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BEGIN:VEVENT
SUMMARY:Keping Huang (MSU)
DTSTART;VALUE=DATE-TIME:20221019T183000Z
DTEND;VALUE=DATE-TIME:20221019T193000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/1
DESCRIPTION:Title: A Tits alternative for endomorphisms of the projective lin
e\nby Keping Huang (MSU) as part of Carleton-Ottawa Number Theory semi
nar\n\n\nAbstract\nWe prove an analog of the Tits alternative for endomorp
hisms of $\\mathbb{P}^1$. In particular\, we show that if $S$ is a finite
ly generated semigroup of endomorphisms of $\\mathbb{P}^1$ over $\\mathbb{
C}$\, then either $S$ has polynomially bounded growth or $S$ contains a no
nabelian free semigroup. We also show that if $f$ and $g$ are polarizable
maps over any field of any characteristic and $\\mathrm{Prep}(f) \\neq \\
mathrm{Prep}(g)$\, then for all sufficiently large $j$\, the semigroup $\\
langle f^j\, g^j \\rangle$ is a free semigroup on two generators. This is
a joint work with Jason Bell\, Wayne Peng\, and Thomas Tucker.\n
LOCATION:
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:20241013T143100Z
UID:CarletonOttawaNT/2
DESCRIPTION:Title: Perfect Powers in power sums\nby Pranabesh Das (Xavier
University of Louisiana) as part of Carleton-Ottawa Number Theory seminar
\n\nAbstract: TBA\n
LOCATION:
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:20241013T143100Z
UID:CarletonOttawaNT/3
DESCRIPTION:Title: A conjectural uniform construction of many rigid Calabi-Ya
u threefolds\nby Adam Logan (Govt. of Canada and Carleton U.) as part
of Carleton-Ottawa Number Theory seminar\n\n\nAbstract\nGiven a rational H
ecke eigenform f of weight 2\, Eichler-Shimura theory gives a construction
of an elliptic curve over Q whose associated modular form is f. Mazur\, v
an Straten\, and others have asked whether there is an analogous construct
ion for Hecke eigenforms f of weight k >2 that produces a variety for whic
h the Galois representation on its etale H^{k−1} (modulo classes of cycl
es if k is odd) is that of f. In weight 3 this is understood by work of El
kies and Schutt\, but in higher weight it remains mysterious\, despite man
y examples in weight 4. In this talk I will present a new construction bas
ed on families of K3 surfaces of Picard number 19 that recovers many exist
ing examples in weight 4 and produces almost 20 new ones.\n
LOCATION:
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:20241013T143100Z
UID:CarletonOttawaNT/4
DESCRIPTION:Title: On the $\\mathfrak{M}_H(G)$-property\nby Soren Kleine
(Universität der Bundeswehr München) as part of Carleton-Ottawa Number T
heory seminar\n\n\nAbstract\nLet $p$ be any rational prime\, and let $E$ b
e an elliptic curve defined over $\\mathbb{Q}$ which has good ordinary red
uction at the prime $p$. We let $K$ be a number field\, which we assume to
be totally imaginary if ${p = 2}$. \n \n Let $K_\\infty$ be a $\\Z_p^2$
-extension of $K$ which contains the cyclotomic $\\Z_p$-extension $K_{cyc}
$ of $K$. The classical $\\mathfrak{M}_H(G)$-conjecture is a statement abo
ut the Pontryagin dual $X(E/K_\\infty)$ of the Selmer group of $E$ over $K
_\\infty$: if \n \\[ H_{cyc} = \\Gal(K_\\infty/K_{cyc}) \\subseteq \\Gal(
K_\\infty/K) =: G\, \\] \n then the quotient $X(E/K_\\infty)/X(E/K_\\inft
y)[p^\\infty]$ of $X(E/K_\\infty)$ by its $p$-torsion submodule\, which is
known to be finitely generated over $\\Z_p[[G]]$\, is conjectured to be a
ctually finitely generated as a $\\Z_p[[H_{cyc}]]$-module. \n \n In this
talk\, we discuss an analogous property for non-cyclotomic $\\Z_p$-extens
ions. To be more precise\, we let $\\mathcal{E}$ be the set of $\\Z_p$-ext
ensions ${L \\subseteq K_\\infty}$ of $K$. For each ${L \\in \\mathcal{E}}
$\, one can ask whether the quotient \n \\[ X(E/K_\\infty)/X(E/K_\\infty)
[p^\\infty] \\] \n is finitely generated as a $\\Z_p[[H]]$-module\, where
now ${H = \\Gal(K_\\infty/L)}$. We prove many equivalent criteria for the
validity of this $\\mathfrak{M}_H(G)$-property\, some of which generalise
previously known conditions for the special case ${H = H_{cyc}}$\, wherea
s several other conditions are completely new. The new conditions involve\
, for example\, the boundedness of $\\lambda$-invariants of the Pontryagin
duals $X(E/L)$ as one runs over the elements ${L \\in \\mathcal{E}}$. By
using the new conditions\, we can show that the $\\mathfrak{M}_H(G)$-prope
rty holds for all but finitely many ${L \\in \\mathcal{E}}$. \n \n Moreo
ver\, we also derive several applications. For example\, we can prove some
special cases of a conjecture of Mazur on the growth of Mordell-Weil rank
s along the $\\Z_p$-extensions in $\\mathcal{E}$. \n \n All of this is j
oint work with Ahmed Matar and Sujatha.\n
LOCATION:
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:20241013T143100Z
UID:CarletonOttawaNT/5
DESCRIPTION:Title: Explicit reciprocity law for finite slope modulalr forms\nby Shilun Wang (Università degli Studi di Padova) as part of Carleton
-Ottawa Number Theory seminar\n\n\nAbstract\nDarmon and Rotger constructed
the generalized diagonal cycles in the product of three\nKuga-Sato variet
ies\, which generalizes the modified diagonal cycle considered by Gross–
Kudla and Gross–Schoen. Recently\, Bertolini\, Seveso and Venerucci foun
d a different way to construct the diagonal cycles. They proved the p-adic
Gross–Zagier formula and the explicit reciprocity law relating to p-adi
c L-function attached to the Garrett–Rankin triple convolution of three
Hida families of modular forms. These formulae have wide range of applicat
ions\, such as Bloch–Kato conjecture and exceptional zero problem. Howe
ver\, we find that both constructions do not have any requirements on the
slope of modular form\, so it is possible to apply their constructions to
the other case that the modular forms are of finite slope. Combining with
the p-adic L-function for modular forms of finite slope constructed by And
reatta and Iovita recently\, we can try to generalize results to the tripl
e convolution of three Coleman families of modular forms.\nIn this talk\,
I will give a brief introduction to how to generalize Bertolini\, Seveso a
nd\nVenerucci’s results and if time permits\, I will try to talk about s
ome applications. All of this is from the work in progress.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Hu (U. Oslo)
DTSTART;VALUE=DATE-TIME:20221123T193000Z
DTEND;VALUE=DATE-TIME:20221123T203000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/6
DESCRIPTION:Title: An upper bound for polynomial log-volume growth of automor
phisms of zero entropy\nby Fei Hu (U. Oslo) as part of Carleton-Ottawa
Number Theory seminar\n\n\nAbstract\nLet f be an automorphism of zero ent
ropy of a smooth projective variety X. \nThe polynomial log-volume growth
$\\operatorname{plov(f)}$ of f is a natural analog of Gromov's log-volume
growth of automorphisms (of positive entropy)\, formally introduced by Can
tat and Paris-Romaskevich for slow dynamics in 2020. \nA surprising fact n
oticed by Lin\, Oguiso\, and Zhang in 2021 is that this dynamical invarian
t plov(f) essentially coincides with the Gelfand-Kirillov dimension of the
twisted homogeneous coordinate ring associated with (X\, f)\, introduced
by Artin\, Tate\, and Van den Bergh in the 1990s.\nIt was conjectured by t
hem that $\\operatorname{plov}(f)$ is bounded above by $d^2$\, where $d =
\\operatorname{dim} X$. \n\nWe prove an upper bound for $\\operatorname{pl
ov}(f)$ in terms of the dimension $d$ of $X$ and another fundamental invar
iant $k$ of $(X\, f)$ (i.e.\, the degree growth rate of iterates $f^n$ wit
h respect to an arbitrary ample divisor on $X$).\nAs a corollary\, we prov
e the above conjecture based on an earlier work of Dinh\, Lin\, Oguiso\, a
nd Zhang.\nThis is joint work with Chen Jiang.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Bharadwaj (Queen's U.)
DTSTART;VALUE=DATE-TIME:20221130T193000Z
DTEND;VALUE=DATE-TIME:20221130T203000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/7
DESCRIPTION:Title: On primitivity and vanishing of Dirichlet series\nby A
bhishek Bharadwaj (Queen's U.) as part of Carleton-Ottawa Number Theory se
minar\n\n\nAbstract\nFor a rational valued periodic function\, we associat
e a Dirichlet series and provide a new necessary and sufficient condition
for the vanishing of this Dirichlet series specialized at positive integer
s. This theme was initiated by Chowla and carried out by Okada for a parti
cular infinite sum. Our approach relies on the decomposition of the Dirich
let characters in terms of primitive characters. Using this\, we find some
new family of natural numbers for which a conjecture of Erd\\"{o}s holds.
\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katharina Mueller (Université Laval)
DTSTART;VALUE=DATE-TIME:20230208T194500Z
DTEND;VALUE=DATE-TIME:20230208T204500Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/8
DESCRIPTION:Title: Iwasawa main conjectures for graphs\nby Katharina Muel
ler (Université Laval) as part of Carleton-Ottawa Number Theory seminar\n
\nLecture held in STEM 664 UOttawa.\n\nAbstract\nWe will give a short intr
oduction to the Iwasawa theory of finite connected graphs. We will then ex
plain the Iwasawa main conjecture for $\\mathbb{Z}_p^l$ coverings. If time
permits we will also discuss work in progress on the non-abelian case.\n\
nThis is joint work with Sören Kleine.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (University of Manitoba)
DTSTART;VALUE=DATE-TIME:20230301T194500Z
DTEND;VALUE=DATE-TIME:20230301T204500Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/9
DESCRIPTION:Title: Diagonal restriction of Eisenstein series and Kudla-Millso
n theta lift\nby Romain Branchereau (University of Manitoba) as part o
f Carleton-Ottawa Number Theory seminar\n\nLecture held in STEM 664 UOttaw
a.\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Dion (Université Laval)
DTSTART;VALUE=DATE-TIME:20230308T194500Z
DTEND;VALUE=DATE-TIME:20230308T204500Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/10
DESCRIPTION:Title: Distribution of Iwasawa invariants for complete graphs\nby Cédric Dion (Université Laval) as part of Carleton-Ottawa Number T
heory seminar\n\nLecture held in STEM 664 UOttawa.\n\nAbstract\nFix a prim
e number $p$. Let $X$ be a finite multigraph and ̈$\\cdots \\rightarrow X
_2\\rightarrow X_1\\rightarrow X$ be a sequence of coverings such that $\\
mathrm{Gal}(X_n/X)\\cong \\mathbb{Z}/p^n\\mathbb{Z}$. McGown–Vallières
and Gonet have shown that there exists invariants $\\mu\,\\lambda$ and $\\
nu$ such that the $p$-part of the number of spanning trees of $X_n$ is giv
en by $p^{\\mu p^n+\\lambda n+\\nu}$ for $n$ large enough. In this talk\,
we will study the distribution of these invariants when $X$ varies in the
family of complete graphs. This is joint work with Antonio Lei\, Anwesh Ra
y and Daniel Vallières.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiacheng Xia (Université Laval)
DTSTART;VALUE=DATE-TIME:20230412T184500Z
DTEND;VALUE=DATE-TIME:20230412T194500Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/11
DESCRIPTION:Title: The orthogonal Kudla conjecture over totally real fields<
/a>\nby Jiacheng Xia (Université Laval) as part of Carleton-Ottawa Number
Theory seminar\n\n\nAbstract\nOn a modular curve\, Gross--Kohnen--Zagier
proves that certain generating series of Heegner points are modular forms
of weight 3/2 with values in the Jacobian. Such a result has been extended
to orthogonal Shimura varieties over totally real fields by Yuan--Zhang--
Zhang for special Chow cycles assuming absolute convergence of the generat
ing series.\n\nBased on the method of Bruinier--Raum over the rationals\,
we plan to fill this gap of absolute convergence over totally real fields.
In this talk\, I will lay out the setting of the problem and explain some
of the new challenges that we face over totally real fields.\n\nThis is a
joint work in progress with Qiao He.\n
LOCATION:
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:20241013T143100Z
UID:CarletonOttawaNT/12
DESCRIPTION:Title: Non-vanishing theorems for central L-values\nby Yukak
o Kezuka (Institut de Mathématiques de Jussieu) as part of Carleton-Ottaw
a Number Theory seminar\n\nAbstract: TBA\n
LOCATION:
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:20241013T143100Z
UID:CarletonOttawaNT/13
DESCRIPTION:Title: An ergodic approach towards an equidistribution result of
Ferrero–Washington\nby Bharathwaj Palvannan (Indian Institute of Sc
ience\, Bangalore) as part of Carleton-Ottawa Number Theory seminar\n\nAbs
tract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nike Vatsal (UBC)
DTSTART;VALUE=DATE-TIME:20230320T170000Z
DTEND;VALUE=DATE-TIME:20230320T180000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/14
DESCRIPTION:Title: Congruences for symmetric square and Rankin L-functions\nby Nike Vatsal (UBC) as part of Carleton-Ottawa Number Theory seminar\
n\nLecture held in STEM 464.\n\nAbstract\nWork of Coates\, Schmidt\, and H
ida dating back almost 40 years shows how to construct p-adic L-functions
for the symmetric square and Rankin-Selberg L-functions associated to modu
lar forms. There constructions work over Q\, and it has long been a folklo
re question as to whether or not their constructions work over integer rin
gs. In this talk we will show how to adapt their construction to give inte
gral results\, and to show that congruent modular forms have congruent p-a
dic L-functions.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabien Pazuki (University of Copenhagen)
DTSTART;VALUE=DATE-TIME:20230329T184500Z
DTEND;VALUE=DATE-TIME:20230329T194500Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/15
DESCRIPTION:Title: Isogeny volcanoes: an ordinary inverse problem\nby Fa
bien Pazuki (University of Copenhagen) as part of Carleton-Ottawa Number T
heory seminar\n\nLecture held in STEM-201.\n\nAbstract\nWe prove that any
abstract $\\ell$-volcano graph can be realized as a connected component of
the $\\ell$-isogeny graph of an ordinary elliptic curve defined over $\\m
athbb{F}_p$\, where $\\ell$ and $p$ are two different primes. This is join
t work with Henry Bambury and Francesco Campagna.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sash Zotine (Queen's U.)
DTSTART;VALUE=DATE-TIME:20230405T184500Z
DTEND;VALUE=DATE-TIME:20230405T194500Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/16
DESCRIPTION:Title: Kawaguchi-Silverman Conjecture for Projectivized Bundles
over Curves\nby Sash Zotine (Queen's U.) as part of Carleton-Ottawa Nu
mber Theory seminar\n\n\nAbstract\nThe Kawaguchi-Silverman Conjecture is a
recent conjecture equating two invariants of a dominant rational map betw
een projective varieties: the first dynamical degree and arithmetic degree
. The first dynamical degree measures the mixing of the map\, and the arit
hmetic degree measures how complicated rational points become after iterat
ion. Recently\, the conjecture was established for several classes of vari
eties\, including projectivized bundles over any non-elliptic curve. We wi
ll discuss my recent work with Brett Nasserden to resolve the elliptic cas
e\, hence proving KSC for all projectivized bundles over curves.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammad Manji (University of Warwick)
DTSTART;VALUE=DATE-TIME:20231010T200000Z
DTEND;VALUE=DATE-TIME:20231010T210000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/17
DESCRIPTION:Title: Iwasawa Theory for GU(2\,1) at inert primes\nby Muham
mad Manji (University of Warwick) as part of Carleton-Ottawa Number Theory
seminar\n\nLecture held in STEM-464.\n\nAbstract\nThe Iwasawa main conjec
ture was stated by Iwasawa in the 1960s\, linking the Riemann Zeta functio
n to certain ideals coming from class field theory\, and proved in 1984 by
Mazur and Wiles. This work was generalised to the setting of modular form
s\, predicting that analytic and algebraic constructions of the p-adic L-f
unction of a modular form agree\, proved by Kato (’04) and Skinner--Urba
n (’06) for ordinary modular forms. For the non-ordinary case there are
some modern approaches which use p-adic Hodge theory and rigid geometry to
formulate and prove cases of the conjecture. I will review these cases an
d discuss my work in the setting of automorphic representations of unitary
groups at non-split primes\, where a new approach uses the L-analytic reg
ulator map of Schneider—Venjakob. My aim is to state a version of the co
njecture which was previously unknown\, and discuss what is still needed t
o prove the conjecture in full.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erman Isik (University of Ottawa)
DTSTART;VALUE=DATE-TIME:20231017T200000Z
DTEND;VALUE=DATE-TIME:20231017T210000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/18
DESCRIPTION:Title: Modular approach to Diophantine equation $x^p+y^p=z^3$ ov
er some number fields\nby Erman Isik (University of Ottawa) as part of
Carleton-Ottawa Number Theory seminar\n\nLecture held in STEM-464.\n\nAbs
tract\nSolving Diophantine equations\, in particular\, Fermat-type equatio
ns is one of the oldest and most widely studied topics in mathematics. Aft
er Wiles’ proof of Fermat’s Last Theorem using his celebrated modulari
ty theorem\, several mathematicians have attempted to extend this approach
to various Diophantine equations and number fields over several number fi
elds.\n\n\nThe method used in the proof of this theorem is now called “m
odular approach”\, which makes use of the relation between modular forms
and elliptic curves. I will first briefly mention the main steps of the m
odular approach\, and then report our asymptotic result (joint work with {
\\"O}zman and Kara) on the solutions of the Fermat-type equation $x^p+y^p=
z^3$ over various number fields.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chatchai Noytaptim (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20231107T210000Z
DTEND;VALUE=DATE-TIME:20231107T220000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/19
DESCRIPTION:Title: Arithmetic Dynamical Questions with Local Rationality
\nby Chatchai Noytaptim (University of Waterloo) as part of Carleton-Ottaw
a Number Theory seminar\n\n\nAbstract\nIn this talk\, we first introduce a
numerical criterion which bounds the degree of any algebraic integer in s
hort intervals (i.e.\, intervals of length less than 4). As an application
\, we classify all unicritical polynomials defined over the maximal totall
y real extension of the field of rational numbers. Using tools from comple
x and p-adic potential theory\, we also classify all quadratic unicritical
polynomials defined over the field of rational numbers in which they have
only finitely many totally real preperiodic points. In particular\, we ar
e able to explicitly compute totally real preperiodic points of some quadr
atic unicritical polynomials by applying the numerical tool and p-adic dyn
amics. This is based on joint work with Clay Petsche.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akash Sengupta (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20231121T210000Z
DTEND;VALUE=DATE-TIME:20231121T220000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/20
DESCRIPTION:Title: Radical Sylvester-Gallai configurations\nby Akash Sen
gupta (University of Waterloo) as part of Carleton-Ottawa Number Theory se
minar\n\n\nAbstract\nIn 1893\, Sylvester asked a basic question in combina
torial geometry: given a finite set of distinct points v_1\,...\, v_m in R
^n such that the line joining any pair of distinct points v_i\,v_j contai
ns a third point v_k in the set\, must all points in the set be collinear?
\n\nThe classical Sylvester-Gallai (SG) theorem says that the answer to Sy
lvester’s question is yes\, i.e. such finite sets of points are all coll
inear. Generalizations of Sylvester's problem\, which are known as Sylvest
er-Gallai type problems have been widely studied by mathematicians\, have
found remarkable applications in algebraic complexity theory and coding th
eory. The underlying theme in all Sylvester-Gallai type questions is the f
ollowing:\n\nAre Sylvester-Gallai type configurations always low-dimension
al?\n\nIn this talk\, we will discuss a non-linear generalization of Sylve
ster's problem\, and its connections with the Stillman uniformity phenomen
on in Commutative Algebra. I’ll talk about an algebraic-geometric approa
ch towards studying such SG-configurations and a result showing that radic
al SG-configurations are indeed low dimensional as conjectured by Gupta in
2014. This is based on joint work with Rafael Oliveira.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Nguyen (Queen's University)
DTSTART;VALUE=DATE-TIME:20231114T210000Z
DTEND;VALUE=DATE-TIME:20231114T220000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/21
DESCRIPTION:Title: Variance over Z and moments of L-functions\nby David
Nguyen (Queen's University) as part of Carleton-Ottawa Number Theory semin
ar\n\n\nAbstract\nOne of the central problems in analytic number theory ha
s been to evaluate moments of the absolute value of L-functions on the cri
tical line. Bounds on these moments are approximations to the Lindelöf hy
pothesis and\, thus\, subconvexity bounds for these L-functions. Besides a
few low moments where rigorous results are known\, sharp bounds on higher
moments are wide open. Recently\, in 2018\, it has been discovered that t
here is a certain connection between asymptotics of moments of L-functions
and variance over the integers (the Keating--Rodgers--Roditty-Gershon--Ru
dnick--Soundararajan conjecture in arithmetic progressions). Certain analo
gues of this conjecture are completely known\, i.e.\, are theorems\, in th
e function field setting. In this lecture\, I plan to explain this new con
nection between asymptotics of variance over Z and those of moments\, and
discuss my work on confirming a smoothed version of this conjecture in a r
estricted range.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chelsea Walton (Rice University)
DTSTART;VALUE=DATE-TIME:20231026T230000Z
DTEND;VALUE=DATE-TIME:20231027T000000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/22
DESCRIPTION:Title: Fields-Carleton Distinguished Lecture (public lecture): M
odernizing Modern Algebra\, I: Category Theory is coming\, whether we like
it or not\nby Chelsea Walton (Rice University) as part of Carleton-Ot
tawa Number Theory seminar\n\nLecture held in 274\, 275 Teraanga Commons\,
Carleton University\, Ottawa.\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harun Kir (Queen's University)
DTSTART;VALUE=DATE-TIME:20231205T210000Z
DTEND;VALUE=DATE-TIME:20231205T220000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/24
DESCRIPTION:Title: The refined Humbert invariant as an ingredient\nby Ha
run Kir (Queen's University) as part of Carleton-Ottawa Number Theory semi
nar\n\nLecture held in STEM-664.\n\nAbstract\nIn this talk\, I will adve
rtise the refined Humbert invariant\, which is the main ingredient of my
research. It was introduced by Ernst Kani(1994) upon observing that ever
y curve $C$ comes equipped with a canonically defined positive definite qu
adratic form $q_C$. This result can be used to define algebraically the (
usual) Humbert invariant (1899) and Humbert surfaces. \n\nThe beauty of th
e refined Humbert invariant is that it translates the geometric questions
into the arithmetic questions. Therefore\, it allows us to solve many int
eresting geometric problems regarding the nature of curves of genus $2$ in
cluding the automorphism groups and the elliptic subcovers of these curves
\, the intersection of the Humbert surfaces\, and the CM points on the Sh
imuracurves in this intersection. \n\nI will also give the classification
of this invariant in the CM case as these illustrations reveal how interes
ting the refined Humbert invariant is.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chelsea Walton (Rice University)
DTSTART;VALUE=DATE-TIME:20231027T173000Z
DTEND;VALUE=DATE-TIME:20231027T183000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/25
DESCRIPTION:Title: Fields-Carleton Distinguished Lecture (research lecture):
Modernizing Modern Algebra\, II: Category Theory is coming\, whether we l
ike it or not\nby Chelsea Walton (Rice University) as part of Carleton
-Ottawa Number Theory seminar\n\nLecture held in 4351 Herzberg Building\,
Macphail Room\, Carleton University\, Ottawa.\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Baril Boudreau (U. Lethbridge)
DTSTART;VALUE=DATE-TIME:20240305T210000Z
DTEND;VALUE=DATE-TIME:20240305T220000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/27
DESCRIPTION:Title: The Distribution of Logarithmic Derivatives of Quadratic
L-functions in Positive Characteristic\nby Felix Baril Boudreau (U. Le
thbridge) as part of Carleton-Ottawa Number Theory seminar\n\nLecture held
in STEM-664.\n\nAbstract\nTo each square-free monic polynomial $D$ in a f
ixed polynomial ring $\\mathbb{F}_q[t]$\, we can associate a real quadrati
c character $\\chi_D$\, and then a Dirichlet $L$-function $L(s\,\\chi_D)$.
We compute the limiting distribution of the family of values $L'(1\,\\chi
_D)/L(1\,\\chi_D)$ as $D$ runs through the square-free monic polynomials o
f $\\mathbb{F}_q[t]$ and establish that this distribution has a smooth den
sity function. Time permitting\, we discuss connections of this result wit
h Euler-Kronecker constants and ideal class groups of quadratic extensions
. This is joint work with Amir Akbary.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fırtına Küçük (University College Dublin)
DTSTART;VALUE=DATE-TIME:20240319T200000Z
DTEND;VALUE=DATE-TIME:20240319T210000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/28
DESCRIPTION:Title: Factorization of algebraic p-adic L-functions of Rankin-S
elberg products\nby Fırtına Küçük (University College Dublin) as
part of Carleton-Ottawa Number Theory seminar\n\n\nAbstract\nIn the first
part of the talk\, I will give a brief review of Artin formalism and its p
-adic variant. Artin formalism gives a factorization of L-functions whenev
er the associated Galois representation decomposes. I will explain why the
p-adic Artin formalism is a non-trivial problem when there are no critica
l L-values. In particular\, I will focus on the case where the Galois repr
esentation arises from a self-Rankin-Selberg product of a newform\, and pr
esent the results in this direction including the one I obtained in my PhD
thesis.\n\nIn the last part of the talk\, I will discuss the case where t
he newform f in question has a theta-critical p-stabilization\, i.e. if f
is in the image of the theta operator. Unlike the ordinary and the non-cri
tical slope cases\, one cannot simply define the p-adic L-function of f in
terms of its interpolative properties. I will discuss technical difficult
ies paralleling this and explain the degenerate properties of the theta-cr
itical forms in terms of the algebro-geometric properties of the eigencurv
e.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Bharadwaj (Queen's U.)
DTSTART;VALUE=DATE-TIME:20240409T200000Z
DTEND;VALUE=DATE-TIME:20240409T210000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/29
DESCRIPTION:Title: Sufficient conditions for a problem of Polya\nby Abhi
shek Bharadwaj (Queen's U.) as part of Carleton-Ottawa Number Theory semin
ar\n\n\nAbstract\nThere is an old result attributed to Polya on identifyin
g algebraic integers by studying the power traces\; and a finite version o
f this result was proved by Bart de Smit. We study the generalisation of t
hese questions\, namely determining algebraic integers by imposing certain
constraints on the power sums. This is a joint work with V Kumar\, A Pal
and R Thangadurai. Time permitting\, we will also describe related results
in an ongoing project.\n
LOCATION:
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:20241013T143100Z
UID:CarletonOttawaNT/30
DESCRIPTION:Title: Solving problems of Erdos using elliptic curves and an el
liptic curve analogue of the Ankeny-Artin-Chowla Conjecture\nby Gary W
alsh (Tutte Institute and University of Ottawa) as part of Carleton-Ottawa
Number Theory seminar\n\n\nAbstract\nWe describe how the Mordell-Weil gro
up of rational points on a certain families of elliptic curves give rise t
o solutions to conjectures of Erdos on powerful numbers\, and state a rela
ted conjecture\, which can be viewed as an elliptic curve analogue of the
Ankeny-Artin-Chowla Conjecture.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arul Shankar (University of Toronto))
DTSTART;VALUE=DATE-TIME:20240513T143000Z
DTEND;VALUE=DATE-TIME:20240513T153000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/31
DESCRIPTION:Title: Conditional bounds on the 2\, 3\, 4\, and 5 torsion of th
e class groups of number fields\nby Arul Shankar (University of Toront
o)) as part of Carleton-Ottawa Number Theory seminar\n\n\nAbstract\nLet n
be a positive integer\, and let K be a degree n number field. It is believ
ed that the class group of K should be a cyclic group\, up to factors that
are negligible compared to the size of the discriminant of K. Another way
of phrasing this is to say that for any fixed m\, the m torsion subgroup
of the class group of K is negligible in size. This is only known for the
2 torsion subgroups of quadratic fields by work of Gauss.\n\nFor other pai
rs m and n\, it is a natural question to obtain nontrivial bounds for the
sizes of the m torsion in the class groups of degree n fields K.\nIn this
talk\, I will discuss joint work with Jacob Tsimerman\, in which we prove
such bounds\, conditional on some standard elliptic curve conjectures\, fo
r the cases m=2\, 3\, 4\, and 5 (and where n is allowed to be any positive
integer).\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammadreza Mohajer (University of Ottawa)
DTSTART;VALUE=DATE-TIME:20240513T173000Z
DTEND;VALUE=DATE-TIME:20240513T183000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/32
DESCRIPTION:Title: Exploring p-adic periods of 1-motive\nby Mohammadreza
Mohajer (University of Ottawa) as part of Carleton-Ottawa Number Theory s
eminar\n\n\nAbstract\nPeriod numbers and p-adic periods are crucial in num
ber theory\, offering insights into transcendence theory and arithmetic ge
ometry. Classical period numbers\, arising from integrals of algebraic dif
ferential forms\, serve as transcendental numbers\, encoding deep arithmet
ic information. Studying classical periods is well-explored in curtain cas
es however\, extending these concepts to their p-adic counterparts present
greater complexity. In this work\, we develop an integration theory for 1
-motives with good reduction\, serving as a generalization of Fontaine-Mes
sing p-adic integration. For 1-motive M with good reduction\, the p-adic n
umbers resulting from this integration are called Fontaine-Messing p-adic
periods of M. We identify a suitable p-adic Betti-like Q-structure inside
the crystalline realisation and we show that a p-adic version Kontsevich-Z
agier conjecture holds for M\, if one takes the Fontaine-Messing p-adic pe
riods of M relative to its p-adic Betti lattice. This theorem is the p-adi
c version of analytic subgroup theorem for 1-motives with good reduction.\
n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier (McGill U.)
DTSTART;VALUE=DATE-TIME:20240513T200000Z
DTEND;VALUE=DATE-TIME:20240513T210000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/33
DESCRIPTION:Title: Statistics of automorphic forms using endoscopy\nby M
athilde Gerbelli-Gauthier (McGill U.) as part of Carleton-Ottawa Number Th
eory seminar\n\n\nAbstract\nClassical questions about modular forms on SL_
2 have direct analogues on higher-rank groups: What is the dimension of sp
aces of forms of a given weight and level? How are the Hecke eigenvalues d
istributed? What is the sign of the functional equation of the associated
L-function? Though exact answers can be hard to obtain in general for grou
ps of higher rank\, I’ll describe some statistical results towards these
questions\, and outline how we obtain them using the stable trace formula
. This is joint work\, some of it in progress\, with Rahul Dalal.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raiza Corpuz (Waikato/Ottawa)
DTSTART;VALUE=DATE-TIME:20240916T200000Z
DTEND;VALUE=DATE-TIME:20240916T210000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/34
DESCRIPTION:Title: Equivalences of the Iwasawa main conjecture\nby Raiza
Corpuz (Waikato/Ottawa) as part of Carleton-Ottawa Number Theory seminar\
n\nLecture held in STEM-464.\n\nAbstract\nLet $p$ be an odd prime\, and su
ppose that $E_1$ and $E_2$ are two elliptic curves which are congruent mod
ulo $p$. Fix an Artin representation $\\tau: G_F \\to \\text{\\rm GL}_2(\\
mathbb{C})$ over a totally real field $F$\, induced from a Hecke character
over a CM-extension $K/F$. We compute the variation of the $\\mu$- and $\
\lambda$-invariants of the Iwasawa Main Conjecture\, as one switches betwe
en $\\tau$-twists of $E_1$ and $E_2$\, thereby establishing an analogue of
Greenberg and Vatsal's result. Moreover\, we show that provided an Euler
system exists\, IMC$(E_1\, \\tau)$ is true if and only if IMC$(E_2\, \\ta
u)$ is true. This is joint work with Daniel Delbourgo from University of W
aikato.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taiga Adachi (Kyushu/Ottawa)
DTSTART;VALUE=DATE-TIME:20241007T200000Z
DTEND;VALUE=DATE-TIME:20241007T210000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/35
DESCRIPTION:Title: Iwasawa theory for weighted graphs\nby Taiga Adachi (
Kyushu/Ottawa) as part of Carleton-Ottawa Number Theory seminar\n\nLecture
held in STEM-464.\n\nAbstract\nLet $p$ be a prime number and $d$ a positi
ve integer. In Iwasawa theory for graphs\, the asymptotic behavior of the
number of the spanning trees in $\\mathbb{Z}_p^d$-towers has been studied.
In this talk\, we generalize several results for graphs to weighted graph
s. We prove an analogue of Iwasawa’s class number formula and that of Ri
emann-Hurwitz formula for $\\mathbb{Z}_p^d$-towers of weighted graphs. Thi
s is a joint work with Kosuke Mizuno and Sohei Tateno.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chatchai Noytaptim (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20241118T210000Z
DTEND;VALUE=DATE-TIME:20241118T220000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/36
DESCRIPTION:by Chatchai Noytaptim (University of Waterloo) as part of Carl
eton-Ottawa Number Theory seminar\n\nInteractive livestream: https://uotta
wa-ca.zoom.us/j/95724297776\nPassword hint: "Hilbert" then the number two
to the three\nLecture held in STEM-664.\nAbstract: TBA\n
LOCATION:https://uottawa-ca.zoom.us/j/95724297776
URL:https://uottawa-ca.zoom.us/j/95724297776
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nic Fellini (Queen's University)
DTSTART;VALUE=DATE-TIME:20241028T190000Z
DTEND;VALUE=DATE-TIME:20241028T200000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/37
DESCRIPTION:Title: Congruence relations of Ankeny--Artin--Chowla type for re
al quadratic fields\nby Nic Fellini (Queen's University) as part of Ca
rleton-Ottawa Number Theory seminar\n\nInteractive livestream: https://uot
tawa-ca.zoom.us/j/95724297776\nPassword hint: "Hilbert" then the number tw
o to the three\nLecture held in STEM-464.\n\nAbstract\nIn 1951\, Ankeny\,
Artin\, and Chowla published a brief note containing four congruence relat
ions involving the class number of Q(sqrt(d)) for positive squarefree inte
gers d = 1 (mod 4). Many of the ideas present in their paper can be seen a
s the precursors to the now developed theory of cyclotomic fields. Curious
ly\, little attention has been paid to the cases of d = 2\, 3 (mod 4) in t
he literature.\n\nIn this talk\, I will describe the present state of affa
irs for congruences of the type proven by Ankeny\, Artin\, and Chowla\, in
dicating where possible\, the connection to p-adic L-functions. Time permi
tting\, I will sketch how the so called "Ankeny--Artin--Chowla conjecture"
is related to special dihedral extensions of Q.\n
LOCATION:https://uottawa-ca.zoom.us/j/95724297776
URL:https://uottawa-ca.zoom.us/j/95724297776
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerry Wang (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20241104T210000Z
DTEND;VALUE=DATE-TIME:20241104T220000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/38
DESCRIPTION:by Jerry Wang (University of Waterloo) as part of Carleton-Ott
awa Number Theory seminar\n\nInteractive livestream: https://uottawa-ca.zo
om.us/j/95724297776\nPassword hint: "Hilbert" then the number two to the t
hree\nAbstract: TBA\n
LOCATION:https://uottawa-ca.zoom.us/j/95724297776
URL:https://uottawa-ca.zoom.us/j/95724297776
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Earp-Lynch (Carleton University)
DTSTART;VALUE=DATE-TIME:20241125T210000Z
DTEND;VALUE=DATE-TIME:20241125T220000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/39
DESCRIPTION:by Ben Earp-Lynch (Carleton University) as part of Carleton-Ot
tawa Number Theory seminar\n\nInteractive livestream: https://uottawa-ca.z
oom.us/j/95724297776\nPassword hint: "Hilbert" then the number two to the
three\nLecture held in STEM-664.\nAbstract: TBA\n
LOCATION:https://uottawa-ca.zoom.us/j/95724297776
URL:https://uottawa-ca.zoom.us/j/95724297776
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Pagano (Concordia University)
DTSTART;VALUE=DATE-TIME:20241202T210000Z
DTEND;VALUE=DATE-TIME:20241202T220000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/40
DESCRIPTION:by Carlo Pagano (Concordia University) as part of Carleton-Ott
awa Number Theory seminar\n\nInteractive livestream: https://uottawa-ca.zo
om.us/j/95724297776\nPassword hint: "Hilbert" then the number two to the t
hree\nLecture held in STEM-664.\nAbstract: TBA\n
LOCATION:https://uottawa-ca.zoom.us/j/95724297776
URL:https://uottawa-ca.zoom.us/j/95724297776
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dong Quan Nguyen (University of Maryland College Park)
DTSTART;VALUE=DATE-TIME:20241007T183000Z
DTEND;VALUE=DATE-TIME:20241007T210000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/41
DESCRIPTION:Title: An analogue of the Kronecker-Weber theorem for rational f
unction fields over ultra-finite fields\nby Dong Quan Nguyen (Universi
ty of Maryland College Park) as part of Carleton-Ottawa Number Theory semi
nar\n\nLecture held in STEM-464.\n\nAbstract\nIn this talk\, I will talk a
bout my recent work that establishes a correspondence between Galois exten
sions of rational function fields over arbitrary fields F_s and Galois ext
ensions of the rational function field over the ultraproduct of the fields
F_s. As an application\, I will discuss an analogue of the Kronecker-Web
er theorem for rational function fields over ultraproducts of finite field
s. I will also describe an analogue of cyclotomic fields for these rationa
l function fields that generalizes the works of Carlitz from the 1930s\, a
nd Hayes in the 1970s. If time permits\, I will talk about how to use the
correspondence established in my work to study the inverse Galois problem
for rational function fields over finite fields.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hatley (Union College)
DTSTART;VALUE=DATE-TIME:20241111T210000Z
DTEND;VALUE=DATE-TIME:20241111T220000Z
DTSTAMP;VALUE=DATE-TIME:20241013T143100Z
UID:CarletonOttawaNT/42
DESCRIPTION:by Jeff Hatley (Union College) as part of Carleton-Ottawa Numb
er Theory seminar\n\nInteractive livestream: https://uottawa-ca.zoom.us/j/
95724297776\nPassword hint: "Hilbert" then the number two to the three\nLe
cture held in STEM-664.\nAbstract: TBA\n
LOCATION:https://uottawa-ca.zoom.us/j/95724297776
URL:https://uottawa-ca.zoom.us/j/95724297776
END:VEVENT
END:VCALENDAR