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BEGIN:VEVENT
SUMMARY:Dzmitry Badziahin (University of Sydney)
DTSTART:20200916T100000Z
DTEND:20200916T110000Z
DTSTAMP:20260404T095652Z
UID:hnts/1
DESCRIPTION:Title: Diophantine approximation on the Veronese curve\nby Dzmitry Badzia
hin (University of Sydney) as part of Heilbronn number theory seminar\n\n\
nAbstract\nPLEASE NOTE THE UNUSUAL TIME\n\nIn the talk we discuss the set
$S_n(\\lambda)$ of simultaneously $\\lambda$-well approximable points in $
\\mathbb R^n$. That are the points $x$ such that the inequality $|| x - p/
q||_\\infty < q^{-\\lambda - \\epsilon}$ has infinitely many solutions in
rational points $p/q$. Investigating the intersection of this set with a s
uitable manifold comprises one of the most challenging problems in Diophan
tine approximation. It is known that the structure of this set\, especiall
y for large $\\lambda$\, depends on the manifold. For some manifolds it ma
y be empty\, while for others it may have relatively large Hausdorff dimen
sion. We will concentrate on the case of the Veronese curve $V_n$. We disc
uss\, what is known about the Hausdorff dimension of the set $S_n(\\lambda
) \\cap V_n$ and will talk about the recent joint results of the speaker a
nd Bugeaud which impose new bounds on that dimension.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danylo Radchenko (ETH Zurich)
DTSTART:20200923T150000Z
DTEND:20200923T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/2
DESCRIPTION:Title: Fourier interpolation from zeros of the Riemann zeta function\nby
Danylo Radchenko (ETH Zurich) as part of Heilbronn number theory seminar\n
\n\nAbstract\nI will talk about a recent result that shows that any suffic
iently nice even analytic function can be recovered from its values at the
nontrivial zeros of $\\zeta(\\frac{1}{2}+is)$ and the values of its Fouri
er transform at logarithms of integers. The proof is based on an explicit
interpolation formula\, whose construction relies on a strengthening of Kn
opp's abundance principle for Dirichlet series with functional equations.
The talk is based on a joint work with Andriy Bondarenko and Kristian Seip
.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Dimitrov (University of Toronto)
DTSTART:20200930T150000Z
DTEND:20200930T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/3
DESCRIPTION:Title: No shadowing bounds on Galois orbits in the complex plane\nby Vess
elin Dimitrov (University of Toronto) as part of Heilbronn number theory s
eminar\n\n\nAbstract\nFor varying pairs of non-isogenous abelian varieties
of a given dimension over a given finite field\, what is the least possib
le arclengths sum under a matching of their Frobenius roots? For varying p
airs of Salem numbers in $[1\,2]$\, what is their least possible distance
in terms of the sum of their degrees?\n\nWe address\, and partly answer\,
these kinds of questions in the seminar\, with a particular focus on the t
wo representatives at hand. The method\, which is based on potential theor
y in the complex plane\, also establishes the Lehmer conjecture for the in
teger monic polynomials $P(X)$ that have\nall their roots limited to the c
omplex disk $|z| < 10^{1/\\deg(P)}$: the extremal case where the Galois or
bit of algebraic integers is maximally equalized around the unit circle. W
e also raise a few apparently new questions that our results motivate.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriele Nebe (RWTH Aachen University)
DTSTART:20201007T150000Z
DTEND:20201007T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/4
DESCRIPTION:Title: Automorphisms of extremal modular lattices\nby Gabriele Nebe (RWTH
Aachen University) as part of Heilbronn number theory seminar\n\n\nAbstra
ct\nThe study of automorphisms of extremal lattices was motivated by simil
ar research for binary self-dual codes. It started by considering extremal
even unimodular lattices in dimensions which are multiples of 24. We know
six such lattices\, the Leech lattice in dimension 24\, four lattices of
dimension 48 and\, since 2010\, also one extremal lattice in dimension 72.
One of the 48-dimensional lattices was found by a computer search for lat
tices with a certain automorphism of order 5.\n\nIn his thesis Michael Jü
rgens extended the theory to automorphisms of modular lattices\, aiming in
the construction of an extremal 3-modular lattice in dimension 36. In the
talk I will present new methods suitable for non unimodular lattices and
results partly obtained in joint work with Dr. Markus Kirschmer.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lior Bary-Soroker (Tel Aviv University)
DTSTART:20201014T150000Z
DTEND:20201014T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/9
DESCRIPTION:Title: Random polynomials\, probabilistic Galois theory\, and finite field ar
ithmetic\nby Lior Bary-Soroker (Tel Aviv University) as part of Heilbr
onn number theory seminar\n\n\nAbstract\nIn the talk we will discuss recen
t advances on the following two questions:\nLet $A(X) = \\sum ±X^i$ be a
random polynomial of degree n with coefficients taking the values $-1\, 1$
independently each with probability $1/2$.\n\nQ1: What is the probability
that $A$ is irreducible as the degree goes to infinity?\n\nQ2: What is th
e typical Galois group of $A$?\n\nOne believes that the answers are YES an
d THE FULL SYMMETRIC GROUP\, respectively.\nThese questions were studied e
xtensively in recent years\, and we will survey the tools developed to att
ack these problems and partial results.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sug Woo Shin (University of California\, Berkeley)
DTSTART:20201021T150000Z
DTEND:20201021T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/10
DESCRIPTION:Title: On GSpin(2n)-valued automorphic Galois representations\nby Sug Wo
o Shin (University of California\, Berkeley) as part of Heilbronn number t
heory seminar\n\n\nAbstract\nI will present my joint work with Arno Kret\,
where we construct a GSpin($2n$)-valued $\\ell$-adic Galois representatio
n attached to a cuspidal cohomological automorphic representation $\\pi$ o
f a suitable quasi-split form of GSO($2n$) over a totally real field\, und
er the hypothesis that pi has a Steinberg component at a finite place. Thi
s uses input from the cohomology of certain Shimura varieties for GSO($2n$
)\; as such we need to take a suitable form of GSO($2n$) depending on the
parity of $n$. (We take the split form if and only if $n$ is even.)\n
LOCATION:https://stable.researchseminars.org/talk/hnts/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Young (Texas A&M University)
DTSTART:20201028T160000Z
DTEND:20201028T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/11
DESCRIPTION:Title: The Weyl bound for Dirichlet $L$-functions\nby Matthew Young (Tex
as A&M University) as part of Heilbronn number theory seminar\n\n\nAbstrac
t\nThe problem of bounding $L$-functions has a long history. For the Riema
nn zeta function\, the method of Weyl gives a subconvexity bound with expo
nent $1/6$\, which is now called the Weyl bound. Many questions on the zet
a function in the t-aspect have a natural analog for Dirichlet $L$-functio
ns in the q-aspect\, but the latter is in general much harder. Indeed\, th
e first subconvexity result for Dirichlet $L$-functions\, due to Burgess i
n the 1960's\, has a weaker exponent $3/16$. In this talk I will discuss w
ork with Ian Petrow that proves the Weyl bound for all Dirichlet $L$-funct
ions.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Rudnev (University of Bristol)
DTSTART:20201104T160000Z
DTEND:20201104T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/12
DESCRIPTION:Title: On convexity and sumsets\nby Misha Rudnev (University of Bristol)
as part of Heilbronn number theory seminar\n\n\nAbstract\nA finite set $A
$ of $n$ reals is convex if the sequence of neighbouring differences is st
rictly monotone. Erdös suggested that that the set of squares of the firs
t $n$ integers may constitute the extremal case\, namely that for any conv
ex $A$\, $|A+A| > n^{2-o(1)}$. The question is still open\, we'll review s
ome partial progress.\n\nWhat about $k- $fold sums $A+A+A+...$? In the cas
e of squares\, they stop growing after $k=2$\, and for $k$th powers they g
row up to $n^k$. In a joint work with Brandon Hanson and Olly Roche-Newton
we show\, using elementary methods\, that if $A=f([n])$\, where $f$ is a
real function with $k-1$ strictly monotone derivatives\, taking sufficient
ly many sums does lead to growth up to $n^{k-o(1)}$. We generalise this by
replacing the interval $[n]$ versus $f([n])$ by any set with small additi
ve doubling versus its image by $f$\, which enables us to apply this to su
m-product type questions.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Lemos (University College London)
DTSTART:20201111T160000Z
DTEND:20201111T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/13
DESCRIPTION:Title: Residual Galois representations of elliptic curves with image in the
normaliser of a non-split Cartan\nby Pedro Lemos (University College L
ondon) as part of Heilbronn number theory seminar\n\n\nAbstract\nDue to th
e work of several mathematicians\, it is known that if p is a prime >37\,
then the image of the residual Galois representation $\\bar{\\rho}_{E\,p}:
G_{\\mathbb{Q}}\\rightarrow {\\rm GL}_2(\\mathbb{F}_p)$ attached to an el
liptic curve $E/\\mathbb{Q}$ without complex multiplication is either ${\\
rm GL}_2(\\mathbb{F}_p)$\, or is contained in the normaliser of a non-spli
t Cartan subgroup of ${\\rm GL}_2(\\mathbb{F}_p)$. I will report on a rece
nt joint work with Samuel Le Fourn\, where we improve this result (at leas
t for large enough primes) by showing that if $p>1.4\\times 10^7$\, then $
\\bar{\\rho}_{E\,p}$ is either surjective\, or its image is the normaliser
of a non-split Cartan subgroup of ${\\rm GL}_2(\\mathbb{F}_p)$.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heekyoung Hahn (Duke University)
DTSTART:20201118T110000Z
DTEND:20201118T120000Z
DTSTAMP:20260404T095652Z
UID:hnts/14
DESCRIPTION:Title: Poles of triple tensor product L-functions involving monomial represe
ntations\nby Heekyoung Hahn (Duke University) as part of Heilbronn num
ber theory seminar\n\n\nAbstract\n**PLEASE NOTE THE UNUSUAL TIME**\n\nLitt
le is known about the order of poles of triple tensor product $L$-function
s in higher rank. In this talk we will investigate the order of the pole o
f the triple tensor product $L$-functions $L(s\,\\pi_1\\times\\pi_2\\times
\\pi_3\,\\otimes^3)$ for cuspidal automorphic representations $\\pi_i$ of
$\\GL_{n_i}(\\mathbb{A}_F)$ in the setting where one of the $\\pi_i$ is a
monomial representation. In the view of Brauer theory\, this is a natural
setting to consider. The results provided in this talk give examples that
can be used as a point of reference for Langlands' beyond endoscopy propos
al.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ghaith Hiary (Ohio State University)
DTSTART:20201125T160000Z
DTEND:20201125T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/15
DESCRIPTION:Title: An Omega-result for $S(t)$\nby Ghaith Hiary (Ohio State Universit
y) as part of Heilbronn number theory seminar\n\n\nAbstract\nI discuss som
e bounds in the theory of the Riemann zeta function\, in particular Omega
results for $S(t)$\, the fluctuating part of the zeros counting function f
or the Riemann zeta function. I outline a new unconditional Omega-result f
or $S(t)$.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Folsom (Amherst College)
DTSTART:20201202T160000Z
DTEND:20201202T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/16
DESCRIPTION:Title: Eisenstein series\, cotangent-zeta sums\, knots\, and quantum modular
forms\nby Amanda Folsom (Amherst College) as part of Heilbronn number
theory seminar\n\n\nAbstract\nQuantum modular forms\, defined in the rati
onal numbers\, transform like modular forms do on the upper half-plane\, u
p to suitably analytic error functions. In this talk we give frameworks fo
r two different examples of quantum modular forms originally due to Zagier
: the Dedekind sum\, and a certain q-hypergeometric sum due to Kontsevich.
For the first\, we extend work of Bettin and Conrey and define twisted Ei
senstein series\, study their period functions\, and establish quantum mod
ularity of certain cotangent-zeta sums. For the second\, we discuss result
s due to Hikami\, Lovejoy\, the author\, and others\, on quantum modular a
nd quantum Jacobi forms related to colored Jones polynomials for certain f
amilies of knots.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arul Shankar (University of Toronto)
DTSTART:20201209T160000Z
DTEND:20201209T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/17
DESCRIPTION:Title: The number of $D_4$-extensions of $\\mathbb{Q}$\nby Arul Shankar
(University of Toronto) as part of Heilbronn number theory seminar\n\n\nAb
stract\nWe will begin with a summary of how Malle's conjecture and Bhargav
a's heuristics can be used to develop the "Malle--Bhargava heuristics"\, p
redicting the asymptotics in families of number fields\, ordered by a gene
ral class of invariants.\n\nWe will then specialize in the case of $D_4$-n
umber fields. Even in this (fairly simple) case\, where the fields can be
parametrized quite explicitly\, the question of determining asymptotics ca
n get quite complicated. We will discuss joint work with Altug\, Varma\, a
nd Wilson\, in which we recover asymptotics when quartic $D_4$ fields are
ordered by conductor. And we will finally discuss joint work with Varma\,
in which we recover Malle's conjecture for octic $D_4$-fields.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chantal David (Concordia University)
DTSTART:20201216T160000Z
DTEND:20201216T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/18
DESCRIPTION:Title: Moments and non-vanishing of cubic Dirichlet $L$-functions at $s =\\f
rac{1}{2}$\nby Chantal David (Concordia University) as part of Heilbro
nn number theory seminar\n\n\nAbstract\nA famous conjecture of Chowla pred
icts that $L(\\frac{1}{2}\,\\chi) \\neq 0$ for all Dirichlet $L$-functions
attached to primitive characters $\\chi$. It was conjectured first in the
case where $\\chi$ is a quadratic character\, which is the most studied c
ase. For quadratic Dirichlet $L$-functions\, Soundararajan proved that at
least 87.5% of the quadratic Dirichlet L-functions do not vanish at $s =\\
frac{1}{2}$. Under GRH\, there are slightly stronger results by Ozlek and
Snyder.\n\nWe present in this talk the first result showing a positive pro
portion of cubic Dirichlet\n$L$-functions non-vanishing at $s =\\frac{1}{2
}$ for the non-Kummer case over function fields. This can be achieved by u
sing the recent breakthrough work on sharp upper bounds for moments of\nSo
undararajan\, Harper and Lester-Radziwill. Our results would transfer over
number fields\,\nbut we would need to assume GRH in this case.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Gulotta (Max Planck Institute Bonn)
DTSTART:20210127T160000Z
DTEND:20210127T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/19
DESCRIPTION:Title: Vanishing theorems for Shimura varieties at unipotent level and Galoi
s representations\nby Daniel Gulotta (Max Planck Institute Bonn) as pa
rt of Heilbronn number theory seminar\n\n\nAbstract\nThe Langlands corresp
ondence relates automorphic forms and Galois representations --- for examp
le\, the modular form $\\eta(z)^2 \\eta(11z)^2$ and the Tate module of the
elliptic curve $y^2 + y = x^3 - x^2 - 10x - 20$ are related in the sense
that they have the same L-function. The p-adic Langlands program aims to
interpolate the Langlands correspondence in p-adic families. In this sett
ing\, the role of automorphic forms is played by the completed cohomology
groups defined by Emerton.\n\nCalegari and Emerton have conjectured that t
he completed cohomology vanishes above a certain degree\, often denoted $q
_0$. In the case of Shimura varieties of Hodge type\, Scholze has proved
the conjecture for compactly supported completed cohomology. We give a st
rengthening of Scholze's result under the additional assumption that the g
roup becomes split over $\\mathbb{Q}_p$. More specifically\, we show that
the compactly supported cohomology vanishes not just at full infinite lev
el at p\, but also at unipotent level at p.\n\nWe also give an application
of the above result to eliminating the nilpotent ideal in certain cases o
f Scholze's construction of Galois representations.\n\nThis talk is based
on joint work with Ana Caraiani and Christian Johansson and on joint work
with Ana Caraiani\, Chi-Yun Hsu\, Christian Johansson\, Lucia Mocz\, Emanu
el Reinecke\, and Sheng-Chi Shih.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Par Kurlberg (KTH Stockholm)
DTSTART:20210203T160000Z
DTEND:20210203T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/20
DESCRIPTION:Title: Distribution of lattice points on hyperbolic circles\nby Par Kurl
berg (KTH Stockholm) as part of Heilbronn number theory seminar\n\n\nAbstr
act\nWe study the distribution of lattice points lying on expanding circle
s in the hyperbolic plane. The angles of lattice points arising from the o
rbit of the modular group $\\operatorname{PSL}(2\,\\mathbb Z)$\, and lying
on hyperbolic circles centered at $i$\, are shown to be equidistributed f
or generic radii (among the ones that contain points). We also show that a
ngles fail to equidistribute on a thin set of exceptional radii\, even in
the presence of growing multiplicity. Surprisingly\, the distribution of a
ngles on hyperbolic circles turns out to be related to the angular distrib
ution of euclidean lattice points lying on circles in the plane\, along a
thin subsequence of radii. This is joint work with\nD. Chatzakos\, S. Lest
er and I. Wigman.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayla Gafni (University of Mississippi)
DTSTART:20210122T160000Z
DTEND:20210122T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/21
DESCRIPTION:Title: Asymptotics of restricted partition functions\nby Ayla Gafni (Uni
versity of Mississippi) as part of Heilbronn number theory seminar\n\n\nAb
stract\n**NOTE THE UNUSUAL TIME AND DAY**\n\nGiven a set $\\mathcal A \\su
bset \\mathbb N$\, the restricted partition function $p_{\\mathcal{A}}(n)$
counts the number of integer partitions of $n$ with all parts in $\\mathc
al A$. In this talk\, we will explore the features of the restricted parti
tions function $p_{\\mathbb P_k}(n)$ where $\\mathcal P_k$ is the set of $
k$-th powers of primes. Powers of primes are both sparse and irregular\, w
hich makes $p_{\\mathbb P_k}(n)$ quite an elusive function to understand.
We will discuss some of the challenges involved in studying restricted par
tition functions and what is known in the case of primes\, $k$-th powers\,
and $k$-th powers of primes.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Obus (City University New York)
DTSTART:20210224T160000Z
DTEND:20210224T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/22
DESCRIPTION:Title: Fun with Mac Lane valuations\nby Andrew Obus (City University New
York) as part of Heilbronn number theory seminar\n\n\nAbstract\nMac Lane'
s technique of "inductive valuations" is over 80 years old\, but has only
recently been used to attack problems about arithmetic surfaces. We will
give an explicit\, hands-on introduction to the theory\, requiring little
background beyond the definition of a non-archimedean valuation. \n\nWe w
ill then outline how this theory is useful for resolving "weak wild" quoti
ent singularities of arithmetic surfaces (joint with Stefan Wewers)\, prov
ing conductor-discriminant inequalities for hyperelliptic and superellipti
c curves (joint with Padmavathi Srinivasan)\, and understanding regular mo
dels of potentially Mumford curves (joint with Daniele Turchetti).\n
LOCATION:https://stable.researchseminars.org/talk/hnts/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahesh Kakde (India Institute of Science)
DTSTART:20210303T160000Z
DTEND:20210303T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/23
DESCRIPTION:Title: Brumer-Stark units\nby Mahesh Kakde (India Institute of Science)
as part of Heilbronn number theory seminar\n\n\nAbstract\nIn this talk I w
ill report on my recent work with Samit Dasgupta that prove existence of t
he Brumer-Stark units (The Brumer-Stark conjecture) and a p-adic analytic
formula for them (a conjecture of Dasgupta). The latter conjecture is tack
led by proving an integral version of the Gross-Stark conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:YoungJu Choie (POSTECH)
DTSTART:20210310T110000Z
DTEND:20210310T120000Z
DTSTAMP:20260404T095652Z
UID:hnts/24
DESCRIPTION:Title: A generating functions of periods of modular forms\nby YoungJu Ch
oie (POSTECH) as part of Heilbronn number theory seminar\n\n\nAbstract\n**
NOTE THE UNUSUAL TIME**\n\nA closed formula for the sum of all Hecke eigen
forms on $\\Gamma_0(N)$\, multiplied by their odd period polynomials in tw
o variables\, as a single product of Jacobi theta series for any squarefre
e level $N$ is known. When $N=1$ this was result given by Zagier in 1991.\
n\nWe discuss more general results regarding on this direction.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Voight (Dartmouth)
DTSTART:20210317T160000Z
DTEND:20210317T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/25
DESCRIPTION:Title: Counting elliptic curves with torsion\, and a probabilistic local-glo
bal principle\nby John Voight (Dartmouth) as part of Heilbronn number
theory seminar\n\n\nAbstract\nCan we detect torsion of a rational elliptic
curve $E$ by looking modulo primes? Well\, for almost all primes $p$\, t
he torsion subgroup $E(\\mathbb{Q})_{\\operatorname{tor}}$ maps injectivel
y into $E(\\mathbb{F}_p)$\; but the converse statement holds only up to is
ogeny\, by a theorem of Katz. In this\ntalk\, we consider a probabilistic
refinement for the elliptic curves themselves: if $m | \n \\#E(\\mathbb{F
}_p)$ for almost all primes $p$\, what is the probability that $m | \\#E(\
\mathbb{Q})_{\\operatorname{tor}}$? We answer this question in a precise
way by giving an asymptotic count of rational elliptic curves by height wi
th certain prescribed Galois image.\n\nThis is joint work with John Cullin
an and Meagan Kenney.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina Roehrig (University of Cologne)
DTSTART:20210210T160000Z
DTEND:20210210T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/26
DESCRIPTION:Title: Siegel theta series for indefinite quadratic forms\nby Christina
Roehrig (University of Cologne) as part of Heilbronn number theory seminar
\n\n\nAbstract\nDue to a result by Vignéras from 1977\, there is a quite
simple way to determine whether a certain theta series admits modular tran
sformation properties. To be more specific\, she showed that solving a dif
ferential equation of second order serves as a criterion for modularity. W
e generalize this result for Siegel theta series of arbitrary genus $n$. I
n order to do so\, we construct Siegel theta series for indefinite quadrat
ic forms by considering functions that solve an $n\\times n$-system of par
tial differential equations. These functions do not only give examples of
Siegel theta series\, but build a basis of the family of Schwartz function
s that generate series that transform like modular forms.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Morgan (Mathematisches Forschungsinstitut Oberwolfach)
DTSTART:20210217T160000Z
DTEND:20210217T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/27
DESCRIPTION:Title: 4-ranks of class groups of biquadratic fields\nby Adam Morgan (Ma
thematisches Forschungsinstitut Oberwolfach) as part of Heilbronn number t
heory seminar\n\n\nAbstract\nLet K be a quadratic number field\, and consi
der the family of biquadratic fields $K_n= K(\\sqrt{n})$ for $n$ a squaref
ree integer. I will discuss joint work with Peter Koymans and Harry Smit i
n which we study\, as $n$ varies\, the 4-rank of the class group of $K_n$\
, showing in particular that for 100 % of squarefree n\, the 4-rank is giv
en by an explicit formula involving the number of prime divisors of n that
are inert in $K$. If time permits I will discuss an elliptic curve analog
ue of this work\, which is joint with Ross Paterson.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maki Nakasuji (Sophia University\, Japan)
DTSTART:20210324T110000Z
DTEND:20210324T120000Z
DTSTAMP:20260404T095652Z
UID:hnts/28
DESCRIPTION:Title: Schur multiple zeta functions and their properties\nby Maki Nakas
uji (Sophia University\, Japan) as part of Heilbronn number theory seminar
\n\n\nAbstract\n**NOTE THE UNUSUAL TIME**\n\nMultiple zeta functions have
been studied at least since Euler\, who found many of their algebraic prop
erties. In particular\, they are greatly developed since the 1980s in seve
ral different contexts such as modular forms\, mixed Tate motives\, quantu
m groups\, moduli spaces of vector bundles\, scattering amplitudes\, etc.\
n\nIn this talk\, we introduce a generalization of the Euler-Zagier type m
ultiple zeta and zeta-star functions\, that we call Schur multiple zeta fu
nctions. These functions are defined as sums over combinatorial objects ca
lled semi-standard Young tableaux. We will show the determinant formulas f
or Schur multiple zeta functions\, which lead to quite non-trivial algebra
ic relations among multiple zeta and zeta-star functions. This is based on
joint work with O. Phuksuwan and Y. Yamasaki. And we will also show relat
ions among Schur multiple zeta functions and zeta-functions of root system
s attached to semisimple Lie algebras\, which is a joint work with K. Mats
umoto. Further\, if time permits we will introduce Schur type poly-Bernoul
li numbers and investigate their properties.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Capuano (Politecnico di Torino)
DTSTART:20210421T150000Z
DTEND:20210421T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/29
DESCRIPTION:Title: GCD results for certain divisibility sequences of polynomials and a c
onjecture of Silverman\nby Laura Capuano (Politecnico di Torino) as pa
rt of Heilbronn number theory seminar\n\n\nAbstract\nA divisibility sequen
ce is a sequence of integers $d_n$ such that\, if $m$ divides $n$\, then $
d_m$ divides $d_n$. Bugeaud\, Corvaja\, Zannier showed that pairs of divis
ibility sequences of the form $a^n-1$ have only limited common factors. Fr
om a geometric point of view\, this divisibility sequence corresponds to a
subgroup of the multiplicative group\, and Silverman conjectured that a s
imilar behaviour should appear in (a large class of) other algebraic group
s.\n\nExtending previous works of Silverman and of Ghioca-Hsia-Tucker on e
lliptic curves over function fields\, we will show how to prove the analog
ue of Silverman’s conjecture over function fields in the case of split s
emiabelian varieties and some generalizations. The proof relies on some re
sults of unlikely intersections. This is a joint work with F. Barroero and
A. Turchet.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Burrin (ETH Zurich)
DTSTART:20210505T150000Z
DTEND:20210505T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/30
DESCRIPTION:Title: A sparse equidistribution problem for expanding horocycles on the mod
ular surface\nby Claire Burrin (ETH Zurich) as part of Heilbronn numbe
r theory seminar\n\n\nAbstract\nThe orbits of the horocycle flow on hyperb
olic surfaces (or orbifolds) are classified: each orbit is either dense or
a closed horocycle around a cusp. Expanding closed horocycles are themsel
ves asymptotically dense\, and in fact become equidistributed on the surfa
ce. The precise rate of equidistribution is of interest\; on the modular s
urface\, Zagier observed that a particular rate is equivalent to the Riema
nn hypothesis being true. In this talk\, I will discuss the asymptotic beh
avior of evenly spaced points along an expanding closed horocycle on the m
odular surface. In this problem\, the number of points depends on the expa
nsion rate of the horocycle\, and the difficulty is that these points are
no more invariant under the horocycle flow. This is based on joint work wi
th Uri Shapira and Shucheng Yu.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seonhee Lim (Seoul National University)
DTSTART:20210512T100000Z
DTEND:20210512T110000Z
DTSTAMP:20260404T095652Z
UID:hnts/31
DESCRIPTION:Title: Effective Hausdorff dimension of bad sets\nby Seonhee Lim (Seoul
National University) as part of Heilbronn number theory seminar\n\n\nAbstr
act\n**NOTE THE UNUSUAL TIME**\n\nIn this talk\, we consider the inhomogen
eous Diophantine approximation: the distribution of $qa$ modulo integers n
ear a target real $b$ (for integer $q$ and a real $a$)\, or more generally
$Aq$ modulo integral vectors near a target vector $b$ (where $q$ is an in
teger vector\, and $A$ is a real matrix). We prove that for all $b$\, the
Hausdorff dimension of the set of matrices that are epsilon badly approxim
able for the target $b$ is not full\, with an effective upper bound. We al
so give an effective bound on the dimension of the set of targets badly ap
proximated by $Aq$ in terms of epsilon\, if the matrix $A$ is not singular
on average. The main part of the talk is joint work with Taehyeong Kim an
d Wooyeon Kim.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naser Sardari (Penn State)
DTSTART:20210519T150000Z
DTEND:20210519T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/32
DESCRIPTION:Title: Higher Fourier interpolation on the plane\nby Naser Sardari (Penn
State) as part of Heilbronn number theory seminar\n\n\nAbstract\nRadchenk
o and Viazovska recently proved an elegant formula that expresses the valu
e of the Schwartz function $f$ at any given point in terms of the values o
f $f$ and its Fourier transform on the set $\\{ \\sqrt{|n|}:n\\in \\Z\\}.$
We develop new interpolation formulas using the values of the higher deri
vatives on new discrete sets. \n\nIn particular\, we prove a conjecture o
f Cohn\, Kumar\, Miller\, Radchenko and Viazovska that was motivated b
y the universal optimality of the hexagonal lattice.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Zywina (Cornell)
DTSTART:20210526T150000Z
DTEND:20210526T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/33
DESCRIPTION:Title: Modular curves and Serre's open image theorem\nby David Zywina (C
ornell) as part of Heilbronn number theory seminar\n\n\nAbstract\nModular
curves can be used to encode important arithmetic information concerning e
lliptic curves. These curves are defined as abstract moduli spaces and in
practice it is useful to have explicit models. We will discuss a way of co
mputing models that makes use of the arithmetic of Eisenstein series. Our
application is towards a computational version of Serre’s open image th
eorem.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brad Rodgers (Queens University)
DTSTART:20210602T150000Z
DTEND:20210602T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/34
DESCRIPTION:Title: The distribution of random polynomials with multiplicative coefficien
ts\nby Brad Rodgers (Queens University) as part of Heilbronn number th
eory seminar\n\n\nAbstract\nA classic paper of Salem and Zygmund investiga
tes the distribution of trigonometric polynomials whose coefficients are c
hosen randomly (say $+1$ or $-1$ with equal probability) and independently
. Salem and Zygmund characterized the typical distribution of such polynom
ials (gaussian) and the typical magnitude of their sup-norms (a degree $N$
polynomial typically has sup-norm of size $\\sqrt{N \\log N}$ for large $
N$). In this talk we will explore what happens when a weak dependence is i
ntroduced between coefficients of the polynomials\; namely we consider pol
ynomials with coefficients given by random multiplicative functions. We co
nsider analogues of Salem and Zygmund's results\, exploring similarities a
nd some differences.\n\nSpecial attention will be given to a beautiful poi
nt-counting argument introduced by Vaughan and Wooley which ends up being
useful.\n\nThis is joint work with Jacques Benatar and Alon Nishry.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fang-Ting Tu (Louisiana State University)
DTSTART:20210428T150000Z
DTEND:20210428T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/35
DESCRIPTION:Title: A Whipple formula revisited\nby Fang-Ting Tu (Louisiana State Uni
versity) as part of Heilbronn number theory seminar\n\n\nAbstract\nThis ta
lk is based on recent joint work with Wen-Ching Winnie Li and Ling Long. W
e consider the hypergeometric data corresponding to a formula due to Whipp
le which relates certain hypergeometric values $_7F_6(1)$ and $_4F_3(1)$.
\n\nWhen the hypergeometric data are primitive and defined over the ration
als\, from identities of hypergeometric character sums\, we explain a spec
ial structure of the corresponding Galois representations behind Whipple's
formula leading to a decomposition that can be described by the Fourier c
oefficients of Hecke eigenforms. In this talk\, I will use an example to d
emonstrate our approach and relate the hypergeometric values to certain pe
riods of modular forms.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Streeter (University of Bristol)
DTSTART:20210929T150000Z
DTEND:20210929T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/36
DESCRIPTION:Title: Weak approximation for del Pezzo surfaces of low degree\nby Sam S
treeter (University of Bristol) as part of Heilbronn number theory seminar
\n\n\nAbstract\nWork of Iskovskih shows that any geometrically rational su
rface is birational to a conic bundle or a del Pezzo surface. In this talk
\, we focus on surfaces in the intersection of these two families through
the lens of weak approximation. In joint work in progress with Julian Deme
io\, we show that a general del Pezzo surface of degree one or two with a
conic fibration satisfies weak weak approximation\, or weak approximation
away from finitely many places. We utilise a result of Denef connecting ar
ithmetic surjectivity (surjectivity on local points at all but finitely ma
ny places) with the scheme-theoretic notion of splitness.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harry Smit (Max Planck Institute for Mathematics)
DTSTART:20211006T150000Z
DTEND:20211006T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/37
DESCRIPTION:Title: Characterizing number fields using L-series\nby Harry Smit (Max P
lanck Institute for Mathematics) as part of Heilbronn number theory semina
r\n\n\nAbstract\nThe celebrated Neukirch-Uchida theorem states that two nu
mber fields with isomorphic absolute Galois group must be isomorphic thems
elves. This result has since been extended to quotients of this Galois gro
up such as the solvable closure and (very recently\, by Saidi and Tamagawa
) the 3-step solvable closure. The abelianization does not\, however\, hav
e this characterizing property. In fact\, many imaginary quadratic number
fields have isomorphic abelianized Galois group.\n\nOne way to supplement
the abelianized Galois group is by adding some information on the (Dirichl
et) L-series of the number fields. We show that in this way it is possible
to not only characterize the number field\, but also the isomorphisms and
homomorphisms between number fields. If time allows\, we discuss how simi
lar techniques can be used to characterize isogeny classes of abelian vari
eties using twists of the L-series attached to the abelian variety.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Yafaev (University College London)
DTSTART:20211013T150000Z
DTEND:20211013T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/38
DESCRIPTION:Title: Lower bounds for Galois orbits of special points and the Andre-Oort c
onjecture\nby Andrei Yafaev (University College London) as part of Hei
lbronn number theory seminar\n\nLecture held in Fry Building 2.04.\n\nAbst
ract\nThe Andre-Oort conjecture has been an open problem for over 30 years
. The last hurdle in its proof (using the strategy using o-minimality) has
been the problem of bounding below the degrees of special points in Shimu
ra varieties. In a joint work with Gal Biniyamini and Harry Schmidt\, we h
ave proved the lower bounds conditional on a conjecture on bounds on heigh
ts of special points. Very recently J. Pila and J. Tsimerman have announce
d the proof of this conjecture thus completing the proof. We will present
the work with G. Biniyamini and H. Schmidt.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youness Lamzouri (IECL (Université de Lorraine))
DTSTART:20211020T150000Z
DTEND:20211020T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/39
DESCRIPTION:Title: Zeros of linear combinations of L-functions near the critical line\nby Youness Lamzouri (IECL (Université de Lorraine)) as part of Heilbro
nn number theory seminar\n\nLecture held in 2.04 Fry building\, University
of Bristol.\n\nAbstract\nIn this talk\, I will present a recent joint wor
k with Yoonbok Lee\, where we investigate the number of zeros of linear co
mbinations of $L$-functions in the vicinity of the critical line. More pre
cisely\, we let $L_1\, \\dots\, L_J$ be distinct primitive $L$-functions b
elonging to a large class (which conjecturally contains all $L$-functions
arising from automorphic representations on $\\text{GL}(n)$)\, and $b_1\,
\\dots\, b_J$ be real numbers. Our main result is an asymptotic formula fo
r the number of zeros of $F(\\sigma+it)=\\sum_{j\\leq J} b_j L_j(\\sigma+i
t)$ in the region $\\sigma\\geq 1/2+1/G(T)$ and $t\\in [T\, 2T]$\, uniform
ly in the range $\\log \\log T \\leq G(T)\\leq (\\log T)^{\\nu}$\, where $
\\nu\\asymp 1/J$. This establishes a general form of a conjecture of Hejha
l in this range. The strategy of the proof relies on comparing the distrib
ution of $F(\\sigma+it)$ to that of an associated probabilistic random mod
el.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samantha Fairchild (Max Planck Institute for Mathematics\, Bonn)
DTSTART:20211027T150000Z
DTEND:20211027T160000Z
DTSTAMP:20260404T095652Z
UID:hnts/40
DESCRIPTION:by Samantha Fairchild (Max Planck Institute for Mathematics\,
Bonn) as part of Heilbronn number theory seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/hnts/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Garcia (University College London)
DTSTART:20211103T160000Z
DTEND:20211103T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/41
DESCRIPTION:by Luis Garcia (University College London) as part of Heilbron
n number theory seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/hnts/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Assif Zaman (University of Toronto)
DTSTART:20211110T160000Z
DTEND:20211110T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/42
DESCRIPTION:Title: An approximate form of Artin's holomorphy conjecture and nonvanishing
of Artin L-functions\nby Assif Zaman (University of Toronto) as part
of Heilbronn number theory seminar\n\n\nAbstract\nLet $k$ be a number fiel
d and $G$ be a finite group\, and let $\\mathfrak{F}_{k}^{G}$ be a family
of number fields $K$ such that $K/k$ is normal with Galois group isomorphi
c to $G$. Together with Robert Lemke Oliver and Jesse Thorner\, we prove f
or many families that for almost all $K \\in \\mathfrak{F}_k^G$\, all of t
he $L$-functions associated to Artin representations whose kernel does not
contain a fixed normal subgroup are holomorphic and non-vanishing in a wi
de region.\n\nThese results have several arithmetic applications. For exam
ple\, we prove a strong effective prime ideal theorem that holds for almos
t all fields in several natural large degree families\, including the fami
ly of degree $n$ $S_n$-extensions for any $n \\geq 2$ and the family of pr
ime degree $p$ extensions (with any Galois structure) for any prime $p \\g
eq 2$. I will discuss this result\, describe the main ideas of the proof\,
and share some applications to bounds on $\\ell$-torsion subgroups of cla
ss groups\, to the extremal order of class numbers\, and to the subconvexi
ty problem for Dedekind zeta functions.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre de Faveri (California Institute of Technology)
DTSTART:20211124T160000Z
DTEND:20211124T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/43
DESCRIPTION:Title: Simple zeros of GL(2) L-functions\nby Alexandre de Faveri (Califo
rnia Institute of Technology) as part of Heilbronn number theory seminar\n
\nLecture held in 2.04 Fry.\n\nAbstract\nI will discuss my recent work on
simple zeros of automorphic L-functions of degree 2. For a primitive holom
orphic form $f$ of arbitrary weight and level\, I show that its completed
L-function has $\\Omega(T^\\delta)$ simple zeros with imaginary part in $[
-T\, T]$\, for any $\\delta < \\frac{2}{27}$. This provides the first powe
r bound in this problem for $f$ of non-trivial level\, where the previous
best bound was $\\Omega(\\log \\log \\log T)$. The proof uses a method of
Conrey-Ghosh combined with ideas of Booker and Booker-Milinovich-Ng\, in a
ddition to a new ingredient coming from zero-density estimates for twists
of $f$. I will explain the basic method\, the obstructions that arise when
$f$ has non-trivial level\, and how to unconditionally get around such ob
structions to obtain a power bound. This argument gives a curious connecti
on between the quality of zero-density estimates for a certain family and
the number of simple zeros for a single element of that family.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jolanta Marzec (University of Silesia)
DTSTART:20211201T160000Z
DTEND:20211201T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/44
DESCRIPTION:Title: Some evidence towards Resnikoff-Saldana conjecture\nby Jolanta Ma
rzec (University of Silesia) as part of Heilbronn number theory seminar\n\
n\nAbstract\nThe Resnikoff-Saldana conjecture proposes a bound for Fourier
coefficients of Siegel modular forms of any degree\, generalizing the cla
ssical Ramanujan-Petersson conjecture. In the talk we consider the case of
degree 2. We show that the conjecture holds for many (to be specified) Fo
urier coefficients of Siegel modular forms which are not generalized Saito
-Kurokawa lifts\, as long as it holds for the ones that are fundamental. T
o do this we employ relations between Fourier coefficients\, local Bessel
periods and Satake parameters\, ultimately translating a result of Weissau
er on the generalized Ramanujan-Petersson conjecture to a bound for Fourie
r coefficients.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Ostafe (The University of New South Wales)
DTSTART:20211208T110000Z
DTEND:20211208T120000Z
DTSTAMP:20260404T095652Z
UID:hnts/45
DESCRIPTION:Title: Multiplicative and additive relations for values of rational function
s and points on elliptic curves\nby Alina Ostafe (The University of Ne
w South Wales) as part of Heilbronn number theory seminar\n\n\nAbstract\nF
or given rational functions $f_1\,\\ldots\,f_s$ defined over a number fiel
d\, Bombieri\, Masser and Zannier (1999) proved that the algebraic numbers
$\\alpha$ for which the values $f_1(\\alpha)\,\\ldots\,f_s(\\alpha)$ are
multiplicatively dependent are of bounded height (unless this is false for
an obvious reason).\n\nMotivated by this\, we present various extensions
and recent finiteness results on multiplicative relations of values of rat
ional functions\, both in zero and positive characteristics. In particular
\, one of our results shows that\, given non-zero rational functions $f_1\
,\\ldots\,f_m\,g_1\,\\ldots\,g_n \\in \\mathbb{Q}(X)$ and an elliptic curv
e $E$ defined over $\\mathbb{Q}$\, for any sufficiently large prime $p$\,
for all but finitely many $\\alpha\\in\\overline{\\mathbb{F}}_p$\, at most
one of the following two can happen: $f_1(\\alpha)\,\\ldots\,f_m(\\alpha)
$ satisfy a short multiplicative relation or the points $(g_1(\\alpha)\,\\
cdot)\, \\ldots\,(g_n(\\alpha)\,\\cdot)\\in E_p$ satisfy a short linear re
lation on the reduction $E_p$ of $E$ modulo $p$.\n
LOCATION:https://stable.researchseminars.org/talk/hnts/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gonzalo Tornaria (Universidad de la República)
DTSTART:20211117T160000Z
DTEND:20211117T170000Z
DTSTAMP:20260404T095652Z
UID:hnts/46
DESCRIPTION:Title: Quinary forms and paramodular forms\nby Gonzalo Tornaria (Univers
idad de la República) as part of Heilbronn number theory seminar\n\n\nAbs
tract\nThe goal of this talk is to explain how one can use orthogonal modu
lar\nforms to find and prove congruences between paramodular forms.\n\nIn
the first part of the talk I will give a brief review of orthogonal\nmodul
ar forms and how the case of SO(5) can be used to compute\nparamodular for
ms\, based on recent work of Rama-T\, Rösner-Weissauer\,\nDummigan-Pacett
i-Rama-T.\n\nIn the second part of the talk I will explain how we use orth
ogonal\nmodular forms to prove congruences of paramodular forms\, includin
g\nexamples of Fretwell and of Golyshev. A key ingredient for this is\nthe
unexpected appearance of orthogonal eigenforms which /do not/\ncorrespond
to paramodular forms (see Rama-T in ANTS 2020).\n
LOCATION:https://stable.researchseminars.org/talk/hnts/46/
END:VEVENT
END:VCALENDAR