasawa theory with deformation theory of Galois representations. This is
joint work with Eknath Ghate.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debanjana Kundu (University of Regina)
DTSTART:20250721T200000Z
DTEND:20250721T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/54
DESCRIPTION:Title: Iwasawa Theory of Elliptic Curves in Quadratic Twist Families\nby Debanjana Kundu (University of Regina) as part of Carleton-Ottawa Nu
mber Theory seminar\n\nLecture held in STEM-664.\n\nAbstract\nIn my talk I
will discuss the variation of Iwasawa invariants of rational elliptic cur
ves in some quadratic twist families using two different approaches. This
is work in progress with Katharina Mueller.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brandon Hansson
DTSTART:20250922T130000Z
DTEND:20250922T140000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/55
DESCRIPTION:Title: Arithmetic combinatorics from high-dimensional probability\n
by Brandon Hansson as part of Carleton-Ottawa Number Theory seminar\n\nLec
ture held in 664.\n\nAbstract\nThe use of probability in combinatorics was
pioneered by Erdos\, rather famously. Recently\, techniques from high-dim
ensional probability have proved fruitful in attacking problems where spar
sity is a prominent feature. I will highlight its role in work joint with
Rudnev\, Shkredov and Zhelezov on the sum-product problem\, and if time pe
rmits\, newer results joint with Waterhouse convolutions in the boolean cu
be.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omer Avci (University of Ottawa)
DTSTART:20250929T130000Z
DTEND:20250929T140000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/56
DESCRIPTION:Title: Torsion of Rational Elliptic Curves over the Galois Extensions o
f $\\mathbb{Q}$\nby Omer Avci (University of Ottawa) as part of Carlet
on-Ottawa Number Theory seminar\n\n\nAbstract\nMazur's celebrated theorem
gives a complete classification of the torsion subgroups $E(\\mathbb{Q})_{
\\mathrm{tors}}$ for elliptic curves $E/\\mathbb{Q}$. This result inspired
the broader problem of classifying $E(L)_{\\mathrm{tors}}$ for elliptic c
urves $E/L$\, where $L$ is a field of characteristic zero. In this talk\,
I will first review results from the literature and some variants of this
problem. I will then focus on the case where $L/\\mathbb{Q}$ is a Galois e
xtension\, outlining our methods and presenting two families of results: w
hen $L = \\mathbb{Q}(\\zeta_p)$ for a prime $p$\, and when $L$ is a $\\mat
hbb{Z}_p$-extension of a quadratic field $K$.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Sajadi (University of Toronto)
DTSTART:20251020T130000Z
DTEND:20251020T140000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/57
DESCRIPTION:Title: A Unified Finiteness Theorem For Curves\nby Sara Sajadi (Uni
versity of Toronto) as part of Carleton-Ottawa Number Theory seminar\n\nLe
cture held in 464.\n\nAbstract\nThis talk presents a unified framework for
finiteness results concerning arithmetic points on algebraic curves\, exp
loring the analogy between number fields and function fields. The number f
ield setting\, joint work with F. Janbazi\, generalizes and extends classi
cal results of Birch–Merriman\, Siegel\, and Faltings. We prove that the
set of Galois-conjugate points on a smooth projective curve with good red
uction outside a fixed finite set of places is finite\, when considered up
to the action of the automorphism group of a proper integral model. Motiv
ated by this\, we consider the function field analogue\, involving a smoot
h and proper family of curves over an affine curve defined over a finite f
ield. In this setting\, we show that for a fixed degree\, there are only f
initely many étale relative divisors over the base\, up to the action of
the family's automorphism group (and including the Frobenius in the isotri
vial case). Together\, these results illustrate both the parallels and dis
tinctions between the two arithmetic settings\, contributing to a broader
unifying perspective on finiteness.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nic Banks (University of Waterloo)
DTSTART:20251006T130000Z
DTEND:20251006T140000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/58
DESCRIPTION:Title: Classification results for intersective polynomials with no inte
gral roots\nby Nic Banks (University of Waterloo) as part of Carleton-
Ottawa Number Theory seminar\n\n\nAbstract\nIn this talk\, I describe the
contents of my recently-defended PhD thesis on strongly intersective polyn
omials. These are polynomials with no integer roots but with a root modulo
every positive integer\, thereby constituting a failure of the local-glob
al principle. We start by describing their relation to Hilbert's 10th Prob
lem and an algorithm of James Ax. These are fascinating objects which make
contact with many areas of math\, including permutation group theory\, sp
litting behaviour of prime ideals in number fields\, and Frobenius element
s from class field theory.\n\nIn particular\, we discuss constraints on th
e splitting behaviour of ramified primes in splitting fields of intersecti
ve polynomials\, building on the work of Berend-Bilu (1996) and Sonn (2008
). We also explain the computation of a list of possible Galois groups of
such polynomials\, which includes many examples and which supports some re
cent conjectures of Ellis & Harper (2024).\n\nTime permitting\, we end by
discussing future work\, including results from permutation group theory a
nd from character theory.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlie Wu (University of Toronto)
DTSTART:20251027T130000Z
DTEND:20251027T140000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/59
DESCRIPTION:Title: Compactness and character varieties\nby Charlie Wu (Universi
ty of Toronto) as part of Carleton-Ottawa Number Theory seminar\n\n\nAbstr
act\nLet $X$ be an orientable genus $g$ surface with $n$ punctures. Relati
ve character varieties are spaces parametrizing isomorphism classes of rep
resentations of $\\pi_1(X)$ satisfying some local conditions around the pu
nctures. When this space is a single point\, some remarkable work of Katz
shows that the unique representation in this space has interesting arithm
etic and complex geometric properties - namely that it is defined over the
ring of integers of a number field and it ``comes from geometry". We disc
uss the geometry of this space when it is larger than a point\, and we giv
e a classification of their compact components. This is joint work with Da
niel Litt.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Baril Boudreau (CICMA)
DTSTART:20251103T140000Z
DTEND:20251103T150000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/60
DESCRIPTION:Title: Abelian varieties with homotheties\nby Felix Baril Boudreau
(CICMA) as part of Carleton-Ottawa Number Theory seminar\n\n\nAbstract\nLe
t $A$ be an Abelian variety defined over a number field $K$. The celebrate
d 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 positive con
stant. If $K$ is a global function field\, the analogous statement fails i
n general\, since Zahrin has shown the existence of ordinary Abelian varie
ties of positive dimensions defined over $K$\, for which $G_\\ell$ only co
ntains finitely many homotheties. In this talk\, I will discuss my ongoing
joint work with Sebastian Petersen (University of Kassel)\, in which we p
rove\, under suitable additional assumptions\, an analogue of Bogomolov--S
erre Theorem when $K$ is a finitely generated field of positive characteri
stic.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luochen Zhao (Morning Side Center)
DTSTART:20251110T140000Z
DTEND:20251110T150000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/61
DESCRIPTION:Title: On the arithmetic of Bernoulli--Hurwitz periods\nby Luochen
Zhao (Morning Side Center) as part of Carleton-Ottawa Number Theory semina
r\n\nLecture held in 664.\n\nAbstract\nLet E be an elliptic curve having g
ood ordinary reduction at a prime p. The values of the classical Eisenstei
n series at E are algebraic and are called Bernoulli--Hurwitz numbers\, an
d they admit a p-adic interpolation by specializing Katz's one-variable Ei
senstein measure at E. We will explain that the periods of this p-adic mea
sure are modular\, i.e.\, are special values of certain weight one higher
level Eisenstein series. Furthermore\, we explain a new proof of the inter
polation by this modularity\, as well as how one can get a p-adic Kronecke
r's first limit formula.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luochen Zhao (Morning Side Center)
DTSTART:20251117T140000Z
DTEND:20251117T150000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/62
DESCRIPTION:Title: On the structure of anticyclotomic Selmer groups of modular form
s\nby Luochen Zhao (Morning Side Center) as part of Carleton-Ottawa Nu
mber Theory seminar\n\nLecture held in 664.\n\nAbstract\nI will report the
recent work with Antonio Lei and Luca Mastella\, in which we determine th
e structure of the Selmer group of a modular form over the anticyclotomic
Zp extension\, assuming the imaginary quadratic field satisfies the Heegne
r hypothesis\, that p splits in it and at which the form has good reductio
n\, and that the bottom generalized Heegner class is primitive. Here the l
ast assumption springs from Gross's treatment of Kolyvagin's bound on Shaf
arevich--Tate groups\, and was put in the Iwasawa theoretic context by Mat
ar--Nekovář and Matar for elliptic curves. This talk will focus on our u
se of the vanishing of BDP Selmer groups in proving the result\, which all
ows us to treat both ordinary and supersingular reduction types uniformly.
\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Forras (University of Ottawa)
DTSTART:20251124T140000Z
DTEND:20251124T150000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/63
DESCRIPTION:Title: Graduated orders in equivariant Iwasawa theory\nby Ben Forra
s (University of Ottawa) as part of Carleton-Ottawa Number Theory seminar\
n\nLecture held in 664.\n\nAbstract\nWe describe graduated orders over reg
ular local rings of dimension at most two\, and explain how this can be us
ed to prove integrality results in equivariant Iwasawa theory.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luochen Zhao (Morning Side Center)
DTSTART:20251114T140000Z
DTEND:20251114T150000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/64
DESCRIPTION:Title: On the structure of anticyclotomic Selmer groups of a supersingu
lar elliptic curve\nby Luochen Zhao (Morning Side Center) as part of C
arleton-Ottawa Number Theory seminar\n\nLecture held in 664.\n\nAbstract\n
Let p be a fixed prime. The study of the variation of Selmer groups attach
ed to a given Galois representation over a Z_p-extension is a central topi
c in Iwasawa theory. When the Galois representation is the Tate module of
a rational elliptic curve having good supersingular reduction at p\, the i
nformation of the Selmer groups becomes rather elusive due to the failure
of Mazur's control theorem. In this expository talk I'll explain a strateg
y (due to Matar) to study the growth of Selmer groups of a supersingular e
lliptic curve over the anticyclotomic Z_p extension\, assuming the indivi
sibility of the Heegner point. Along the way\, we will introduce Kobayashi
's modification of Selmer groups (i.e.\, plus/minus Selmer groups)\, and e
xplain how they could be fitted together to yield information on the usual
Selmer groups.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Grieve (Carleton University)
DTSTART:20251208T150000Z
DTEND:20251208T160000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/65
DESCRIPTION:Title: Complexity thresholds for divisors and explicit effective Diopha
ntine approximation of rational points\nby Nathan Grieve (Carleton Uni
versity) as part of Carleton-Ottawa Number Theory seminar\n\nLecture held
in Carleton University (Room HP 4351).\n\nAbstract\nI will survey recent r
esults which surround complexity thresholds for divisors\, including measu
res of positivity and singularities thereof\, and explain how they interpl
ay with Diophantine approximation of algebraic points. A portion of these
results include recent joint work C. Noytaptim. Further\, I will place e
mphasis on explicit and effective results.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Fazzari (University of Genova)
DTSTART:20260224T150000Z
DTEND:20260224T160000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/66
DESCRIPTION:Title: On the third moment of log-zeta and a twisted pair correlation c
onjecture\nby Alessandro Fazzari (University of Genova) as part of Car
leton-Ottawa Number Theory seminar\n\nLecture held in 664.\n\nAbstract\nI
will present joint work with Maxim Gerspach on lower-order terms in Selber
g's central limit theorem. In particular\, we compute precise asymptotic f
ormulas for the third moment of both the real and imaginary parts of the l
ogarithm of the Riemann zeta function. Our results are conditional on the
Riemann Hypothesis\, Hejhal's triple correlation\, and a new conjecture de
scribing the interaction between prime powers and Montgomery's pair correl
ation function. To support this conjecture\, which we refer to as the "twi
sted" pair correlation conjecture\, we prove it unconditionally in a limit
ed range and under the Hardy-Littlewood conjecture in a larger range.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ari Shnidman (Temple University)
DTSTART:20260305T210000Z
DTEND:20260305T220000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/67
DESCRIPTION:Title: On the geometric origin of rational points on modular curves
\nby Ari Shnidman (Temple University) as part of Carleton-Ottawa Number Th
eory seminar\n\nLecture held in 664.\n\nAbstract\nBuilding on recent work
of Zywina\, we show that all known rational points on all modular curves a
re explained by geometry in a precise sense. Along the way\, we refine Zyw
ina's explicit (conditional) classification of the images of the Galois re
presentations of elliptic curves over Q\, which places all Galois images i
n finitely many twist families of modular curves. I'll discuss how these r
esults fit into Mazur's Program B. This is joint work with Derickx\, Hashi
moto\, and Najman.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan-Pablo Llerena (University of Ottawa)
DTSTART:20260309T200000Z
DTEND:20260309T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/68
DESCRIPTION:Title: ***CANCELED*** Numerical study of refined conjectures of the Bir
ch--Swinnerton-Dyer type\nby Juan-Pablo Llerena (University of Ottawa)
as part of Carleton-Ottawa Number Theory seminar\n\nLecture held in 664.\
n\nAbstract\nIn 1987\, Mazur and Tate stated conjectures which\, in some c
ases\, resemble the classical Birch--Swinnerton-Dyer conjecture and its p-
adic analog. We will present some of these refined conjectures\, which we
studied numerically using SageMath. Furthermore\, we will mention some dis
crepancies that we found in the original statement of these conjectures. L
astly\, we will talk about a slight modification of these conjectures that
appear to hold numerically.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sunil Lakshmana Naik (Queen's University)
DTSTART:20260319T190000Z
DTEND:20260319T200000Z
DTSTAMP:20260422T143609Z
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 Car
leton-Ottawa Number Theory seminar\n\nLecture held in 664.\n\nAbstract\nIn
this talk\, we will discuss the largest prime factor of Fourier coefficie
nts of non-CM normalized cuspidal Hecke eigenforms in short intervals. Thi
s requires an explicit version of the Chebotarev density theorem in an int
erval of length ${x \\over (\\log x)^A}$ for any $A > 0$\, modifying an ea
rlier work of Balog and Ono. Furthermore\, we present a strengthening of a
work of Rouse and Thorner to establish a lower bound on the largest prime
factor of Fourier coefficients in an interval of length $x^{{1 \\over 2}
+ \\epsilon}$ for any $\\epsilon > 0$. This is a joint work with Sanoli Gu
n.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Logan
DTSTART:20260323T200000Z
DTEND:20260323T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/70
DESCRIPTION:Title: The degree of irrationality of del Pezzo surfaces\nby Adam L
ogan as part of Carleton-Ottawa Number Theory seminar\n\n\nAbstract\nThe d
egree of irrationality of a variety is the smallest degree of a dominant m
ap to a rational variety of the same dimension\, while del Pezzo surfaces
are surfaces on which the anticanonical divisor is ample. Over an algebra
ically closed field\, all del Pezzo surfaces are rational and therefore ha
ve degree of irrationality equal to 1\, but over a general field this does
not hold. We determine the possible degrees of irrationality of del Pezz
o surfaces of all degrees over local fields\, number fields\, and arbitrar
y fields. This is joint work with Tony Várilly-Alvarado and David Zureic
k-Brown.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (McGill University)
DTSTART:20260330T200000Z
DTEND:20260330T210000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/71
DESCRIPTION:Title: Generating series of modular symbols in SL_n\nby Romain Bran
chereau (McGill University) as part of Carleton-Ottawa Number Theory semin
ar\n\n\nAbstract\nIn the 1980s\, Kudla and Millson constructed modular for
ms whose Fourier coefficients are intersection numbers between totally geo
desic cycles in orthogonal locally symmetric spaces. I will present a simi
lar construction for cycles in the symmetric space of SL_n\, incorporating
the work of Kudla–Millson as well as recent work of Bergeron–Charollo
is–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://researchseminars.org/talk/CarletonOttawaNT/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rylan Gajek-Leonard (Union College)
DTSTART:20260319T170000Z
DTEND:20260319T180000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/72
DESCRIPTION:Title: Mazur--Tate elements of non-ordinary modular forms with Serre we
ight larger than two\nby Rylan Gajek-Leonard (Union College) as part o
f Carleton-Ottawa Number Theory seminar\n\nLecture held in 464.\n\nAbstrac
t\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 formulas
for the Iwasawa invariants of the Mazur-Tate elements attached to f of wei
ght kDifferent approaches to Arakelov theory\nby Antoine Sedillot
(University of Regensburg) as part of Carleton-Ottawa Number Theory semin
ar\n\nLecture held in 664.\n\nAbstract\nIn this talk\, I will introduce th
e philosophy of Arakelov geometry and present different approaches that al
low for transferring geometric observations into arithmetic information ov
er various kinds of fields\, such as global fields\, finitely generated ex
tensions of the prime field\, and fields of complex meromorphic functions
studied in Nevanlinna theory. More precisely\, we will introduce the moder
n formalism of adelic curves of Chen and Moriwaki and their topological co
unterpart\, aiming at interpreting Arakelov geometry via Zariski-Riemann t
ype spaces.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artane Siad (Tsinghua University)
DTSTART:20260218T180000Z
DTEND:20260218T190000Z
DTSTAMP:20260422T143609Z
UID:CarletonOttawaNT/74
DESCRIPTION:Title: On anomalies in the class groups of monogenised and unit-monogen
ised number fields\nby Artane Siad (Tsinghua University) as part of Ca
rleton-Ottawa Number Theory seminar\n\nLecture held in STEM-664.\n\nAbstra
ct\nIn this talk\, I will detail developments in our understanding of clas
s group anomalies in monogenised and unit-monogenised fields and outline a
few concrete consequences in arithmetic statistics. Variously based on jo
int work with Shankar-Swaminathan\, Shnidman\, and Venkatesh.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/74/
END:VEVENT
END:VCALENDAR