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BEGIN:VEVENT
SUMMARY:Keping Huang (MSU)
DTSTART;VALUE=DATE-TIME:20221019T183000Z
DTEND;VALUE=DATE-TIME:20221019T193000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20221026T190000Z
DTEND;VALUE=DATE-TIME:20221026T200000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20221102T183000Z
DTEND;VALUE=DATE-TIME:20221102T193000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20221109T193000Z
DTEND;VALUE=DATE-TIME:20221109T203000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20221116T193000Z
DTEND;VALUE=DATE-TIME:20221116T203000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20221123T193000Z
DTEND;VALUE=DATE-TIME:20221123T203000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20221130T193000Z
DTEND;VALUE=DATE-TIME:20221130T203000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20230208T194500Z
DTEND;VALUE=DATE-TIME:20230208T204500Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20230301T194500Z
DTEND;VALUE=DATE-TIME:20230301T204500Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20230308T194500Z
DTEND;VALUE=DATE-TIME:20230308T204500Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20230412T184500Z
DTEND;VALUE=DATE-TIME:20230412T194500Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20230215T194500Z
DTEND;VALUE=DATE-TIME:20230215T204500Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20230315T140000Z
DTEND;VALUE=DATE-TIME:20230315T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20230320T170000Z
DTEND;VALUE=DATE-TIME:20230320T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20230329T184500Z
DTEND;VALUE=DATE-TIME:20230329T194500Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20230405T184500Z
DTEND;VALUE=DATE-TIME:20230405T194500Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20231010T200000Z
DTEND;VALUE=DATE-TIME:20231010T210000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20231017T200000Z
DTEND;VALUE=DATE-TIME:20231017T210000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20231107T210000Z
DTEND;VALUE=DATE-TIME:20231107T220000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20231121T210000Z
DTEND;VALUE=DATE-TIME:20231121T220000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20231114T210000Z
DTEND;VALUE=DATE-TIME:20231114T220000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20231026T230000Z
DTEND;VALUE=DATE-TIME:20231027T000000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20231205T210000Z
DTEND;VALUE=DATE-TIME:20231205T220000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20231027T173000Z
DTEND;VALUE=DATE-TIME:20231027T183000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20240305T210000Z
DTEND;VALUE=DATE-TIME:20240305T220000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20240319T200000Z
DTEND;VALUE=DATE-TIME:20240319T210000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20240409T200000Z
DTEND;VALUE=DATE-TIME:20240409T210000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20240513T130000Z
DTEND;VALUE=DATE-TIME:20240513T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20240513T143000Z
DTEND;VALUE=DATE-TIME:20240513T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20240513T173000Z
DTEND;VALUE=DATE-TIME:20240513T183000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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;VALUE=DATE-TIME:20240513T200000Z
DTEND;VALUE=DATE-TIME:20240513T210000Z
DTSTAMP;VALUE=DATE-TIME:20240614T060551Z
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
END:VCALENDAR