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BEGIN:VEVENT
SUMMARY:Gautier Ponsinet (Max Planck Institute)
DTSTART:20200625T143000Z
DTEND:20200625T160000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/1
DESCRIPTION:Title: Universal norms of p-adic Galois representations and the Fargues-Fontain
e curve\nby Gautier Ponsinet (Max Planck Institute) as part of CRM-CIC
MA Québec Vermont Seminar Series\n\nLecture held in En ligne/Web.\n\nAbst
ract\nIn 1996\, Coates and Greenberg computed explicitly the module of uni
versal norms for abelian varieties over perfectoid field extensions. The
computation of this module is employed in Iwasawa theory\, notably to prov
e "control theorems" for Selmer groups\, generalizing Mazur's foundational
work on the Iwasawa theory of abelian varieties over Zp-extensions. \n\n
Coates and Greenberg raised the natural question on possible generalisatio
ns of their result to p-adic representations. In this talk\, I will prese
nt a new approach to this question relying on the classification of vector
bundles over the Fargues-Fontaine curve\, which allows us to answer Coate
and Greenberg's question affirmatively in new cases.\n
LOCATION:https://researchseminars.org/talk/NumTheory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haining Wang (McGill University)
DTSTART:20200625T180000Z
DTEND:20200625T193000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/2
DESCRIPTION:Title: Level raising and Gross-Schoen diagonal cycles\nby Haining Wang (McG
ill University) as part of CRM-CICMA Québec Vermont Seminar Series\n\nLec
ture held in En ligne/Web.\n\nAbstract\nI will discuss my recent work on a
rithmetic level raising on triple product of Shimura curves and its applic
ations to Bloch-Kato type conjecture for triple product of modular forms.\
n
LOCATION:https://researchseminars.org/talk/NumTheory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Shusterman (Harvard University)
DTSTART:20210121T190000Z
DTEND:20210121T203000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/4
DESCRIPTION:Title: Short exponential sums and their applications over function fields\n
by Mark Shusterman (Harvard University) as part of CRM-CICMA Québec Vermo
nt Seminar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nIn joint w
ork with Will Sawin\, we obtain (square-root) cancellation in quite genera
l incomplete exponential sums for the ring F_q[x] of polynomials in one va
riable over a finite field. This has applications to problems in analytic
number theory such as the Chowla conjecture\, Bateman-Horn conjecture\, an
d the number of real quadratic function fields with a huge class group.\n
LOCATION:https://researchseminars.org/talk/NumTheory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Cauchi (Universitat Politècnica de Catalunya)
DTSTART:20210121T143000Z
DTEND:20210121T160000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/5
DESCRIPTION:Title: On higher regulators for Siegel Shimura varieties\nby Antonio Cauchi
(Universitat Politècnica de Catalunya) as part of CRM-CICMA Québec Verm
ont Seminar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nIn this t
alk\, we will report some progress towards the Beilinson conjectures for S
himura varieties associated to the symplectic group GSp(6). We will expla
in how to construct classes in its motivic cohomology and how to compute t
heir image by Beilinson's higher regulator in terms of Rankin-Selberg type
automorphic integrals. Using results of Pollack and Shah\, we relate the
integral to a non-critical special value of the degree 8 spin L-function.
If time permits\, we will describe parallel work in progress\, which relat
es the residue at s=1 of these automorphic integrals to the existence of a
Tate class coming from a Hilbert modular subvariety. This relation partia
lly answers a question of Gross and Savin on motives with Galois group of
type G2. This is joint work with Francesco Lemma and Joaquin Rodrigues Jac
into.\n
LOCATION:https://researchseminars.org/talk/NumTheory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaisa Matomäki (Turku\, Finland)
DTSTART:20210204T143000Z
DTEND:20210204T160000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/6
DESCRIPTION:Title: Almost primes in almost all very short intervals\nby Kaisa Matomäki
(Turku\, Finland) as part of CRM-CICMA Québec Vermont Seminar Series\n\n
Lecture held in En ligne/Web.\n\nAbstract\nBy probabilistic models one exp
ects that\, as soon as $h \\to \\infty$ with $X \\to \\infty$\, short inte
rvals of the type $(x- h \\log X\, x]$ contain primes for almost all $x \\
in (X/2\, X]$. However\, this is far from being established. In the talk I
discuss related questions and in particular describe how to prove the abo
ve claim when one is satisfied with finding $P_2$-numbers (numbers that ha
ve at most two prime factors) instead of primes.\n
LOCATION:https://researchseminars.org/talk/NumTheory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Love (Stanford University)
DTSTART:20210204T190000Z
DTEND:20210204T203000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/7
DESCRIPTION:Title: Explicit Rational Equivalences of Points on Surfaces\nby Jonathan Lo
ve (Stanford University) as part of CRM-CICMA Québec Vermont Seminar Seri
es\n\nLecture held in En ligne/Web.\n\nAbstract\nThe Chow group of zero-cy
cles on a smooth projective surface X is obtained by taking the free abeli
an group generated by closed points on X\, and declaring two elements (“
zero-cycles”) to be equal if their difference is a sum of divisors of ra
tional functions on curves in X\; in this setting we say the zero-cycles a
re “rationally equivalent.” These Chow groups are notoriously difficul
t to compute\; while a set of conjectures due to Bloch and Beilinson predi
ct certain relations must hold in these groups when X is defined over a nu
mber field\, there are very few non-trivial cases in which these relations
have been proven to hold. In this talk\, I will discuss several technique
s that can be used to compute rational equivalences exhibiting some of the
expected relations\, in the case that X is a product of two elliptic curv
es over Q.\n
LOCATION:https://researchseminars.org/talk/NumTheory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olof Sisask (Stockholm University)
DTSTART:20210218T143000Z
DTEND:20210218T160000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/8
DESCRIPTION:Title: Breaking the logarithmic barrier in Roth's theorem\nby Olof Sisask (
Stockholm University) as part of CRM-CICMA Québec Vermont Seminar Series\
n\nLecture held in En ligne/Web.\n\nAbstract\nWe present an improvement to
Roth's theorem on arithmetic progressions\, implying the first non-trivia
l case of a conjecture of Erdős: if a subset A of {1\,2\,3\,...} is not t
oo sparse\, in that the sum of its reciprocals diverges\, then A must cont
ain infinitely many three-term arithmetic progressions. Although a problem
in number theory and combinatorics on the surface\, it turns out to have
fascinating links with geometry\, harmonic analysis and probability\, and
we shall aim to give something of a flavour of this.\n
LOCATION:https://researchseminars.org/talk/NumTheory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Eberhard (Cambridge University)
DTSTART:20210304T143000Z
DTEND:20210304T160000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/9
DESCRIPTION:Title: Irreducibility of the characteristic polynomial of a random integer matr
ix\nby Sean Eberhard (Cambridge University) as part of CRM-CICMA Québ
ec Vermont Seminar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nCo
nsider a random polynomial with integer coefficients. A natural conjecture
is that the polynomial is irreducible with high probability and its Galoi
s group is S_n. This question has been studied for various models of rando
m polynomial. The usual two models are the "bounded degree model"\, in whi
ch the degree is constant and the coefficients are large\, and the "bounde
d height model"\, in which the coefficients are drawn uniformly from a fix
ed interval and the degree becomes large. We will study a variant of the b
ounded height model: take a large n x n matrix with independent +-1 entrie
s and take its characteristic polynomial. To study this question we will c
ombine ideas from the bounded height model with random matrix theory over
a finite field. The method we use is dependent on both the extended Rieman
n hypothesis and the classification of finite simple groups.\n
LOCATION:https://researchseminars.org/talk/NumTheory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Logan (University of Ottawa)
DTSTART:20210304T184500Z
DTEND:20210304T200000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/10
DESCRIPTION:Title: Three modular fivefolds\nby Adam Logan (University of Ottawa) as pa
rt of CRM-CICMA Québec Vermont Seminar Series\n\nLecture held in En ligne
/Web.\n\nAbstract\nEichler and Shimura showed that to every rational Hecke
eigenform of weight 2 there is associated an isogeny class of elliptic cu
rves with the same L-function (and Wiles\, Taylor-Wiles\, et al. proved 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 flavou
r since all such forms arise from imaginary quadratic fields with class gr
oup of exponent dividing 2. There have been many attempts to associate C
alabi-Yau threefolds to eigenforms of weight 4 in such a way that the inte
resting part of the L-function of the threefold matches that of the modula
r 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-functi
ons involve an eigenform of weight 6. Two of the examples are proved\; o
ne is known to have a Calabi-Yau desingularization\, but the other is not.
In connection with these we will describe some new results (joint with
Colin Ingalls) on resolutions of singularities of double covers. The third
example\, still conjectural\, appears to point to a previously unknown id
entity of hypergeometric functions. We will also show how to use an idea
of Burek to find quotients of our varieties for which the point counts ca
n be expressed in terms of a single eigenform of weight 6.\n
LOCATION:https://researchseminars.org/talk/NumTheory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jori Merikoski (University of Turku)
DTSTART:20210318T133000Z
DTEND:20210318T150000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/11
DESCRIPTION:Title: On the largest prime factor of n^2+1\nby Jori Merikoski (University
of Turku) as part of CRM-CICMA Québec Vermont Seminar Series\n\nLecture
held in En ligne/Web.\n\nAbstract\nIt is an open conjecture that there 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 that the l
argest prime factor of n^2+1 is infinitely often greater than n^{1.279}. T
his improves the result of de la Bretèche and Drappeau who obtained the e
xponent 1.2182\, improving the exponent 1.2024 obtained by Deshouillers an
d Iwaniec. The main new ingredients in the proof are Harman's sieve method
and a new bilinear estimate which is proved by applying the Deshouillers-
Iwaniec bounds for sums of Kloosterman sums. Assuming Selberg's eigenvalue
conjecture the exponent 1.279 may be increased to 1.312.\n
LOCATION:https://researchseminars.org/talk/NumTheory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naser Sardari (Penn State University)
DTSTART:20210318T180000Z
DTEND:20210318T190000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/12
DESCRIPTION:Title: Higher Fourier interpolation on the plane\nby Naser Sardari (Penn S
tate University) as part of CRM-CICMA Québec Vermont Seminar Series\n\nLe
cture held in En ligne/Web.\n\nAbstract\nLet $l\\geq 6$ be any integer\, w
here $l\\equiv 2$ mod $4$. Let $f(x)=\\int e^{i\\pi \\tau |x|^2}d\\mu(\\ta
u)$ 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 co
mpact subset of $\\tau \\in\\CC$\, where $\\Im(\\tau)\,\\Im(-\\frac{1}{\\t
au})>\\sin(\\frac{\\pi}{l}).$ For every integer $k\\geq 0$ and $x\\in \\R^
2\,$\n\nWe express $f(x)$ by the values of $\\frac{d^k f}{du^k}$ and $\\fr
ac{d^k \\mathcal{F}f}{du^k}$\n at $u=\\frac{2n}{\\lambda}\,$ where $u=|x|
^2$ and $\\lambda=2\\cos(\\frac{\\pi}{l}).$ We show that the condition $\\
Im(\\tau)\,\\Im(-\\frac{1}{\\tau})>\\sin(\\frac{\\pi}{l})$ is optimal.\n\n
We also identify the cokernel to these values with a specific space of hol
omorphic modular forms of weight $2k+1$ associated to the Hecke triangle g
roup $(2\,l\,\\infty)$.\nUsing our explicit formulas for $l=6$ and develop
ing new methods\, we prove a conjecture of Cohn\, Kumar\, Miller\, Radchen
ko and Viazovska~\\cite[Conjecture 7.5]{Maryna3} motivated by the universa
l optimality of the hexagonal lattice.\n
LOCATION:https://researchseminars.org/talk/NumTheory/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Myerson (University of Warwick)
DTSTART:20210401T133000Z
DTEND:20210401T150000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/13
DESCRIPTION:Title: Form in many variables: p-adic repulsion\nby Simon Myerson (Univers
ity of Warwick) as part of CRM-CICMA Québec Vermont Seminar Series\n\nLec
ture held in En ligne/Web.\n\nAbstract\nConsider the integral zeroes of on
e or more\, not necessarily diagonal\, integral polynomials in many variab
les with the same degree. The basic principles for applying the circle met
hod here were laid out by Birch. One way to improve on his work is repulsi
on: showing that the exponential sum over the polynomials can be large onl
y on small\, well separated regions. I will describe a p-adic version of r
epulsion.\n
LOCATION:https://researchseminars.org/talk/NumTheory/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asher Auel (Dartmouth College)
DTSTART:20210401T180000Z
DTEND:20210401T190000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/14
DESCRIPTION:Title: Brauer classes split by genus one curves\nby Asher Auel (Dartmouth
College) as part of CRM-CICMA Québec Vermont Seminar Series\n\nLecture he
ld in En ligne/Web.\n\nAbstract\nIt is an open problem\, even over the rat
ional numbers\, to decide whether every Brauer class is split by the funct
ion field of a genus one curve. The problem has been solved for Brauer cla
sses 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 modular curve
s and methods from explicit descent for elliptic curves.\n
LOCATION:https://researchseminars.org/talk/NumTheory/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caroline Turnage-Butterbaugh (Carleton College)
DTSTART:20210429T133000Z
DTEND:20210429T150000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/15
DESCRIPTION:Title: Gaps between zeros of the Riemann zeta-function\nby Caroline Turnag
e-Butterbaugh (Carleton College) as part of CRM-CICMA Québec Vermont Semi
nar 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 $2\\pi / \\log \\gamm
a_n$ as $n\\to \\infty$. An important goal is to prove unconditionally tha
t these distances between consecutive zeros can much\, much smaller than t
he average for a positive proportion of zeros. We will discuss the motivat
ion behind this endeavor\, progress made assuming the Riemann Hypothesis\,
and recent work with A. Simonič and T. Trudgian to obtain an uncondition
al result that holds for a positive proportion of zeros.\n
LOCATION:https://researchseminars.org/talk/NumTheory/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cameron Franc (McMaster University)
DTSTART:20210429T180000Z
DTEND:20210429T193000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/16
DESCRIPTION:Title: Noncongruence modular forms and unbounded denominators\nby Cameron
Franc (McMaster University) as part of CRM-CICMA Québec Vermont Seminar S
eries\n\nLecture held in En ligne/Web.\n\nAbstract\nThe modular group PSL2
(Z) contains many noncongruence subgroups of finite index. In this talk we
will explain some results on computing with the modular group\, and in pa
rticular we will explain how to classify genus zero subgroups with a singl
e cusp. Surprisingly\, there are many such groups. Then we will discuss th
e unbounded denominator conjecture for some new cases of noncongruence sub
groups of genus zero\, using a method of Atkin and Swinnerton-Dyer\, suppl
emented with some results on vector-valued modular forms. The most difficu
lt step in this approach is to solve a system of diophantine equations def
ining an Artinian ideal. This is joint work with Andrew Fiori.\n
LOCATION:https://researchseminars.org/talk/NumTheory/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terence Tao (UCLA)
DTSTART:20210909T170000Z
DTEND:20210909T183000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/17
DESCRIPTION:Title: Approximants for classical arithmetic functions\nby Terence Tao (UC
LA) as part of CRM-CICMA Québec Vermont Seminar Series\n\nLecture held in
En ligne/Web.\n\nAbstract\nMany classical arithmetic functions such as th
e M\\"obius function \\mu(n)\, the von Mangoldt function \\Lambda(n)\, or
the higher order divisor functions d_k(n) are notoriously difficult to wor
k with: for instance obtaining cancellation for \\sum_{n \\leq x} \\mu(n)
\\mu(n+1) is part of the Chowla conjecture\, obtaining an asymptotic for \
\sum_{n \\leq x} \\Lambda(n) \\Lambda(n+2) would give the twin prime conje
cture\, 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 w
hen k\,l > 2). However\, in all these cases one can propose _approximants
_ \\mu^\\sharp\, \\Lambda^\\sharp\, d_k^\\sharp to these functions that ar
e substantially easier to work with (mostly by virtue of being "Type I sum
s") and which are (either rigorously or heuristically) close to the origin
al functions \\mu\, \\Lambda\, d_k in various useful ways. We present rec
ent and forthcoming work with Ter\\"av\\"ainen\, Matom\\"aki--Shao--Ter\\"
av\\"ainen\, and Matom\\"aki--Radziwi{\\l}{\\l}--Shao--Ter\\"av\\"ainen us
ing these approximants to control Gowers uniformity norms and related stat
istics for these functions\, as well as to verify cases of a unified Hardy
-Littlewood-Chowla conjecture in the presence of a Siegel zero.\n
LOCATION:https://researchseminars.org/talk/NumTheory/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Calegari (The University of Chicago)
DTSTART:20210909T190000Z
DTEND:20210909T203000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/18
DESCRIPTION:Title: The unbounded denominators conjecture\nby Frank Calegari (The Unive
rsity of Chicago) as part of CRM-CICMA Québec Vermont Seminar Series\n\nL
ecture held in En ligne/Web.\n\nAbstract\n(Joint work with Vesselin Dimitr
ov and Yunqing Tang). The arithmetic theory of modular forms usually con
siders functions on the upper half plane which transform nicely under a
“congruence subgroup" of SL_2(Z)\, that is\, a subgroup of SL_2(Z) conta
ining all matrices congruent to 1 mod N for some integer N. But as was al
ready known to Klein\, SL_2(Z) has many finite index subgroups which are *
not* congruence subgroups. It turns out that the modular forms for these
non-congruence subgroups behave quite differently. One longstanding open
problem which characterizes whether a modular form comes from a congruence
subgroup or not is the so-called “unbounded denominators conjecture”.
In this talk\, we give an overview of the proof of this conjecture\, sta
rting with an introduction to the conjecture itself. Organisateur : quebe
cvermontnumbertheory@gmail.com\n
LOCATION:https://researchseminars.org/talk/NumTheory/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youness Lamzouri (IECL)
DTSTART:20211125T180000Z
DTEND:20211125T193000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katharina Mueller (Université Laval)
DTSTART:20211125T200000Z
DTEND:20211125T213000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Bell (Waterloo)
DTSTART:20211209T180000Z
DTEND:20211209T193000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samit Dasgupta (Duke)
DTSTART:20211209T200000Z
DTEND:20211209T213000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lazar Radicevic (MPI Bonn)
DTSTART:20220113T180000Z
DTEND:20220113T193000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/23
DESCRIPTION:Title: Explicit realization of elements of the Tate-Shafarevich group construc
ted from Kolyvagin classes\nby Lazar Radicevic (MPI Bonn) as part of C
RM-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 exp
lain 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 adapt the e
xisting methods to compute Heegner points to our situation\, and explicitl
y compute them as elements of E(L). Finally\, we compute explicit equation
s 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\, and hence
are counterexamples to the Hasse principle.\n
LOCATION:https://researchseminars.org/talk/NumTheory/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Ostafe (University of South Wale)
DTSTART:20220113T200000Z
DTEND:20220113T213000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/24
DESCRIPTION:Title: On some multiplicative problems for matrices\nby Alina Ostafe (Univ
ersity 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 will consi
der various counting problems with multiplicatively dependent integer matr
ices\, while the second part will consider a matrix analogue of the Lang p
roblem on torsion points on plane curves. Although bearing similar multipl
icative flavour\, these two parts are different in methods and results\, w
ith the first one being analytic and the second algebraic. In both cases\,
the non-commutativity of matrices affects the methods we apply\, which ar
e very \ndifferent from those used for their scalar analogues. \n\nMore pr
ecisely\, in the first part we give lower and upper bounds for the number
of tuples of `multiplicatively dependent' integer matrices in a box\, whic
h is motivated by recent work by Pappalardi\, Sha\, Shparlinski and Stewar
t (2018) for the scalar case. In the second part we present some results t
owards a matrix analogue of Lang's problem for $2\\times 2$ matrices defin
ed over $\\C$. \n\nWe also pose several problems.\n
LOCATION:https://researchseminars.org/talk/NumTheory/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marion Jeannin (Université Lyon 1)
DTSTART:20220127T180000Z
DTEND:20220127T193000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/25
DESCRIPTION:Title: Semistability of G-torsors and integration questions in characteristic
p>0\nby Marion Jeannin (Université Lyon 1) as part of CRM-CICMA Québ
ec Vermont Seminar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nCo
nstructing quotients is a natural but difficult question in algebraic geom
etry. 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 over X obt
ained from a reductive group over k by base change. Semistability for G-t
orsors can be defined by several ways. In this talk we present Atiyah--Bo
tt and Behrend's approaches. We then explain why the first approach can b
e extended to some positive characteristics and why both of these approach
es 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 th
eorem of Morozov\, which classifies\, in characteristic 0\, parabolic suba
lgebras of a reductive group by means of their nilradical. \n\nIn the seco
nd part of the talk\, I will present this analogue and detail some of the
positive characteristic issues its proof raised. More specifically\, I wi
ll focus on integration questions for nil algebras in this context: roughl
y speaking I will discuss the existence of a map that plays the role of th
e exponential map (defined by its power series)\, even in small characteri
stics.\n
LOCATION:https://researchseminars.org/talk/NumTheory/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Jones (University of Illinois at Chicago)
DTSTART:20220127T200000Z
DTEND:20220127T213000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (Paris)
DTSTART:20220210T180000Z
DTEND:20220210T193000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Lester (King's College)
DTSTART:20220224T180000Z
DTEND:20220224T193000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/28
DESCRIPTION:Title: Spacing statistics for lattice points on circles\nby Steve Lester (
King's College) as part of CRM-CICMA Québec Vermont Seminar Series\n\nLec
ture held in En ligne/Web.\n\nAbstract\nIn this talk I will describe the d
istribution of lattice points lying on circles. A striking result of Káta
i and Környei shows that along a density one subsequence of admissible ra
dii the angles of lattice points lying on circles are uniformly distribute
d in the limit as the radius tends to infinity. Their result goes further\
, proving that uniform distribution persists even at very small scales\, m
eaning that the angles are uniformly distributed within quickly shrinking
arcs. A more refined problem is to understand how the lattice points are s
paced together at the local scale\, e.g. given a circle containing N latti
ce points determine the number of gaps between consecutive angles of size
less than 1/N. I will discuss some recent joint work with Pär Kurlberg i
n which we compute the nearest neighbor spacing of the angles along a dens
ity one subsequence of admissible radii.\n
LOCATION:https://researchseminars.org/talk/NumTheory/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Witthaus (Essen)
DTSTART:20220224T200000Z
DTEND:20220224T213000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai-Wen Lan (Minnesota)
DTSTART:20220310T200000Z
DTEND:20220310T213000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lori Watson (Wake Forest University)
DTSTART:20220324T170000Z
DTEND:20220324T183000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amit Ophir (Jerusalem)
DTSTART:20220324T190000Z
DTEND:20220324T203000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Bennett (UBC)
DTSTART:20220407T170000Z
DTEND:20220407T183000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/33
DESCRIPTION:Title: Recent progress on Polynomial-Exponential Diophantine equations\nby
Mike Bennett (UBC) as part of CRM-CICMA Québec Vermont Seminar Series\n\
nLecture held in En ligne/Web.\n\nAbstract\nI will survey work on explicit
solution of certain Diophantine equations that arise in various contexts\
, including determination of values of Fourier coefficients of modular for
ms\, and gaps between perfect powers. These results rely upon the combinat
ion of bounds for linear forms in logarithms\, p-adic and otherwise\, with
machinery for ternary Diophantine equations based upon the modularity of
Galois representations attached to Frey-Hellegouarch curves. This is joint
work with Samir Siksek\, Adela Gherga\, Vandita Patel and Philippe Michau
d-Jacobs.\n
LOCATION:https://researchseminars.org/talk/NumTheory/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Rosu (Bonn and Leiden)
DTSTART:20220421T170000Z
DTEND:20220421T183000Z
DTSTAMP:20260422T212605Z
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 held in E
n ligne/Web.\n\nAbstract\nWe consider certain families of sextic twists of
the elliptic curve y^2=x^3+1 that are not defined over Q\, but over Q[sqr
t(-3)]. We compute a formula that relates the central value of their L-fun
ctions L(E\, 1) to the square of a trace of a modular function evaluated a
t a CM point. Assuming the Birch and Swinnerton-Dyer conjecture\, when the
value above is non-zero\, we should recover the order of the Tate-Shafare
vich group\, and we show that the value is indeed an integer square.\n
LOCATION:https://researchseminars.org/talk/NumTheory/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christophe Aistleitner (Graz)
DTSTART:20220421T190000Z
DTEND:20220421T203000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/35
DESCRIPTION:Title: On the metric theory of approximations by reduced fractions\nby Chr
istophe Aistleitner (Graz) as part of CRM-CICMA Québec Vermont Seminar Se
ries\n\nLecture held in En ligne/Web.\n\nAbstract\nIn 2019 Dimitris Koukou
lopoulos and James Maynard solved the Duffin-Schaeffer conjecture\, a cent
ral problem in metric Diophantine approximation that had been open since 1
941. Very roughly speaking\, the Koukoulopoulos-Maynard theorem states tha
t there is a simple convergence/divergence criterion which allows to decid
e whether (Lebesgue-)almost all real numbers allow infinitely many coprime
rational approximations of a certain quality\, or not. In this talk I wil
l report on very recent joint work with Bence Borda and Manuel Hauke (both
from TU Graz as well) which goes beyond the existence of infinititely man
y solutions\, and gives an actual asymptotics for the typical number of co
prime rational approximations up to a certain threshold in the divergence
case. I will relate some of the history of the subject\, and try to convey
some of the (probablistic) philosophy behind the problem. The proof relie
s mainly on sieve theory and the "anatomy of integers"\, and in particular
on the method of GCD graphs which was introduced by Koukoulopoulos-Maynar
d in their proof.\n
LOCATION:https://researchseminars.org/talk/NumTheory/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chan-Ho Kim (KIAS)
DTSTART:20220505T170000Z
DTEND:20220505T183000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/36
DESCRIPTION:Title: ANNULÉ/CANCEL - Structural refinements of Birch and Swinnerton-Dyer co
njecture and Gross-Zagier formula\nby Chan-Ho Kim (KIAS) as part of CR
M-CICMA Québec Vermont Seminar Series\n\nLecture held in En ligne/Web.\n\
nAbstract\nWe discuss refined applications of (a part of) the Iwasawa main
conjecture for elliptic curves to the non-triviality of Kato's Kolyvagin
systems and the structure of Selmer groups of elliptic curves of arbitrary
rank. The former is the cyclotomic version of Kolyvagin's conjecture and
the latter can be viewed as a structural refinement of Birch and Swinnerto
n-Dyer conjecture. Using the result on the structure of Selmer groups\, we
are able to compare directly the collection of Kurihara numbers\, which i
s the modular symbol version of Kato's Kolyvagin systems\, with Heegner po
int Kolyvagin systems. This comparison itself can be regarded as a structu
ral refinement of Gross-Zagier formula from the viewpoint of Kolyvagin sys
tems.\n
LOCATION:https://researchseminars.org/talk/NumTheory/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederick Manners (USCD)
DTSTART:20220505T190000Z
DTEND:20220505T203000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natasha Morrison (Victoria)
DTSTART:20220519T170000Z
DTEND:20220519T183000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Sahasrabudhe (Cambridge)
DTSTART:20220519T190000Z
DTEND:20220519T203000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chandrashekhar Khare (UCLA)
DTSTART:20220915T170000Z
DTEND:20220915T183000Z
DTSTAMP:20260422T212605Z
UID:NumTheory/40
DESCRIPTION:Title: The Wiles-Lenstra-Diamond numerical criterion in higher codimensions\nby Chandrashekhar Khare (UCLA) as part of CRM-CICMA Québec Vermont Sem
inar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nI will report on
recent joint work with Srikanth Iyengar and Jeff Manning. We give a deve
lopment of numerical criterion that was used by Wiles as an essential ingr
edient in his approach to modularity of elliptic curves over $\\Q$. The p
atching method introduced by Wiles and Taylor has been developed considera
bly while the numerical criterion has lagged behind. We prove new commut
ative algebra results that lead to a generalisation of the Wiles-Lenstra-D
iamond numerical criterion in situations of positive defect (as arise when
proving modularity of elliptic curves over number fields with a complex p
lace). A key step in our work is the definition of congruence modules in
higher codimensions which should be relevant to studying eigenvarieties at
classical points.\n
LOCATION:https://researchseminars.org/talk/NumTheory/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Jimenez Urroz (UPC)
DTSTART:20220915T190000Z
DTEND:20220915T203000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Litt (Toronto)
DTSTART:20220929T170000Z
DTEND:20220929T183000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youness Lamzouri (Toronto)
DTSTART:20220929T190000Z
DTEND:20220929T203000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ari Shnidman (Hebrew University of Jerusalem)
DTSTART:20221027T143000Z
DTEND:20221027T160000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alia Hamieh (UNBC)
DTSTART:20221027T180000Z
DTEND:20221027T193000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gil Moss (Utah)
DTSTART:20221110T153000Z
DTEND:20221110T170000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksiy Klurman (Bristol)
DTSTART:20221110T190000Z
DTEND:20221110T203000Z
DTSTAMP:20260422T212605Z
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://researchseminars.org/talk/NumTheory/47/
END:VEVENT
END:VCALENDAR