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BEGIN:VEVENT
SUMMARY:Keping Huang (MSU)
DTSTART;VALUE=DATE-TIME:20221019T183000Z
DTEND;VALUE=DATE-TIME:20221019T193000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071808Z
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:20230208T071808Z
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:20230208T071808Z
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:20230208T071808Z
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:20230208T071808Z
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:20230208T071808Z
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:20230208T071808Z
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:20230208T071808Z
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\nInter
active livestream: https://uottawa-ca.zoom.us/j/95724297776\nPassword hint
: "Hilbert" then the number two to the three\nLecture held in STEM 664 UOt
tawa.\n\nAbstract\nWe will give a short introduction to the Iwasawa theory
of finite connected graphs. We will then explain the Iwasawa main conject
ure 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 Söre
n Kleine.\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/8/
URL:https://uottawa-ca.zoom.us/j/95724297776
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (University of Manitoba)
DTSTART;VALUE=DATE-TIME:20230301T194500Z
DTEND;VALUE=DATE-TIME:20230301T204500Z
DTSTAMP;VALUE=DATE-TIME:20230208T071808Z
UID:CarletonOttawaNT/9
DESCRIPTION:by Romain Branchereau (University of Manitoba) 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 UOttawa.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/9/
URL:https://uottawa-ca.zoom.us/j/95724297776
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Dion (Université Laval)
DTSTART;VALUE=DATE-TIME:20230308T194500Z
DTEND;VALUE=DATE-TIME:20230308T204500Z
DTSTAMP;VALUE=DATE-TIME:20230208T071808Z
UID:CarletonOttawaNT/10
DESCRIPTION:by Cédric Dion (Université Laval) as part of Carleton-Ottawa
Number Theory seminar\n\nInteractive livestream: https://uottawa-ca.zoom.
us/j/95724297776\nPassword hint: "Hilbert" then the number two to the thre
e\nLecture held in STEM 664 UOttawa.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/10/
URL:https://uottawa-ca.zoom.us/j/95724297776
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiacheng Xia (Université Laval)
DTSTART;VALUE=DATE-TIME:20230412T184500Z
DTEND;VALUE=DATE-TIME:20230412T194500Z
DTSTAMP;VALUE=DATE-TIME:20230208T071808Z
UID:CarletonOttawaNT/11
DESCRIPTION:by Jiacheng Xia (Université Laval) as part of Carleton-Ottawa
Number Theory seminar\n\nInteractive livestream: https://uottawa-ca.zoom.
us/j/95724297776\nPassword hint: "Hilbert" then the number two to the thre
e\nLecture held in STEM 664 UOttawa.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/11/
URL:https://uottawa-ca.zoom.us/j/95724297776
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:20230208T071808Z
UID:CarletonOttawaNT/12
DESCRIPTION:by Yukako Kezuka (Institut de Mathématiques de Jussieu) as pa
rt of Carleton-Ottawa Number Theory seminar\n\nInteractive livestream: htt
ps://uottawa-ca.zoom.us/j/95724297776\nPassword hint: "Hilbert" then the n
umber two to the three\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/12/
URL:https://uottawa-ca.zoom.us/j/95724297776
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:20230208T071808Z
UID:CarletonOttawaNT/13
DESCRIPTION:by Bharathwaj Palvannan (Indian Institute of Science\, Bangalo
re) as part of Carleton-Ottawa Number Theory seminar\n\nInteractive livest
ream: https://uottawa-ca.zoom.us/j/95724297776\nPassword hint: "Hilbert" t
hen the number two to the three\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/13/
URL:https://uottawa-ca.zoom.us/j/95724297776
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nike Vatsal (UBC)
DTSTART;VALUE=DATE-TIME:20230320T170000Z
DTEND;VALUE=DATE-TIME:20230320T180000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071808Z
UID:CarletonOttawaNT/14
DESCRIPTION:by Nike Vatsal (UBC) as part of Carleton-Ottawa Number Theory
seminar\n\nInteractive livestream: https://uottawa-ca.zoom.us/j/9572429777
6\nPassword hint: "Hilbert" then the number two to the three\nLecture held
in STEM 464.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CarletonOttawaNT/14/
URL:https://uottawa-ca.zoom.us/j/95724297776
END:VEVENT
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