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BEGIN:VEVENT
SUMMARY:Gautier Ponsinet (Max Planck Institute)
DTSTART:20200625T143000Z
DTEND:20200625T160000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/1
DESCRIPTION:Title: Universal norms of p-adic Galois representations and the Fargues-
Fontaine curve\nby Gautier Ponsinet (Max Planck Institute) as part of
CRM-CICMA Québec Vermont Seminar Series\n\nLecture held in En ligne/Web.\
n\nAbstract\nIn 1996\, Coates and Greenberg computed explicitly the module
of universal norms for abelian varieties over perfectoid field extensions
. The computation of this module is employed in Iwasawa theory\, notably
to prove "control theorems" for Selmer groups\, generalizing Mazur's found
ational work on the Iwasawa theory of abelian varieties over Zp-extensions
. \n\nCoates and Greenberg raised the natural question on possible genera
lisations of their result to p-adic representations. In this talk\, I wil
l present a new approach to this question relying on the classification of
vector bundles over the Fargues-Fontaine curve\, which allows us to answe
r Coate and Greenberg's question affirmatively in new cases.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haining Wang (McGill University)
DTSTART:20200625T180000Z
DTEND:20200625T193000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/2
DESCRIPTION:Title: Level raising and Gross-Schoen diagonal cycles\nby Haining Wa
ng (McGill University) as part of CRM-CICMA Québec Vermont Seminar Series
\n\nLecture held in En ligne/Web.\n\nAbstract\nI will discuss my recent wo
rk on arithmetic level raising on triple product of Shimura curves and its
applications to Bloch-Kato type conjecture for triple product of modular
forms.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Shusterman (Harvard University)
DTSTART:20210121T190000Z
DTEND:20210121T203000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/4
DESCRIPTION:Title: Short exponential sums and their applications over function field
s\nby Mark Shusterman (Harvard University) as part of CRM-CICMA Québe
c Vermont Seminar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nIn
joint work with Will Sawin\, we obtain (square-root) cancellation in quite
general incomplete exponential sums for the ring F_q[x] of polynomials in
one variable over a finite field. This has applications to problems in an
alytic number theory such as the Chowla conjecture\, Bateman-Horn conjectu
re\, and the number of real quadratic function fields with a huge class gr
oup.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Cauchi (Universitat Politècnica de Catalunya)
DTSTART:20210121T143000Z
DTEND:20210121T160000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/5
DESCRIPTION:Title: On higher regulators for Siegel Shimura varieties\nby Antonio
Cauchi (Universitat Politècnica de Catalunya) as part of CRM-CICMA Québ
ec Vermont Seminar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nIn
this talk\, we will report some progress towards the Beilinson conjecture
s for Shimura varieties associated to the symplectic group GSp(6). We wil
l explain how to construct classes in its motivic cohomology and how to co
mpute their image by Beilinson's higher regulator in terms of Rankin-Selbe
rg type automorphic integrals. Using results of Pollack and Shah\, we rela
te the integral to a non-critical special value of the degree 8 spin L-fun
ction. If time permits\, we will describe parallel work in progress\, whic
h relates the residue at s=1 of these automorphic integrals to the existen
ce of a Tate class coming from a Hilbert modular subvariety. This relation
partially answers a question of Gross and Savin on motives with Galois gr
oup of type G2. This is joint work with Francesco Lemma and Joaquin Rodrig
ues Jacinto.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaisa Matomäki (Turku\, Finland)
DTSTART:20210204T143000Z
DTEND:20210204T160000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/6
DESCRIPTION:Title: Almost primes in almost all very short intervals\nby Kaisa Ma
tomäki (Turku\, Finland) as part of CRM-CICMA Québec Vermont Seminar Ser
ies\n\nLecture held in En ligne/Web.\n\nAbstract\nBy probabilistic models
one expects that\, as soon as $h \\to \\infty$ with $X \\to \\infty$\, sho
rt intervals of the type $(x- h \\log X\, x]$ contain primes for almost al
l $x \\in (X/2\, X]$. However\, this is far from being established. In the
talk I discuss related questions and in particular describe how to prove
the above claim when one is satisfied with finding $P_2$-numbers (numbers
that have at most two prime factors) instead of primes.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Love (Stanford University)
DTSTART:20210204T190000Z
DTEND:20210204T203000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/7
DESCRIPTION:Title: Explicit Rational Equivalences of Points on Surfaces\nby Jona
than Love (Stanford University) as part of CRM-CICMA Québec Vermont Semin
ar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nThe Chow group of
zero-cycles on a smooth projective surface X is obtained by taking the fre
e abelian group generated by closed points on X\, and declaring two elemen
ts (“zero-cycles”) to be equal if their difference is a sum of divisor
s of rational functions on curves in X\; in this setting we say the zero-c
ycles are “rationally equivalent.” These Chow groups are notoriously d
ifficult to compute\; while a set of conjectures due to Bloch and Beilinso
n predict certain relations must hold in these groups when X is defined ov
er a number field\, there are very few non-trivial cases in which these re
lations have been proven to hold. In this talk\, I will discuss several te
chniques that can be used to compute rational equivalences exhibiting some
of the expected relations\, in the case that X is a product of two ellipt
ic curves over Q.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olof Sisask (Stockholm University)
DTSTART:20210218T143000Z
DTEND:20210218T160000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/8
DESCRIPTION:Title: Breaking the logarithmic barrier in Roth's theorem\nby Olof S
isask (Stockholm University) as part of CRM-CICMA Québec Vermont Seminar
Series\n\nLecture held in En ligne/Web.\n\nAbstract\nWe present an improve
ment to Roth's theorem on arithmetic progressions\, implying the first non
-trivial case of a conjecture of Erdős: if a subset A of {1\,2\,3\,...} i
s not too sparse\, in that the sum of its reciprocals diverges\, then A mu
st contain infinitely many three-term arithmetic progressions. Although a
problem in number theory and combinatorics on the surface\, it turns out t
o have fascinating links with geometry\, harmonic analysis and probability
\, and we shall aim to give something of a flavour of this.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Eberhard (Cambridge University)
DTSTART:20210304T143000Z
DTEND:20210304T160000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/9
DESCRIPTION:Title: Irreducibility of the characteristic polynomial of a random integ
er matrix\nby Sean Eberhard (Cambridge University) as part of CRM-CICM
A Québec Vermont Seminar Series\n\nLecture held in En ligne/Web.\n\nAbstr
act\nConsider a random polynomial with integer coefficients. A natural con
jecture is that the polynomial is irreducible with high probability and it
s Galois group is S_n. This question has been studied for various models o
f random polynomial. The usual two models are the "bounded degree model"\,
in which the degree is constant and the coefficients are large\, and the
"bounded height model"\, in which the coefficients are drawn uniformly fro
m a fixed interval and the degree becomes large. We will study a variant o
f the bounded height model: take a large n x n matrix with independent +-1
entries and take its characteristic polynomial. To study this question we
will combine ideas from the bounded height model with random matrix theor
y over a finite field. The method we use is dependent on both the extended
Riemann hypothesis and the classification of finite simple groups.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Logan (University of Ottawa)
DTSTART:20210304T184500Z
DTEND:20210304T200000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/10
DESCRIPTION:Title: Three modular fivefolds\nby Adam Logan (University of Ottawa
) as part of CRM-CICMA Québec Vermont Seminar Series\n\nLecture held in E
n ligne/Web.\n\nAbstract\nEichler and Shimura showed that to every rationa
l Hecke eigenform of weight 2 there is associated an isogeny class of elli
ptic curves with the same L-function (and Wiles\, Taylor-Wiles\, et al. pr
oved a very famous converse). Work of Elkies and Schutt gives a similar
result for eigenforms of weight 3\, though the result has a very different
flavour since all such forms arise from imaginary quadratic fields with c
lass group of exponent dividing 2. There have been many attempts to asso
ciate Calabi-Yau threefolds to eigenforms of weight 4 in such a way that t
he interesting part of the L-function of the threefold matches that of the
modular form\, but in general the problem of doing so is open. In this
talk we give three examples of double covers of projective 5-space whose L
-functions involve an eigenform of weight 6. Two of the examples are pro
ved\; one is known to have a Calabi-Yau desingularization\, but the other
is not. In connection with these we will describe some new results (join
t with Colin Ingalls) on resolutions of singularities of double covers. Th
e third example\, still conjectural\, appears to point to a previously unk
nown identity of hypergeometric functions. We will also show how to use
an idea of Burek to find quotients of our varieties for which the point co
unts can be expressed in terms of a single eigenform of weight 6.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jori Merikoski (University of Turku)
DTSTART:20210318T133000Z
DTEND:20210318T150000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/11
DESCRIPTION:Title: On the largest prime factor of n^2+1\nby Jori Merikoski (Uni
versity of Turku) as part of CRM-CICMA Québec Vermont Seminar Series\n\nL
ecture held in En ligne/Web.\n\nAbstract\nIt is an open conjecture that th
ere are infinitely many prime numbers of the form n^2+1. To approach this
we may consider the largest prime factor of n^2+1. In this talk I show tha
t the largest prime factor of n^2+1 is infinitely often greater than n^{1.
279}. This improves the result of de la Bretèche and Drappeau who obtaine
d the exponent 1.2182\, improving the exponent 1.2024 obtained by Deshouil
lers and Iwaniec. The main new ingredients in the proof are Harman's sieve
method and a new bilinear estimate which is proved by applying the Deshou
illers-Iwaniec bounds for sums of Kloosterman sums. Assuming Selberg's eig
envalue conjecture the exponent 1.279 may be increased to 1.312.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naser Sardari (Penn State University)
DTSTART:20210318T180000Z
DTEND:20210318T190000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/12
DESCRIPTION:Title: Higher Fourier interpolation on the plane\nby Naser Sardari
(Penn State University) as part of CRM-CICMA Québec Vermont Seminar Serie
s\n\nLecture held in En ligne/Web.\n\nAbstract\nLet $l\\geq 6$ be any inte
ger\, where $l\\equiv 2$ mod $4$. Let $f(x)=\\int e^{i\\pi \\tau |x|^2}d\\
mu(\\tau)$ and $\\mathcal{F}(f)$ be the Fourier transform of $f$\, where $
x\\in \\R^2$ and $\\mu$ is a measure with bounded variation and supported
on a compact subset of $\\tau \\in\\CC$\, where $\\Im(\\tau)\,\\Im(-\\frac
{1}{\\tau})>\\sin(\\frac{\\pi}{l}).$ For every integer $k\\geq 0$ and $x\\
in \\R^2\,$\n\nWe express $f(x)$ by the values of $\\frac{d^k f}{du^k}$ an
d $\\frac{d^k \\mathcal{F}f}{du^k}$\n at $u=\\frac{2n}{\\lambda}\,$ where
$u=|x|^2$ and $\\lambda=2\\cos(\\frac{\\pi}{l}).$ We show that the condit
ion $\\Im(\\tau)\,\\Im(-\\frac{1}{\\tau})>\\sin(\\frac{\\pi}{l})$ is optim
al.\n\nWe also identify the cokernel to these values with a specific space
of holomorphic modular forms of weight $2k+1$ associated to the Hecke tri
angle group $(2\,l\,\\infty)$.\nUsing our explicit formulas for $l=6$ and
developing new methods\, we prove a conjecture of Cohn\, Kumar\, Miller\,
Radchenko and Viazovska~\\cite[Conjecture 7.5]{Maryna3} motivated by the u
niversal optimality of the hexagonal lattice.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Myerson (University of Warwick)
DTSTART:20210401T133000Z
DTEND:20210401T150000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/13
DESCRIPTION:Title: Form in many variables: p-adic repulsion\nby Simon Myerson (
University of Warwick) as part of CRM-CICMA Québec Vermont Seminar Series
\n\nLecture held in En ligne/Web.\n\nAbstract\nConsider the integral zeroe
s of one or more\, not necessarily diagonal\, integral polynomials in many
variables with the same degree. The basic principles for applying the cir
cle method here were laid out by Birch. One way to improve on his work is
repulsion: showing that the exponential sum over the polynomials can be la
rge only on small\, well separated regions. I will describe a p-adic versi
on of repulsion.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asher Auel (Dartmouth College)
DTSTART:20210401T180000Z
DTEND:20210401T190000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/14
DESCRIPTION:Title: Brauer classes split by genus one curves\nby Asher Auel (Dar
tmouth College) as part of CRM-CICMA Québec Vermont Seminar Series\n\nLec
ture held in En ligne/Web.\n\nAbstract\nIt is an open problem\, even over
the rational numbers\, to decide whether every Brauer class is split by th
e function field of a genus one curve. The problem has been solved for Bra
uer classes of index at most 6 over any field. In this talk\, I'll report
on work with Ben Antieau relating this problem to the arithmetic of modula
r curves and methods from explicit descent for elliptic curves.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caroline Turnage-Butterbaugh (Carleton College)
DTSTART:20210429T133000Z
DTEND:20210429T150000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/15
DESCRIPTION:Title: Gaps between zeros of the Riemann zeta-function\nby Caroline
Turnage-Butterbaugh (Carleton College) as part of CRM-CICMA Québec Vermo
nt Seminar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nLet $0 < \
\gamma_1 \\le \\gamma_2 \\le \\cdots $ denote the ordinates of the complex
zeros of the Riemann zeta-function function in the upper half-plane. The
average distance between $\\gamma_n$ and $\\gamma_{n+1)$ is $2\\pi / \\log
\\gamma_n$ as $n\\to \\infty$. An important goal is to prove unconditiona
lly that these distances between consecutive zeros can much\, much smaller
than the average for a positive proportion of zeros. We will discuss the
motivation behind this endeavor\, progress made assuming the Riemann Hypot
hesis\, and recent work with A. Simonič and T. Trudgian to obtain an unco
nditional result that holds for a positive proportion of zeros.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cameron Franc (McMaster University)
DTSTART:20210429T180000Z
DTEND:20210429T193000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/16
DESCRIPTION:Title: Noncongruence modular forms and unbounded denominators\nby C
ameron Franc (McMaster University) as part of CRM-CICMA Québec Vermont Se
minar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nThe modular gro
up PSL2(Z) contains many noncongruence subgroups of finite index. In this
talk we will explain some results on computing with the modular group\, an
d in particular we will explain how to classify genus zero subgroups with
a single cusp. Surprisingly\, there are many such groups. Then we will dis
cuss the unbounded denominator conjecture for some new cases of noncongrue
nce subgroups of genus zero\, using a method of Atkin and Swinnerton-Dyer\
, supplemented with some results on vector-valued modular forms. The most
difficult step in this approach is to solve a system of diophantine equati
ons defining an Artinian ideal. This is joint work with Andrew Fiori.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terence Tao (UCLA)
DTSTART:20210909T170000Z
DTEND:20210909T183000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/17
DESCRIPTION:Title: Approximants for classical arithmetic functions\nby Terence
Tao (UCLA) as part of CRM-CICMA Québec Vermont Seminar Series\n\nLecture
held in En ligne/Web.\n\nAbstract\nMany classical arithmetic functions suc
h as the M\\"obius function \\mu(n)\, the von Mangoldt function \\Lambda(n
)\, or the higher order divisor functions d_k(n) are notoriously difficult
to work with: for instance obtaining cancellation for \\sum_{n \\leq x} \
\mu(n) \\mu(n+1) is part of the Chowla conjecture\, obtaining an asymptoti
c for \\sum_{n \\leq x} \\Lambda(n) \\Lambda(n+2) would give the twin prim
e conjecture\, and even guessing the full main term expansion for \\sum_{n
\\leq x} d_k(n) d_l(n+1) is a non-trivial task (and verifying it is still
open when k\,l > 2). However\, in all these cases one can propose _appro
ximants_ \\mu^\\sharp\, \\Lambda^\\sharp\, d_k^\\sharp to these functions
that are substantially easier to work with (mostly by virtue of being "Typ
e I sums") and which are (either rigorously or heuristically) close to the
original functions \\mu\, \\Lambda\, d_k in various useful ways. We pres
ent recent and forthcoming work with Ter\\"av\\"ainen\, Matom\\"aki--Shao-
-Ter\\"av\\"ainen\, and Matom\\"aki--Radziwi{\\l}{\\l}--Shao--Ter\\"av\\"a
inen using these approximants to control Gowers uniformity norms and relat
ed statistics for these functions\, as well as to verify cases of a unifie
d Hardy-Littlewood-Chowla conjecture in the presence of a Siegel zero.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Calegari (The University of Chicago)
DTSTART:20210909T190000Z
DTEND:20210909T203000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/18
DESCRIPTION:Title: The unbounded denominators conjecture\nby Frank Calegari (Th
e University of Chicago) as part of CRM-CICMA Québec Vermont Seminar Seri
es\n\nLecture held in En ligne/Web.\n\nAbstract\n(Joint work with Vesselin
Dimitrov and Yunqing Tang). The arithmetic theory of modular forms usua
lly considers functions on the upper half plane which transform nicely und
er a “congruence subgroup" of SL_2(Z)\, that is\, a subgroup of SL_2(Z)
containing all matrices congruent to 1 mod N for some integer N. But as w
as already known to Klein\, SL_2(Z) has many finite index subgroups which
are *not* congruence subgroups. It turns out that the modular forms for t
hese non-congruence subgroups behave quite differently. One longstanding
open problem which characterizes whether a modular form comes from a congr
uence subgroup or not is the so-called “unbounded denominators conjectur
e”. In this talk\, we give an overview of the proof of this conjecture\
, starting with an introduction to the conjecture itself. Organisateur :
quebecvermontnumbertheory@gmail.com\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youness Lamzouri (IECL)
DTSTART:20211125T180000Z
DTEND:20211125T193000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/19
DESCRIPTION:by Youness Lamzouri (IECL) as part of CRM-CICMA Québec Vermon
t Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katharina Mueller (Université Laval)
DTSTART:20211125T200000Z
DTEND:20211125T213000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/20
DESCRIPTION:by Katharina Mueller (Université Laval) as part of CRM-CICMA
Québec Vermont Seminar Series\n\nLecture held in En ligne/Web.\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Bell (Waterloo)
DTSTART:20211209T180000Z
DTEND:20211209T193000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/21
DESCRIPTION:by Jason Bell (Waterloo) as part of CRM-CICMA Québec Vermont
Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samit Dasgupta (Duke)
DTSTART:20211209T200000Z
DTEND:20211209T213000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/22
DESCRIPTION:by Samit Dasgupta (Duke) as part of CRM-CICMA Québec Vermont
Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lazar Radicevic (MPI Bonn)
DTSTART:20220113T180000Z
DTEND:20220113T193000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/23
DESCRIPTION:Title: Explicit realization of elements of the Tate-Shafarevich group c
onstructed from Kolyvagin classes\nby Lazar Radicevic (MPI Bonn) as pa
rt of CRM-CICMA Québec Vermont Seminar Series\n\nLecture held in En ligne
/Web.\n\nAbstract\nWe consider the Kolyvagin cohomology classes associated
to an elliptic curve E defined over Q from a computational point of view.
We explain how to go from a model of a class as an element of (E(L)/pE(L)
)Gal(L/Q)\, where p is prime and L is a dihedral extension of Q of degree
2p\, to a geometric model as a genus one curve embedded in Pp−1. We adap
t the existing methods to compute Heegner points to our situation\, and ex
plicitly compute them as elements of E(L). Finally\, we compute explicit e
quations for several genus one curves that represent non-trivial elements
of the p-torsion part of the Tate-Shafarevich group of E\, for p≤11\, an
d hence are counterexamples to the Hasse principle.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Ostafe (University of South Wale)
DTSTART:20220113T200000Z
DTEND:20220113T213000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/24
DESCRIPTION:Title: On some multiplicative problems for matrices\nby Alina Ostaf
e (University of South Wale) as part of CRM-CICMA Québec Vermont Seminar
Series\n\nLecture held in En ligne/Web.\n\nAbstract\nIn this talk we will
discuss two multiplicative problems for matrices: in the first part we wil
l consider various counting problems with multiplicatively dependent integ
er matrices\, while the second part will consider a matrix analogue of the
Lang problem on torsion points on plane curves. Although bearing similar
multiplicative flavour\, these two parts are different in methods and resu
lts\, with the first one being analytic and the second algebraic. In both
cases\, the non-commutativity of matrices affects the methods we apply\, w
hich are very \ndifferent from those used for their scalar analogues. \n\n
More precisely\, in the first part we give lower and upper bounds for the
number of tuples of `multiplicatively dependent' integer matrices in a box
\, which is motivated by recent work by Pappalardi\, Sha\, Shparlinski and
Stewart (2018) for the scalar case. In the second part we present some re
sults towards a matrix analogue of Lang's problem for $2\\times 2$ matrice
s defined over $\\C$. \n\nWe also pose several problems.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marion Jeannin (Université Lyon 1)
DTSTART:20220127T180000Z
DTEND:20220127T193000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/25
DESCRIPTION:Title: Semistability of G-torsors and integration questions in characte
ristic p>0\nby Marion Jeannin (Université Lyon 1) as part of CRM-CICM
A Québec Vermont Seminar Series\n\nLecture held in En ligne/Web.\n\nAbstr
act\nConstructing quotients is a natural but difficult question in algebra
ic geometry. A key tool for this purpose is the notion of semistability.
Let k be a field and X be a k-curve. Let also G be a reductive group ove
r X obtained from a reductive group over k by base change. Semistability
for G-torsors can be defined by several ways. In this talk we present Ati
yah--Bott and Behrend's approaches. We then explain why the first approac
h can be extended to some positive characteristics and why both of these a
pproaches lead to the same notion (when they are both well-defined). For
this\, I established during my PhD an analogue in positive characteristic
of a theorem of Morozov\, which classifies\, in characteristic 0\, parabol
ic subalgebras of a reductive group by means of their nilradical. \n\nIn t
he second part of the talk\, I will present this analogue and detail some
of the positive characteristic issues its proof raised. More specifically
\, I will focus on integration questions for nil algebras in this context:
roughly speaking I will discuss the existence of a map that plays the rol
e of the exponential map (defined by its power series)\, even in small cha
racteristics.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Jones (University of Illinois at Chicago)
DTSTART:20220127T200000Z
DTEND:20220127T213000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/26
DESCRIPTION:by Nathan Jones (University of Illinois at Chicago) as part of
CRM-CICMA Québec Vermont Seminar Series\n\nLecture held in En ligne/Web.
\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (Paris)
DTSTART:20220210T180000Z
DTEND:20220210T193000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/27
DESCRIPTION:by Romain Branchereau (Paris) as part of CRM-CICMA Québec Ver
mont Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Lester (King's College)
DTSTART:20220224T180000Z
DTEND:20220224T193000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/28
DESCRIPTION:Title: Spacing statistics for lattice points on circles\nby Steve L
ester (King's College) as part of CRM-CICMA Québec Vermont Seminar Series
\n\nLecture held in En ligne/Web.\n\nAbstract\nIn this talk I will describ
e the distribution of lattice points lying on circles. A striking result o
f Kátai and Környei shows that along a density one subsequence of admiss
ible radii the angles of lattice points lying on circles are uniformly dis
tributed in the limit as the radius tends to infinity. Their result goes f
urther\, proving that uniform distribution persists even at very small sca
les\, meaning that the angles are uniformly distributed within quickly shr
inking arcs. A more refined problem is to understand how the lattice point
s are spaced together at the local scale\, e.g. given a circle containing
N lattice points determine the number of gaps between consecutive angles o
f size less than 1/N. I will discuss some recent joint work with Pär Kur
lberg in which we compute the nearest neighbor spacing of the angles along
a density one subsequence of admissible radii.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Witthaus (Essen)
DTSTART:20220224T200000Z
DTEND:20220224T213000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/29
DESCRIPTION:by Robin Witthaus (Essen) as part of CRM-CICMA Québec Vermont
Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai-Wen Lan (Minnesota)
DTSTART:20220310T200000Z
DTEND:20220310T213000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/30
DESCRIPTION:by Kai-Wen Lan (Minnesota) as part of CRM-CICMA Québec Vermon
t Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lori Watson (Wake Forest University)
DTSTART:20220324T170000Z
DTEND:20220324T183000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/31
DESCRIPTION:by Lori Watson (Wake Forest University) as part of CRM-CICMA Q
uébec Vermont Seminar Series\n\nLecture held in En ligne/Web.\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amit Ophir (Jerusalem)
DTSTART:20220324T190000Z
DTEND:20220324T203000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/32
DESCRIPTION:by Amit Ophir (Jerusalem) as part of CRM-CICMA Québec Vermont
Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Bennett (UBC)
DTSTART:20220407T170000Z
DTEND:20220407T183000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/33
DESCRIPTION:Title: Recent progress on Polynomial-Exponential Diophantine equations<
/a>\nby Mike Bennett (UBC) as part of CRM-CICMA Québec Vermont Seminar Se
ries\n\nLecture held in En ligne/Web.\n\nAbstract\nI will survey work on e
xplicit solution of certain Diophantine equations that arise in various co
ntexts\, including determination of values of Fourier coefficients of modu
lar forms\, and gaps between perfect powers. These results rely upon the c
ombination of bounds for linear forms in logarithms\, p-adic and otherwise
\, with machinery for ternary Diophantine equations based upon the modular
ity of Galois representations attached to Frey-Hellegouarch curves. This i
s joint work with Samir Siksek\, Adela Gherga\, Vandita Patel and Philippe
Michaud-Jacobs.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Rosu (Bonn and Leiden)
DTSTART:20220421T170000Z
DTEND:20220421T183000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/34
DESCRIPTION:Title: Twists of elliptic curves with CM\nby Eugenia Rosu (Bonn and
Leiden) as part of CRM-CICMA Québec Vermont Seminar Series\n\nLecture he
ld in En ligne/Web.\n\nAbstract\nWe consider certain families of sextic tw
ists of the elliptic curve y^2=x^3+1 that are not defined over Q\, but ove
r Q[sqrt(-3)]. We compute a formula that relates the central value of thei
r L-functions L(E\, 1) to the square of a trace of a modular function eval
uated at a CM point. Assuming the Birch and Swinnerton-Dyer conjecture\, w
hen the value above is non-zero\, we should recover the order of the Tate-
Shafarevich group\, and we show that the value is indeed an integer square
.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christophe Aistleitner (Graz)
DTSTART:20220421T190000Z
DTEND:20220421T203000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/35
DESCRIPTION:Title: On the metric theory of approximations by reduced fractions\
nby Christophe Aistleitner (Graz) as part of CRM-CICMA Québec Vermont Sem
inar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nIn 2019 Dimitris
Koukoulopoulos and James Maynard solved the Duffin-Schaeffer conjecture\,
a central problem in metric Diophantine approximation that had been open
since 1941. Very roughly speaking\, the Koukoulopoulos-Maynard theorem sta
tes that there is a simple convergence/divergence criterion which allows t
o decide whether (Lebesgue-)almost all real numbers allow infinitely many
coprime rational approximations of a certain quality\, or not. In this tal
k I will report on very recent joint work with Bence Borda and Manuel Hauk
e (both from TU Graz as well) which goes beyond the existence of infinitit
ely many solutions\, and gives an actual asymptotics for the typical numbe
r of coprime rational approximations up to a certain threshold in the dive
rgence case. I will relate some of the history of the subject\, and try to
convey some of the (probablistic) philosophy behind the problem. The proo
f relies mainly on sieve theory and the "anatomy of integers"\, and in par
ticular on the method of GCD graphs which was introduced by Koukoulopoulos
-Maynard in their proof.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chan-Ho Kim (KIAS)
DTSTART:20220505T170000Z
DTEND:20220505T183000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/36
DESCRIPTION:Title: ANNULÉ/CANCEL - Structural refinements of Birch and Swinnerton-
Dyer conjecture and Gross-Zagier formula\nby Chan-Ho Kim (KIAS) as par
t of CRM-CICMA Québec Vermont Seminar Series\n\nLecture held in En ligne/
Web.\n\nAbstract\nWe discuss refined applications of (a part of) the Iwasa
wa main conjecture for elliptic curves to the non-triviality of Kato's Kol
yvagin systems and the structure of Selmer groups of elliptic curves of ar
bitrary rank. The former is the cyclotomic version of Kolyvagin's conjectu
re and the latter can be viewed as a structural refinement of Birch and Sw
innerton-Dyer conjecture. Using the result on the structure of Selmer grou
ps\, we are able to compare directly the collection of Kurihara numbers\,
which is the modular symbol version of Kato's Kolyvagin systems\, with Hee
gner point Kolyvagin systems. This comparison itself can be regarded as a
structural refinement of Gross-Zagier formula from the viewpoint of Kolyva
gin systems.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederick Manners (USCD)
DTSTART:20220505T190000Z
DTEND:20220505T203000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/37
DESCRIPTION:by Frederick Manners (USCD) as part of CRM-CICMA Québec Vermo
nt Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natasha Morrison (Victoria)
DTSTART:20220519T170000Z
DTEND:20220519T183000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/38
DESCRIPTION:by Natasha Morrison (Victoria) as part of CRM-CICMA Québec Ve
rmont Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Sahasrabudhe (Cambridge)
DTSTART:20220519T190000Z
DTEND:20220519T203000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/39
DESCRIPTION:by Julian Sahasrabudhe (Cambridge) as part of CRM-CICMA Québe
c Vermont Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chandrashekhar Khare (UCLA)
DTSTART:20220915T170000Z
DTEND:20220915T183000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/40
DESCRIPTION:Title: The Wiles-Lenstra-Diamond numerical criterion in higher codimens
ions\nby Chandrashekhar Khare (UCLA) as part of CRM-CICMA Québec Verm
ont Seminar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nI will re
port on recent joint work with Srikanth Iyengar and Jeff Manning. We give
a development of numerical criterion that was used by Wiles as an essenti
al ingredient in his approach to modularity of elliptic curves over $\\Q$.
The patching method introduced by Wiles and Taylor has been developed co
nsiderably while the numerical criterion has lagged behind. We prove new
commutative algebra results that lead to a generalisation of the Wiles-Le
nstra-Diamond numerical criterion in situations of positive defect (as ari
se when proving modularity of elliptic curves over number fields with a co
mplex place). A key step in our work is the definition of congruence modu
les in higher codimensions which should be relevant to studying eigenvarie
ties at classical points.\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Jimenez Urroz (UPC)
DTSTART:20220915T190000Z
DTEND:20220915T203000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/41
DESCRIPTION:by Jorge Jimenez Urroz (UPC) as part of CRM-CICMA Québec Verm
ont Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Litt (Toronto)
DTSTART:20220929T170000Z
DTEND:20220929T183000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/42
DESCRIPTION:by Daniel Litt (Toronto) as part of CRM-CICMA Québec Vermont
Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youness Lamzouri (Toronto)
DTSTART:20220929T190000Z
DTEND:20220929T203000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/43
DESCRIPTION:by Youness Lamzouri (Toronto) as part of CRM-CICMA Québec Ver
mont Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ari Shnidman (Hebrew University of Jerusalem)
DTSTART:20221027T143000Z
DTEND:20221027T160000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/44
DESCRIPTION:by Ari Shnidman (Hebrew University of Jerusalem) as part of CR
M-CICMA Québec Vermont Seminar Series\n\nLecture held in En ligne/Web.\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alia Hamieh (UNBC)
DTSTART:20221027T180000Z
DTEND:20221027T193000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/45
DESCRIPTION:by Alia Hamieh (UNBC) as part of CRM-CICMA Québec Vermont Sem
inar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gil Moss (Utah)
DTSTART:20221110T153000Z
DTEND:20221110T170000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/46
DESCRIPTION:by Gil Moss (Utah) as part of CRM-CICMA Québec Vermont Semina
r Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksiy Klurman (Bristol)
DTSTART:20221110T190000Z
DTEND:20221110T203000Z
DTSTAMP:20260404T100032Z
UID:NumTheory/47
DESCRIPTION:by Oleksiy Klurman (Bristol) as part of CRM-CICMA Québec Verm
ont Seminar Series\n\nLecture held in En ligne/Web.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumTheory/47/
END:VEVENT
END:VCALENDAR