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BEGIN:VEVENT
SUMMARY:Dzmitry Badziahin (University of Sydney)
DTSTART;VALUE=DATE-TIME:20200916T100000Z
DTEND;VALUE=DATE-TIME:20200916T110000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/1
DESCRIPTION:Title: Dio
phantine approximation on the Veronese curve\nby Dzmitry Badziahin (Un
iversity of Sydney) as part of Heilbronn number theory seminar\n\n\nAbstra
ct\nPLEASE NOTE THE UNUSUAL TIME\n\nIn the talk we discuss the set $S_n(\\
lambda)$ of simultaneously $\\lambda$-well approximable points in $\\mathb
b R^n$. That are the points $x$ such that the inequality $|| x - p/q||_\\i
nfty < q^{-\\lambda - \\epsilon}$ has infinitely many solutions in rationa
l points $p/q$. Investigating the intersection of this set with a suitable
manifold comprises one of the most challenging problems in Diophantine ap
proximation. It is known that the structure of this set\, especially for l
arge $\\lambda$\, depends on the manifold. For some manifolds it may be em
pty\, while for others it may have relatively large Hausdorff dimension. W
e will concentrate on the case of the Veronese curve $V_n$. We discuss\, w
hat 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 and Buge
aud which impose new bounds on that dimension.\n
LOCATION:https://researchseminars.org/talk/hnts/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danylo Radchenko (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20200923T150000Z
DTEND;VALUE=DATE-TIME:20200923T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/2
DESCRIPTION:Title: Fou
rier interpolation from zeros of the Riemann zeta function\nby Danylo
Radchenko (ETH Zurich) as part of Heilbronn number theory seminar\n\n\nAbs
tract\nI will talk about a recent result that shows that any sufficiently
nice even analytic function can be recovered from its values at the nontri
vial zeros of $\\zeta(\\frac{1}{2}+is)$ and the values of its Fourier tran
sform at logarithms of integers. The proof is based on an explicit interpo
lation formula\, whose construction relies on a strengthening of Knopp's a
bundance principle for Dirichlet series with functional equations. The tal
k is based on a joint work with Andriy Bondarenko and Kristian Seip.\n
LOCATION:https://researchseminars.org/talk/hnts/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Dimitrov (University of Toronto)
DTSTART;VALUE=DATE-TIME:20200930T150000Z
DTEND;VALUE=DATE-TIME:20200930T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/3
DESCRIPTION:Title: No
shadowing bounds on Galois orbits in the complex plane\nby Vesselin Di
mitrov (University of Toronto) as part of Heilbronn number theory seminar\
n\n\nAbstract\nFor varying pairs of non-isogenous abelian varieties of a g
iven dimension over a given finite field\, what is the least possible arcl
engths sum under a matching of their Frobenius roots? For varying pairs of
Salem numbers in $[1\,2]$\, what is their least possible distance in term
s of the sum of their degrees?\n\nWe address\, and partly answer\, these k
inds of questions in the seminar\, with a particular focus on the two repr
esentatives at hand. The method\, which is based on potential theory in th
e complex plane\, also establishes the Lehmer conjecture for the integer m
onic polynomials $P(X)$ that have\nall their roots limited to the complex
disk $|z| < 10^{1/\\deg(P)}$: the extremal case where the Galois orbit of
algebraic integers is maximally equalized around the unit circle. We also
raise a few apparently new questions that our results motivate.\n
LOCATION:https://researchseminars.org/talk/hnts/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriele Nebe (RWTH Aachen University)
DTSTART;VALUE=DATE-TIME:20201007T150000Z
DTEND;VALUE=DATE-TIME:20201007T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/4
DESCRIPTION:Title: Aut
omorphisms of extremal modular lattices\nby Gabriele Nebe (RWTH Aachen
University) as part of Heilbronn number theory seminar\n\n\nAbstract\nThe
study of automorphisms of extremal lattices was motivated by similar rese
arch for binary self-dual codes. It started by considering extremal even u
nimodular lattices in dimensions which are multiples of 24. We know six su
ch lattices\, the Leech lattice in dimension 24\, four lattices of dimensi
on 48 and\, since 2010\, also one extremal lattice in dimension 72. One of
the 48-dimensional lattices was found by a computer search for lattices w
ith a certain automorphism of order 5.\n\nIn his thesis Michael Jürgens e
xtended the theory to automorphisms of modular lattices\, aiming in the co
nstruction 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://researchseminars.org/talk/hnts/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lior Bary-Soroker (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20201014T150000Z
DTEND;VALUE=DATE-TIME:20201014T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/9
DESCRIPTION:Title: Ran
dom polynomials\, probabilistic Galois theory\, and finite field arithmeti
c\nby Lior Bary-Soroker (Tel Aviv University) as part of Heilbronn num
ber theory seminar\n\n\nAbstract\nIn the talk we will discuss recent advan
ces on the following two questions:\nLet $A(X) = \\sum ±X^i$ be a random
polynomial of degree n with coefficients taking the values $-1\, 1$ indepe
ndently 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 the typic
al Galois group of $A$?\n\nOne believes that the answers are YES and THE F
ULL SYMMETRIC GROUP\, respectively.\nThese questions were studied extensiv
ely in recent years\, and we will survey the tools developed to attack the
se problems and partial results.\n
LOCATION:https://researchseminars.org/talk/hnts/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sug Woo Shin (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20201021T150000Z
DTEND;VALUE=DATE-TIME:20201021T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/10
DESCRIPTION:Title: On
GSpin(2n)-valued automorphic Galois representations\nby Sug Woo Shin
(University of California\, Berkeley) as part of Heilbronn number theory s
eminar\n\n\nAbstract\nI will present my joint work with Arno Kret\, where
we construct a GSpin($2n$)-valued $\\ell$-adic Galois representation attac
hed to a cuspidal cohomological automorphic representation $\\pi$ of a sui
table quasi-split form of GSO($2n$) over a totally real field\, under the
hypothesis that pi has a Steinberg component at a finite place. This 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://researchseminars.org/talk/hnts/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Young (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20201028T160000Z
DTEND;VALUE=DATE-TIME:20201028T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/11
DESCRIPTION:Title: Th
e Weyl bound for Dirichlet $L$-functions\nby Matthew Young (Texas A&M
University) as part of Heilbronn number theory seminar\n\n\nAbstract\nThe
problem of bounding $L$-functions has a long history. For the Riemann zeta
function\, the method of Weyl gives a subconvexity bound with exponent $1
/6$\, which is now called the Weyl bound. Many questions on the zeta funct
ion in the t-aspect have a natural analog for Dirichlet $L$-functions in t
he q-aspect\, but the latter is in general much harder. Indeed\, the first
subconvexity result for Dirichlet $L$-functions\, due to Burgess in the 1
960's\, has a weaker exponent $3/16$. In this talk I will discuss work wit
h Ian Petrow that proves the Weyl bound for all Dirichlet $L$-functions.\n
LOCATION:https://researchseminars.org/talk/hnts/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Rudnev (University of Bristol)
DTSTART;VALUE=DATE-TIME:20201104T160000Z
DTEND;VALUE=DATE-TIME:20201104T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/12
DESCRIPTION:Title: On
convexity and sumsets\nby Misha Rudnev (University of Bristol) as par
t of Heilbronn number theory seminar\n\n\nAbstract\nA finite set $A$ of $n
$ reals is convex if the sequence of neighbouring differences is strictly
monotone. Erdös suggested that that the set of squares of the first $n$ i
ntegers may constitute the extremal case\, namely that for any convex $A$\
, $|A+A| > n^{2-o(1)}$. The question is still open\, we'll review some par
tial progress.\n\nWhat about $k- $fold sums $A+A+A+...$? In the case of sq
uares\, they stop growing after $k=2$\, and for $k$th powers they grow up
to $n^k$. In a joint work with Brandon Hanson and Olly Roche-Newton we sho
w\, using elementary methods\, that if $A=f([n])$\, where $f$ is a real fu
nction with $k-1$ strictly monotone derivatives\, taking sufficiently many
sums does lead to growth up to $n^{k-o(1)}$. We generalise this by replac
ing the interval $[n]$ versus $f([n])$ by any set with small additive doub
ling versus its image by $f$\, which enables us to apply this to sum-produ
ct type questions.\n
LOCATION:https://researchseminars.org/talk/hnts/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Lemos (University College London)
DTSTART;VALUE=DATE-TIME:20201111T160000Z
DTEND;VALUE=DATE-TIME:20201111T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/13
DESCRIPTION:Title: Re
sidual Galois representations of elliptic curves with image in the normali
ser of a non-split Cartan\nby Pedro Lemos (University College London)
as part of Heilbronn number theory seminar\n\n\nAbstract\nDue to the work
of several mathematicians\, it is known that if p is a prime >37\, then th
e image of the residual Galois representation $\\bar{\\rho}_{E\,p}: G_{\\m
athbb{Q}}\\rightarrow {\\rm GL}_2(\\mathbb{F}_p)$ attached to an elliptic
curve $E/\\mathbb{Q}$ without complex multiplication is either ${\\rm GL}_
2(\\mathbb{F}_p)$\, or is contained in the normaliser of a non-split Carta
n subgroup of ${\\rm GL}_2(\\mathbb{F}_p)$. I will report on a recent join
t work with Samuel Le Fourn\, where we improve this result (at least for l
arge 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 n
on-split Cartan subgroup of ${\\rm GL}_2(\\mathbb{F}_p)$.\n
LOCATION:https://researchseminars.org/talk/hnts/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heekyoung Hahn (Duke University)
DTSTART;VALUE=DATE-TIME:20201118T110000Z
DTEND;VALUE=DATE-TIME:20201118T120000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/14
DESCRIPTION:Title: Po
les of triple tensor product L-functions involving monomial representation
s\nby Heekyoung Hahn (Duke University) as part of Heilbronn number the
ory seminar\n\n\nAbstract\n**PLEASE NOTE THE UNUSUAL TIME**\n\nLittle is k
nown about the order of poles of triple tensor product $L$-functions in hi
gher rank. In this talk we will investigate the order of the pole of the t
riple 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 monomia
l 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 proposal.\n
LOCATION:https://researchseminars.org/talk/hnts/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ghaith Hiary (Ohio State University)
DTSTART;VALUE=DATE-TIME:20201125T160000Z
DTEND;VALUE=DATE-TIME:20201125T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/15
DESCRIPTION:Title: An
Omega-result for $S(t)$\nby Ghaith Hiary (Ohio State University) as p
art of Heilbronn number theory seminar\n\n\nAbstract\nI discuss some bound
s in the theory of the Riemann zeta function\, in particular Omega results
for $S(t)$\, the fluctuating part of the zeros counting function for the
Riemann zeta function. I outline a new unconditional Omega-result for $S(t
)$.\n
LOCATION:https://researchseminars.org/talk/hnts/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Folsom (Amherst College)
DTSTART;VALUE=DATE-TIME:20201202T160000Z
DTEND;VALUE=DATE-TIME:20201202T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/16
DESCRIPTION:Title: Ei
senstein series\, cotangent-zeta sums\, knots\, and quantum modular forms<
/a>\nby Amanda Folsom (Amherst College) as part of Heilbronn number theory
seminar\n\n\nAbstract\nQuantum modular forms\, defined in the rational nu
mbers\, transform like modular forms do on the upper half-plane\, up to su
itably analytic error functions. In this talk we give frameworks for two d
ifferent examples of quantum modular forms originally due to Zagier: the D
edekind sum\, and a certain q-hypergeometric sum due to Kontsevich. For th
e first\, we extend work of Bettin and Conrey and define twisted Eisenstei
n series\, study their period functions\, and establish quantum modularity
of certain cotangent-zeta sums. For the second\, we discuss results due t
o Hikami\, Lovejoy\, the author\, and others\, on quantum modular and quan
tum Jacobi forms related to colored Jones polynomials for certain families
of knots.\n
LOCATION:https://researchseminars.org/talk/hnts/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arul Shankar (University of Toronto)
DTSTART;VALUE=DATE-TIME:20201209T160000Z
DTEND;VALUE=DATE-TIME:20201209T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/17
DESCRIPTION:Title: Th
e number of $D_4$-extensions of $\\mathbb{Q}$\nby Arul Shankar (Univer
sity of Toronto) as part of Heilbronn number theory seminar\n\n\nAbstract\
nWe will begin with a summary of how Malle's conjecture and Bhargava's heu
ristics can be used to develop the "Malle--Bhargava heuristics"\, predicti
ng the asymptotics in families of number fields\, ordered by a general cla
ss of invariants.\n\nWe will then specialize in the case of $D_4$-number f
ields. Even in this (fairly simple) case\, where the fields can be paramet
rized quite explicitly\, the question of determining asymptotics can get q
uite complicated. We will discuss joint work with Altug\, Varma\, and Wils
on\, in which we recover asymptotics when quartic $D_4$ fields are ordered
by conductor. And we will finally discuss joint work with Varma\, in whic
h we recover Malle's conjecture for octic $D_4$-fields.\n
LOCATION:https://researchseminars.org/talk/hnts/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chantal David (Concordia University)
DTSTART;VALUE=DATE-TIME:20201216T160000Z
DTEND;VALUE=DATE-TIME:20201216T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/18
DESCRIPTION:Title: Mo
ments and non-vanishing of cubic Dirichlet $L$-functions at $s =\\frac{1}{
2}$\nby Chantal David (Concordia University) as part of Heilbronn numb
er theory seminar\n\n\nAbstract\nA famous conjecture of Chowla predicts th
at $L(\\frac{1}{2}\,\\chi) \\neq 0$ for all Dirichlet $L$-functions attach
ed to primitive characters $\\chi$. It was conjectured first in the case w
here $\\chi$ is a quadratic character\, which is the most studied case. Fo
r quadratic Dirichlet $L$-functions\, Soundararajan proved that at least 8
7.5% 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 proportion
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 using th
e recent breakthrough work on sharp upper bounds for moments of\nSoundarar
ajan\, Harper and Lester-Radziwill. Our results would transfer over number
fields\,\nbut we would need to assume GRH in this case.\n
LOCATION:https://researchseminars.org/talk/hnts/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Gulotta (Max Planck Institute Bonn)
DTSTART;VALUE=DATE-TIME:20210127T160000Z
DTEND;VALUE=DATE-TIME:20210127T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/19
DESCRIPTION:Title: Va
nishing theorems for Shimura varieties at unipotent level and Galois repre
sentations\nby Daniel Gulotta (Max Planck Institute Bonn) as part of H
eilbronn number theory seminar\n\n\nAbstract\nThe Langlands correspondence
relates automorphic forms and Galois representations --- for example\, th
e modular form $\\eta(z)^2 \\eta(11z)^2$ and the Tate module of the ellipt
ic curve $y^2 + y = x^3 - x^2 - 10x - 20$ are related in the sense that th
ey have the same L-function. The p-adic Langlands program aims to interpo
late the Langlands correspondence in p-adic families. In this setting\, t
he role of automorphic forms is played by the completed cohomology groups
defined by Emerton.\n\nCalegari and Emerton have conjectured that the comp
leted cohomology vanishes above a certain degree\, often denoted $q_0$. I
n the case of Shimura varieties of Hodge type\, Scholze has proved the con
jecture for compactly supported completed cohomology. We give a strengthe
ning of Scholze's result under the additional assumption that the group be
comes split over $\\mathbb{Q}_p$. More specifically\, we show that the co
mpactly supported cohomology vanishes not just at full infinite level 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 of Schol
ze's construction of Galois representations.\n\nThis talk is based on join
t work with Ana Caraiani and Christian Johansson and on joint work with An
a Caraiani\, Chi-Yun Hsu\, Christian Johansson\, Lucia Mocz\, Emanuel Rein
ecke\, and Sheng-Chi Shih.\n
LOCATION:https://researchseminars.org/talk/hnts/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Par Kurlberg (KTH Stockholm)
DTSTART;VALUE=DATE-TIME:20210203T160000Z
DTEND;VALUE=DATE-TIME:20210203T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/20
DESCRIPTION:Title: Di
stribution of lattice points on hyperbolic circles\nby Par Kurlberg (K
TH Stockholm) as part of Heilbronn number theory seminar\n\n\nAbstract\nWe
study the distribution of lattice points lying on expanding circles in th
e hyperbolic plane. The angles of lattice points arising from the orbit of
the modular group $\\operatorname{PSL}(2\,\\mathbb Z)$\, and lying on hyp
erbolic circles centered at $i$\, are shown to be equidistributed for gene
ric radii (among the ones that contain points). We also show that angles f
ail to equidistribute on a thin set of exceptional radii\, even in the pre
sence of growing multiplicity. Surprisingly\, the distribution of angles o
n hyperbolic circles turns out to be related to the angular distribution o
f euclidean lattice points lying on circles in the plane\, along a thin su
bsequence of radii. This is joint work with\nD. Chatzakos\, S. Lester and
I. Wigman.\n
LOCATION:https://researchseminars.org/talk/hnts/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayla Gafni (University of Mississippi)
DTSTART;VALUE=DATE-TIME:20210122T160000Z
DTEND;VALUE=DATE-TIME:20210122T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/21
DESCRIPTION:Title: As
ymptotics of restricted partition functions\nby Ayla Gafni (University
of Mississippi) as part of Heilbronn number theory seminar\n\n\nAbstract\
n**NOTE THE UNUSUAL TIME AND DAY**\n\nGiven a set $\\mathcal A \\subset \\
mathbb N$\, the restricted partition function $p_{\\mathcal{A}}(n)$ counts
the number of integer partitions of $n$ with all parts in $\\mathcal A$.
In this talk\, we will explore the features of the restricted partitions f
unction $p_{\\mathbb P_k}(n)$ where $\\mathcal P_k$ is the set of $k$-th p
owers of primes. Powers of primes are both sparse and irregular\, which ma
kes $p_{\\mathbb P_k}(n)$ quite an elusive function to understand. We will
discuss some of the challenges involved in studying restricted partition
functions and what is known in the case of primes\, $k$-th powers\, and $k
$-th powers of primes.\n
LOCATION:https://researchseminars.org/talk/hnts/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Obus (City University New York)
DTSTART;VALUE=DATE-TIME:20210224T160000Z
DTEND;VALUE=DATE-TIME:20210224T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/22
DESCRIPTION:Title: Fu
n with Mac Lane valuations\nby Andrew Obus (City University New York)
as part of Heilbronn number theory seminar\n\n\nAbstract\nMac Lane's techn
ique of "inductive valuations" is over 80 years old\, but has only recentl
y been used to attack problems about arithmetic surfaces. We will give an
explicit\, hands-on introduction to the theory\, requiring little backgro
und beyond the definition of a non-archimedean valuation. \n\nWe will the
n outline how this theory is useful for resolving "weak wild" quotient sin
gularities of arithmetic surfaces (joint with Stefan Wewers)\, proving con
ductor-discriminant inequalities for hyperelliptic and superelliptic curve
s (joint with Padmavathi Srinivasan)\, and understanding regular models of
potentially Mumford curves (joint with Daniele Turchetti).\n
LOCATION:https://researchseminars.org/talk/hnts/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahesh Kakde (India Institute of Science)
DTSTART;VALUE=DATE-TIME:20210303T160000Z
DTEND;VALUE=DATE-TIME:20210303T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/23
DESCRIPTION:Title: Br
umer-Stark units\nby Mahesh Kakde (India Institute of Science) as part
of Heilbronn number theory seminar\n\n\nAbstract\nIn this talk I will rep
ort on my recent work with Samit Dasgupta that prove existence of the Brum
er-Stark units (The Brumer-Stark conjecture) and a p-adic analytic formula
for them (a conjecture of Dasgupta). The latter conjecture is tackled by
proving an integral version of the Gross-Stark conjecture.\n
LOCATION:https://researchseminars.org/talk/hnts/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:YoungJu Choie (POSTECH)
DTSTART;VALUE=DATE-TIME:20210310T110000Z
DTEND;VALUE=DATE-TIME:20210310T120000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/24
DESCRIPTION:Title: A
generating functions of periods of modular forms\nby YoungJu Choie (PO
STECH) as part of Heilbronn number theory seminar\n\n\nAbstract\n**NOTE TH
E UNUSUAL TIME**\n\nA closed formula for the sum of all Hecke eigenforms o
n $\\Gamma_0(N)$\, multiplied by their odd period polynomials in two varia
bles\, as a single product of Jacobi theta series for any squarefree level
$N$ is known. When $N=1$ this was result given by Zagier in 1991.\n\nWe d
iscuss more general results regarding on this direction.\n
LOCATION:https://researchseminars.org/talk/hnts/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Voight (Dartmouth)
DTSTART;VALUE=DATE-TIME:20210317T160000Z
DTEND;VALUE=DATE-TIME:20210317T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/25
DESCRIPTION:Title: Co
unting elliptic curves with torsion\, and a probabilistic local-global pri
nciple\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 $p$\, the tors
ion subgroup $E(\\mathbb{Q})_{\\operatorname{tor}}$ maps injectively into
$E(\\mathbb{F}_p)$\; but the converse statement holds only up to isogeny\,
by a theorem of Katz. In this\ntalk\, we consider a probabilistic refine
ment for the elliptic curves themselves: if $m | \n \\#E(\\mathbb{F}_p)$ f
or 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 with cert
ain prescribed Galois image.\n\nThis is joint work with John Cullinan and
Meagan Kenney.\n
LOCATION:https://researchseminars.org/talk/hnts/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina Roehrig (University of Cologne)
DTSTART;VALUE=DATE-TIME:20210210T160000Z
DTEND;VALUE=DATE-TIME:20210210T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/26
DESCRIPTION:Title: Si
egel theta series for indefinite quadratic forms\nby Christina Roehrig
(University of Cologne) as part of Heilbronn number theory seminar\n\n\nA
bstract\nDue to a result by Vignéras from 1977\, there is a quite simple
way to determine whether a certain theta series admits modular transformat
ion properties. To be more specific\, she showed that solving a differenti
al equation of second order serves as a criterion for modularity. We gener
alize this result for Siegel theta series of arbitrary genus $n$. In order
to do so\, we construct Siegel theta series for indefinite quadratic form
s by considering functions that solve an $n\\times n$-system of partial di
fferential equations. These functions do not only give examples of Siegel
theta series\, but build a basis of the family of Schwartz functions that
generate series that transform like modular forms.\n
LOCATION:https://researchseminars.org/talk/hnts/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Morgan (Mathematisches Forschungsinstitut Oberwolfach)
DTSTART;VALUE=DATE-TIME:20210217T160000Z
DTEND;VALUE=DATE-TIME:20210217T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/27
DESCRIPTION:Title: 4-
ranks of class groups of biquadratic fields\nby Adam Morgan (Mathemati
sches Forschungsinstitut Oberwolfach) as part of Heilbronn number theory s
eminar\n\n\nAbstract\nLet K be a quadratic number field\, and consider the
family of biquadratic fields $K_n= K(\\sqrt{n})$ for $n$ a squarefree int
eger. I will discuss joint work with Peter Koymans and Harry Smit in which
we study\, as $n$ varies\, the 4-rank of the class group of $K_n$\, showi
ng in particular that for 100 % of squarefree n\, the 4-rank is given by a
n explicit formula involving the number of prime divisors of n that are in
ert in $K$. If time permits I will discuss an elliptic curve analogue of t
his work\, which is joint with Ross Paterson.\n
LOCATION:https://researchseminars.org/talk/hnts/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maki Nakasuji (Sophia University\, Japan)
DTSTART;VALUE=DATE-TIME:20210324T110000Z
DTEND;VALUE=DATE-TIME:20210324T120000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/28
DESCRIPTION:Title: Sc
hur multiple zeta functions and their properties\nby Maki Nakasuji (So
phia University\, Japan) as part of Heilbronn number theory seminar\n\n\nA
bstract\n**NOTE THE UNUSUAL TIME**\n\nMultiple zeta functions have been st
udied at least since Euler\, who found many of their algebraic properties.
In particular\, they are greatly developed since the 1980s in several dif
ferent contexts such as modular forms\, mixed Tate motives\, quantum group
s\, moduli spaces of vector bundles\, scattering amplitudes\, etc.\n\nIn t
his talk\, we introduce a generalization of the Euler-Zagier type multiple
zeta and zeta-star functions\, that we call Schur multiple zeta functions
. These functions are defined as sums over combinatorial objects called se
mi-standard Young tableaux. We will show the determinant formulas for Schu
r multiple zeta functions\, which lead to quite non-trivial algebraic rela
tions among multiple zeta and zeta-star functions. This is based on joint
work with O. Phuksuwan and Y. Yamasaki. And we will also show relations am
ong Schur multiple zeta functions and zeta-functions of root systems attac
hed to semisimple Lie algebras\, which is a joint work with K. Matsumoto.
Further\, if time permits we will introduce Schur type poly-Bernoulli numb
ers and investigate their properties.\n
LOCATION:https://researchseminars.org/talk/hnts/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Capuano (Politecnico di Torino)
DTSTART;VALUE=DATE-TIME:20210421T150000Z
DTEND;VALUE=DATE-TIME:20210421T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/29
DESCRIPTION:Title: GC
D results for certain divisibility sequences of polynomials and a conjectu
re of Silverman\nby Laura Capuano (Politecnico di Torino) as part of H
eilbronn number theory seminar\n\n\nAbstract\nA divisibility sequence is a
sequence of integers $d_n$ such that\, if $m$ divides $n$\, then $d_m$ di
vides $d_n$. Bugeaud\, Corvaja\, Zannier showed that pairs of divisibility
sequences of the form $a^n-1$ have only limited common factors. From a ge
ometric point of view\, this divisibility sequence corresponds to a subgro
up of the multiplicative group\, and Silverman conjectured that a similar
behaviour should appear in (a large class of) other algebraic groups.\n\nE
xtending previous works of Silverman and of Ghioca-Hsia-Tucker on elliptic
curves over function fields\, we will show how to prove the analogue of S
ilverman’s conjecture over function fields in the case of split semiabel
ian varieties and some generalizations. The proof relies on some results o
f unlikely intersections. This is a joint work with F. Barroero and A. Tur
chet.\n
LOCATION:https://researchseminars.org/talk/hnts/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Burrin (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20210505T150000Z
DTEND;VALUE=DATE-TIME:20210505T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/30
DESCRIPTION:Title: A
sparse equidistribution problem for expanding horocycles on the modular su
rface\nby Claire Burrin (ETH Zurich) as part of Heilbronn number theor
y seminar\n\n\nAbstract\nThe orbits of the horocycle flow on hyperbolic su
rfaces (or orbifolds) are classified: each orbit is either dense or a clos
ed horocycle around a cusp. Expanding closed horocycles are themselves asy
mptotically dense\, and in fact become equidistributed on the surface. The
precise rate of equidistribution is of interest\; on the modular surface\
, Zagier observed that a particular rate is equivalent to the Riemann hypo
thesis being true. In this talk\, I will discuss the asymptotic behavior o
f evenly spaced points along an expanding closed horocycle on the modular
surface. In this problem\, the number of points depends on the expansion r
ate of the horocycle\, and the difficulty is that these points are no more
invariant under the horocycle flow. This is based on joint work with Uri
Shapira and Shucheng Yu.\n
LOCATION:https://researchseminars.org/talk/hnts/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seonhee Lim (Seoul National University)
DTSTART;VALUE=DATE-TIME:20210512T100000Z
DTEND;VALUE=DATE-TIME:20210512T110000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/31
DESCRIPTION:Title: Ef
fective Hausdorff dimension of bad sets\nby Seonhee Lim (Seoul Nationa
l University) as part of Heilbronn number theory seminar\n\n\nAbstract\n**
NOTE THE UNUSUAL TIME**\n\nIn this talk\, we consider the inhomogeneous Di
ophantine approximation: the distribution of $qa$ modulo integers near a t
arget real $b$ (for integer $q$ and a real $a$)\, or more generally $Aq$ m
odulo integral vectors near a target vector $b$ (where $q$ is an integer v
ector\, and $A$ is a real matrix). We prove that for all $b$\, the Hausdor
ff dimension of the set of matrices that are epsilon badly approximable fo
r the target $b$ is not full\, with an effective upper bound. We also give
an effective bound on the dimension of the set of targets badly approxima
ted by $Aq$ in terms of epsilon\, if the matrix $A$ is not singular on ave
rage. The main part of the talk is joint work with Taehyeong Kim and Wooye
on Kim.\n
LOCATION:https://researchseminars.org/talk/hnts/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naser Sardari (Penn State)
DTSTART;VALUE=DATE-TIME:20210519T150000Z
DTEND;VALUE=DATE-TIME:20210519T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/32
DESCRIPTION:Title: Hi
gher Fourier interpolation on the plane\nby Naser Sardari (Penn State)
as part of Heilbronn number theory seminar\n\n\nAbstract\nRadchenko and V
iazovska recently proved an elegant formula that expresses the value of th
e Schwartz function $f$ at any given point in terms of the values of $f$ a
nd its Fourier transform on the set $\\{ \\sqrt{|n|}:n\\in \\Z\\}.$ We dev
elop new interpolation formulas using the values of the higher derivatives
on new discrete sets. \n\nIn particular\, we prove a conjecture of Cohn\
, Kumar\, Miller\, Radchenko and Viazovska that was motivated by the u
niversal optimality of the hexagonal lattice.\n
LOCATION:https://researchseminars.org/talk/hnts/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Zywina (Cornell)
DTSTART;VALUE=DATE-TIME:20210526T150000Z
DTEND;VALUE=DATE-TIME:20210526T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/33
DESCRIPTION:by David Zywina (Cornell) as part of Heilbronn number theory s
eminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/hnts/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brad Rodgers (Queens University)
DTSTART;VALUE=DATE-TIME:20210602T150000Z
DTEND;VALUE=DATE-TIME:20210602T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/34
DESCRIPTION:by Brad Rodgers (Queens University) as part of Heilbronn numbe
r theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/hnts/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fang-Ting Tu (Louisiana State University)
DTSTART;VALUE=DATE-TIME:20210428T150000Z
DTEND;VALUE=DATE-TIME:20210428T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T190956Z
UID:hnts/35
DESCRIPTION:Title: A
Whipple formula revisited\nby Fang-Ting Tu (Louisiana State University
) as part of Heilbronn number theory seminar\n\n\nAbstract\nThis talk is b
ased on recent joint work with Wen-Ching Winnie Li and Ling Long. We consi
der the hypergeometric data corresponding to a formula due to Whipple whic
h relates certain hypergeometric values $_7F_6(1)$ and $_4F_3(1)$. \n\nWhe
n the hypergeometric data are primitive and defined over the rationals\, f
rom identities of hypergeometric character sums\, we explain a special str
ucture of the corresponding Galois representations behind Whipple's formul
a leading to a decomposition that can be described by the Fourier coeffici
ents of Hecke eigenforms. In this talk\, I will use an example to demonstr
ate our approach and relate the hypergeometric values to certain periods o
f modular forms.\n
LOCATION:https://researchseminars.org/talk/hnts/35/
END:VEVENT
END:VCALENDAR