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BEGIN:VEVENT
SUMMARY:Andrew Granville (Université de Montréal)
DTSTART;VALUE=DATE-TIME:20200430T150000Z
DTEND;VALUE=DATE-TIME:20200430T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/1
DESCRIPTION:Title: Frobenius's postage stamp problem\, and beyond...\nby A
ndrew Granville (Université de Montréal) as part of Number Theory Web Se
minar\n\n\nAbstract\nWe study this famous old problem from the modern pers
pective of additive combinatorics\, and then look at generalizations.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Sutherland (MIT)
DTSTART;VALUE=DATE-TIME:20200507T150000Z
DTEND;VALUE=DATE-TIME:20200507T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/2
DESCRIPTION:Title: Sums of three cubes\nby Andrew Sutherland (MIT) as part
of Number Theory Web Seminar\n\n\nAbstract\nIn 1953 Mordell asked whether
one can represent 3 as a sum of three cubes in any way other than $1^3+1^
3+1^3$ and $4^3+4^3 -5^3$. Mordell's question spurred many computational i
nvestigations over the years\, and while none found a new solution for 3\,
they eventually determined which of the first 100 positive integers $k$ c
an be represented as a sum of three cubes in all but one case: $k=42$.\n\n
In this talk I will present joint work with Andrew Booker that used Charit
y Engine's crowd-sourced compute grid to affirmatively answer Mordell's qu
estion\, as well as settling the case $k=42$. I will also discuss a conjec
ture of Heath-Brown that predicts the existence of infinitely many more so
lutions and explains why they are so difficult to find.\n\nMSC:11Y50\, MSC
:11D25\, ACM:F.2.2\, ACM:G.2.3\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Blomer (Universität Bonn)
DTSTART;VALUE=DATE-TIME:20200514T150000Z
DTEND;VALUE=DATE-TIME:20200514T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/3
DESCRIPTION:Title: Joint equidistribution and fractional moments of L-func
tions\nby Valentin Blomer (Universität Bonn) as part of Number Theory Web
Seminar\n\n\nAbstract\nIntegral points on spheres of large radius $D^{1/2
}$ equidstribute (subject to appropriate congruence conditions)\, and so d
o Heegner points of large discriminant $D$ on the modular curve. Both sets
have roughly the same cardinality\, and there is a natural way to associa
te with each point on the sphere a Heegner point. Do these pairs equidstri
bute in the product space of the sphere and the modular curve as $D$ tends
to infinity?\n\nA seemingly very different\, but structurally similar joi
nt equidistribution problem can be asked for the supersingular reduction a
t two different primes of elliptic curves with CM by an order of large dis
criminant $D$.\n\nBoth equidistribution problems have been studied by ergo
dic methods under certain conditions on $D$. I will explain how to use num
ber theory and families of high degree $L$-functions to obtain an effectiv
e equidistribution statement with a rate of convergence\, assuming GRH. Th
is is joint work in progress with F. Brumley.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Waldschmidt (Sorbonne University)
DTSTART;VALUE=DATE-TIME:20200512T080000Z
DTEND;VALUE=DATE-TIME:20200512T090000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/4
DESCRIPTION:Title: Representation of integers by cyclotomic binary forms\n
by Michel Waldschmidt (Sorbonne University) as part of Number Theory Web S
eminar\n\n\nAbstract\nThe representation of positive integers as a sum of
two squares is a classical problem studied by Landau and Ramanujan. A simi
lar result has been obtained by Bernays for positive definite binary form.
In joint works with Claude Levesque and Etienne Fouvry\, we consider the
representation of integers by the binary forms which are deduced from the
cyclotomic polynomials. One main tool is a recent result of Stewart and Xi
ao which generalizes the theorem of Bernays to binary forms of higher degr
ee.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Voloch (University of Canterbury)
DTSTART;VALUE=DATE-TIME:20200609T000000Z
DTEND;VALUE=DATE-TIME:20200609T010000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/6
DESCRIPTION:Title: Value sets of sparse polynomials\nby Felipe Voloch (Uni
versity of Canterbury) as part of Number Theory Web Seminar\n\n\nAbstract\
nWe obtain a lower bound on the size of the value set $f(F_p)$ of a sparse
polynomial $f(x)$ in $F_p[x]$ over a finite field of $p$ elements when $p
$ is prime. This bound is uniform with respect to the degree and depends o
n the number of terms of $f$.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Browning (IST Austria)
DTSTART;VALUE=DATE-TIME:20200604T150000Z
DTEND;VALUE=DATE-TIME:20200604T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/7
DESCRIPTION:Title: Random Diophantine equations\nby Timothy Browning (IST
Austria) as part of Number Theory Web Seminar\n\n\nAbstract\nI’ll survey
some of the key challenges around the solubility of polynomial Diophantin
e equations over the integers.\n\nWhile studying individual equations is o
ften extraordinarily difficult\, the situation is more accessible if we me
rely ask what happens on average and if we restrict to the so-called Fano
range\, where the number of variables exceeds the degree of the polynomial
. Indeed\, about 20 years ago\, it was conjectured by Poonen and Voloch t
hat random Fano hypersurfaces satisfy the Hasse principle\, which is the s
implest necessary condition for solubility. After discussing related resu
lts I’ll report on joint work with Pierre Le Boudec and Will Sawin where
we establish this conjecture for all Fano hypersurfaces\, except cubic su
rfaces.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Sarnak (IAS and Princeton University)
DTSTART;VALUE=DATE-TIME:20200625T150000Z
DTEND;VALUE=DATE-TIME:20200625T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/8
DESCRIPTION:Title: Integer points on affine cubic surfaces\nby Peter Sarna
k (IAS and Princeton University) as part of Number Theory Web Seminar\n\n\
nAbstract\nThe level sets of a cubic polynomial in four or more variables
tends to have many integer solutions\, while ones in two variables a limit
ed number of solutions. Very little is known in case of three variables. F
or cubics which are character varieties (thus carrying a nonlinear group o
f morphisms) a Diophantine analysis has been developed and we will describ
e it. Passing from solutions in integers to integers in say a real quadrat
ic field there is a fundamental change which is closely connected to chall
enging questions about one-commutators in $SL_2$ over such rings.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin Lauter (Microsoft Research Redmond Labs)
DTSTART;VALUE=DATE-TIME:20200519T000000Z
DTEND;VALUE=DATE-TIME:20200519T010000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/9
DESCRIPTION:Title: How to keep your secrets in a post-quantum world\nby Kr
istin Lauter (Microsoft Research Redmond Labs) as part of Number Theory We
b Seminar\n\n\nAbstract\nAs we move towards a world which includes quantum
computers which exist at scale\, we are forced to consider the question o
f what hard problems in mathematics our next generation of cryptographic s
ystems will be based on. Supersingular Isogeny Graphs were proposed for u
se in cryptography in 2006 by Charles\, Goren\, and Lauter. Supersingular
Isogeny Graphs are examples of Ramanujan graphs\, which are optimal expan
der graphs. These graphs have the property that relatively short walks o
n the graph approximate the uniform distribution\, and for this reason\, w
alks on expander graphs are often used as a good source of randomness in c
omputer science. But the reason these graphs are important for cryptograp
hy is that finding paths in these graphs\, i.e. routing\, is hard: there a
re no known subexponential algorithms to solve this problem\, either class
ically or on a quantum computer. For this reason\, cryptosystems based on
the hardness of problems on Supersingular Isogeny Graphs are currently un
der consideration for standardization in the NIST Post-Quantum Cryptograph
y (PQC) Competition. This talk will introduce these graphs\, the cryptogr
aphic applications\, and the various algorithmic approaches which have bee
n tried to attack these systems.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zeev Rudnick (Tel-Aviv University)
DTSTART;VALUE=DATE-TIME:20200521T150000Z
DTEND;VALUE=DATE-TIME:20200521T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/10
DESCRIPTION:Title: Prime lattice points in ovals\nby Zeev Rudnick (Tel-Avi
v University) as part of Number Theory Web Seminar\n\n\nAbstract\nThe stud
y of the number of lattice points in dilated regions has a long history\,
with several outstanding open problems. In this lecture\, I will describe
a new variant of the problem\, in which we study the distribution of latti
ce points with prime coordinates. We count lattice points in which both co
ordinates are prime\, suitably weighted\, which lie in the dilate of a con
vex planar domain having smooth boundary\, with nowhere vanishing curvatur
e. We obtain an asymptotic formula\, with the main term being the area of
the dilated domain\, and our goal is to study the remainder term. Assuming
the Riemann Hypothesis\, we give a sharp upper bound\, and further assumi
ng that the positive imaginary parts of the zeros of the Riemann zeta func
tions are linearly independent over the rationals allows us to give a form
ula for the value distribution function of the properly normalized remaind
er term. (joint work with Bingrong Huang).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Trevor Wooley (Purdue University)
DTSTART;VALUE=DATE-TIME:20200528T150000Z
DTEND;VALUE=DATE-TIME:20200528T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/11
DESCRIPTION:Title: Bracket quadratics\, Hua’s Lemma and Vinogradov’s m
ean value theorem\nby Trevor Wooley (Purdue University) as part of Number
Theory Web Seminar\n\n\nAbstract\nA little over a decade ago\, Ben Green p
osed the problem of showing that all large integers are the sum of at most
a bounded number of bracket quadratic polynomials of the shape $n[n\\thet
a]$\, for natural numbers $n$\, in which $\\theta$ is an irrational number
such as the square-root of 2. This was resolved in the PhD thesis of Vick
y Neale\, although no explicit bound was given concerning the number of va
riables required to achieve success. In this talk we describe a version of
Hua’s lemma for this problem that can be applied via the Hardy-Littlewo
od method to obtain a conclusion with 5 variables. The associated argument
differs according to whether $\\theta$ is a quadratic irrational or not.
We also explain how related versions of Hua’s lemma may be interpreted i
n terms of discrete restriction variants of Vinogradov’s mean value theo
rem\, thus providing a route to generalisation.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elon Lindenstrauss (Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20200618T150000Z
DTEND;VALUE=DATE-TIME:20200618T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/12
DESCRIPTION:Title: Diagonalizable flows\, joinings\, and arithmetic applic
ations\nby Elon Lindenstrauss (Hebrew University of Jerusalem) as part of
Number Theory Web Seminar\n\n\nAbstract\nRigidity properties of higher ran
k diagonalizable actions have proved to be powerful tools in understanding
the distribution properties of rational tori in arithmetic quotients. Per
haps the simplest\, and best known\, example of such an equidistribution q
uestion is the equidistribution of CM points of a given discriminant on th
e modular curve. The equidistribution of CM points was established by Duke
using analytic methods\, but for finer questions (and questions regarding
equidistribution on higher rank spaces) the ergodic theoretic approach ha
s proved to be quite powerful.\n\nI will survey some of the results in thi
s direction\, including several results about joint distributions of colle
ctions of points in product spaces by Aka\, Einsiedler\, Khayutin\, Shapir
a\, Wieser and other researchers.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Maynard (University of Oxford)
DTSTART;VALUE=DATE-TIME:20200702T150000Z
DTEND;VALUE=DATE-TIME:20200702T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/13
DESCRIPTION:Title: Primes in arithmetic progressions to large moduli\nby J
ames Maynard (University of Oxford) as part of Number Theory Web Seminar\n
\n\nAbstract\nHow many primes are there which are less than $x$ and congru
ent to $a$ modulo $q$? This is one of the most important questions in anal
ytic number theory\, but also one of the hardest - our current knowledge i
s limited\, and any direct improvements require solving exceptionally diff
icult questions to do with exceptional zeros and the Generalized Riemann H
ypothesis!\n\nIf we ask for 'averaged' results then we can do better\, and
powerful work of Bombieri and Vinogradov gives good answers for $q$ less
than the square-root of $x$. For many applications this is as good as the
Generalized Riemann Hypothesis itself! Going beyond this 'square-root' bar
rier is a notorious problem which has been achieved only in special situat
ions\, perhaps most notably this was the key component in the work of Zhan
g on bounded gaps between primes. I'll talk about recent work going beyond
this barrier in some new situations. This relies on fun connections betwe
en algebraic geometry\, spectral theory of automorphic forms\, Fourier ana
lysis and classical prime number theory. The talk is intended for a genera
l audience.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Shparlinski (UNSW Sydney)
DTSTART;VALUE=DATE-TIME:20200623T080000Z
DTEND;VALUE=DATE-TIME:20200623T090000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/14
DESCRIPTION:Title: Weyl sums: large\, small and typical\nby Igor Shparlins
ki (UNSW Sydney) as part of Number Theory Web Seminar\n\n\nAbstract\nAbstr
act: While Vinogradov’s Mean Value Theorem\, in the form given by J. Bou
rgain\, C. Demeter and L. Guth (2016) and T. Wooley (2016-2019)\, gives an
essentially optimal result on the power moments of the Weyl sums \n$$\nS
(u\;N) =\\sum_{1\\le n \\le N} \\exp(2 \\pi i (u_1n+…+u_dn^d))\n$$\nwher
e $u = (u_1\,...\,u_d) \\in [0\,1)^d$\, very little is known about the di
stribution\, or even existence\, of $u \\in [0\,1)^d$\, for which these su
ms are very large\, or small\, or close to their average value $N^{1/2}$.
In this talk\, we describe recent progress towards these and some related
questions.\n\nWe also present some new bounds on $S(u\;N)$ which hold for
almost all $(u_i)_{i\\in I}$ and all $(u_j)_{j\\in J}$\, where $I \\cup J$
is a partition of $\\{1\,…\,\,d\\}$. These bounds improve similar resul
ts of T. Wooley (2015). Our method also applies to binomial sums \n$$\nT(x
\,y\; N) = \\sum_{1\\le n \\le N} \\exp(2 \\pi i (xn+yn^d))\n$$\nwith $x\,
y \\in [0\,1)$\, in which case we improve some results of M.B. Erdogan and
G. Shakan (2019).\n\nThis is a joint work with Changhao Chen and Bryce Ke
rr.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Balakrishnan (Boston University)
DTSTART;VALUE=DATE-TIME:20200716T150000Z
DTEND;VALUE=DATE-TIME:20200716T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/15
DESCRIPTION:Title: A tale of three curves\nby Jennifer Balakrishnan (Bosto
n University) as part of Number Theory Web Seminar\n\n\nAbstract\nWe will
describe variants of the Chabauty-Coleman method\nand quadratic Chabauty t
o determine rational points on curves. In so\ndoing\, we will highlight so
me recent examples where the techniques\nhave been used: this includes a p
roblem of Diophantus originally\nsolved by Wetherell and the problem of th
e "cursed curve"\, the split\nCartan modular curve of level 13. This is jo
int work with Netan Dogra\,\nSteffen Mueller\, Jan Tuitman\, and Jan Vonk.
\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Bilu (University of Bordeaux)
DTSTART;VALUE=DATE-TIME:20200611T150000Z
DTEND;VALUE=DATE-TIME:20200611T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/16
DESCRIPTION:Title: Trinomials\, singular moduli and Riffaut's conjecture\n
by Yuri Bilu (University of Bordeaux) as part of Number Theory Web Seminar
\n\n\nAbstract\nRiffaut (2019) conjectured that a singular modulus of degr
ee h>2 cannot be a root of a trinomial with rational coefficients. We show
that this conjecture follows from the GRH\, and obtain partial unconditio
nal results. A joint work with Florian Luca and Amalia Pizarro.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lillian Pierce (Duke University)
DTSTART;VALUE=DATE-TIME:20200709T150000Z
DTEND;VALUE=DATE-TIME:20200709T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/17
DESCRIPTION:Title: On Bourgain’s counterexample for the Schrödinger max
imal function\nby Lillian Pierce (Duke University) as part of Number Theor
y Web Seminar\n\n\nAbstract\nThere is a long and visible history of applic
ations of analytic methods to number theory. More recently we are starting
to recognize applications of number-theoretic methods to analysis. In thi
s talk we will describe an important recent application in this direction.
\n\nIn 1980\, Carleson asked a question in PDE's: for what class of initi
al data functions does a pointwise a.e. convergence result hold for the so
lution of the linear Schrödinger equation? Over the next decades\, many p
eople developed counterexamples to show “necessary conditions\,” and o
n the other hand positive results to show “sufficient conditions.” In
2016 Bourgain wrote a 3-page paper using facts from number theory to const
ruct a family of counterexamples. A 2019 Annals paper of Du and Zhang then
resolved the question by proving positive results that push the “suffic
ient conditions” to meet Bourgain’s “necessary conditions."\n\nBourg
ain’s construction was regarded as somewhat mysterious. In this talk\, w
e give an overview of how to rigorously derive Bourgain’s construction u
sing ideas from number theory. Our strategy is to start from “zero knowl
edge" and gradually optimize the set-up to arrive at the final counterexam
ple. This talk will be broadly accessible.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bas Edixhoven (Leiden University)
DTSTART;VALUE=DATE-TIME:20200526T080000Z
DTEND;VALUE=DATE-TIME:20200526T090000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/18
DESCRIPTION:Title: Geometric quadratic Chabauty\nby Bas Edixhoven (Leiden
University) as part of Number Theory Web Seminar\n\n\nAbstract\nJoint work
with Guido Lido (see arxiv preprint). Determining all rational points on
a curve of genus at least $2$ can be difficult. Chabauty's method (1941) i
s to intersect\, for a prime number p\, in the p-adic Lie group of $p$-adi
c points of the jacobian\, the closure of the Mordell-Weil group with the
p-adic points of the curve. If the Mordell-Weil rank is less than the genu
s then this method has never failed. Minhyong Kim's non-abelian Chabauty p
rogramme aims to remove the condition on the rank. The simplest case\, cal
led quadratic Chabauty\, was developed by Balakrishnan\, Dogra\, Mueller\,
Tuitman and Vonk\, and applied in a tour de force to the so-called cursed
curve (rank and genus both $3$). Our work gives a version of this method
that uses only `simple algebraic geometry' (line bundles over the jacobian
and models over the integers). For the talk\, no knowledge of all this al
gebraic geometry is required\, it will be accessible to all number theoris
ts.\n\nReferences: https://arxiv.org/abs/1910.10752\nArizona Winter School
2020: http://swc.math.arizona.edu/index.html\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph H. Silverman (Brown University)
DTSTART;VALUE=DATE-TIME:20200730T150000Z
DTEND;VALUE=DATE-TIME:20200730T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/19
DESCRIPTION:Title: More Tips on Keeping Secrets in a Post-Quantum World: L
attice-Based Cryptography\nby Joseph H. Silverman (Brown University) as pa
rt of Number Theory Web Seminar\n\n\nAbstract\nWhat do internet commerce\,
online banking\, and updates to your phone apps have in common? All of t
hem depend on modern public key cryptography for security. For example\,
there is the RSA cryptosystem that is used by many internet browsers\, an
d there is the elliptic curve based ECDSA digital signature scheme that i
s used in many applications\, including Bitcoin. All of these cryptograph
ic construction are doomed if/when someone (NSA? Russia? China?) builds
a full-scale operational quantum computer. It hasn't happened yet\, as
far as we know\, but there are vast resources being thrown at the problem
\, and slow-but-steady progress is being made. So the search is on for cr
yptographic algorithms that are secure against quantum computers. The f
irst part of my talk will be a mix of math and history and prognosticatio
n centered around the themes of quantum computers and public key cryptogr
aphy. The second part will discuss cryptographic constructions based on h
ard lattice problems\, which is one of the approaches being proposed to b
uild a post-quantum cryptographic infrastructure.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaisa Matomäki (University of Turku)
DTSTART;VALUE=DATE-TIME:20200602T080000Z
DTEND;VALUE=DATE-TIME:20200602T090000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/20
DESCRIPTION:Title: Multiplicative functions in short intervals revisited\n
by Kaisa Matomäki (University of Turku) as part of Number Theory Web Semi
nar\n\n\nAbstract\nA few years ago Maksym Radziwill and I showed that the
average of a multiplicative function in almost all very short intervals $[
x\, x+h]$ is close to its average on a long interval $[x\, 2x]$. This resu
lt has since been utilized in many applications.\n\nIn a work in progress
that I will talk about\, Radziwill and I revisit the problem and generalis
e our result to functions which vanish often as well as prove a power-savi
ng upper bound for the number of exceptional intervals (i.e. we show that
there are $O(X/h^\\kappa)$ exceptional $x \\in [X\, 2X]$). \n\nWe apply th
is result for instance to studying gaps between norm forms of an arbitrary
number field.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjorn Poonen (MIT)
DTSTART;VALUE=DATE-TIME:20200806T150000Z
DTEND;VALUE=DATE-TIME:20200806T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/21
DESCRIPTION:Title: Tetrahedra with rational dihedral angles\nby Bjorn Poon
en (MIT) as part of Number Theory Web Seminar\n\n\nAbstract\nIn 1895\, Hil
l discovered a 1-parameter family of tetrahedra whose dihedral angles are
all rational multiples of $\\pi$. In 1976\, Conway and Jones related the p
roblem of finding all such tetrahedra to solving a polynomial equation in
roots of unity. Many previous authors have solved polynomial equations in
roots of unity\, but never with more than $12$ monomials\, and the Conway-
Jones polynomial has $105$ monomials! I will explain the method we use to
solve it and our discovery that the full classification consists of two $1
$-parameter families and an explicit finite list of sporadic tetrahedra.\n
\nBuilding on this work\, we classify all configurations of vectors in $\\
R^3$ such that the angle between each pair is a rational multiple of $\\pi
$. Sample result: Ignoring trivial families and scalar multiples\, any con
figuration with more than $9$ vectors is contained in a particular $15$-ve
ctor configuration. \n\nThis is joint work with Kiran Kedlaya\, Alexander
Kolpakov\, and Michael Rubinstein.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harald Andrés Helfgott (Göttingen/CNRS (IMJ))
DTSTART;VALUE=DATE-TIME:20200616T080000Z
DTEND;VALUE=DATE-TIME:20200616T090000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/22
DESCRIPTION:Title: Optimality of the logarithmic upper-bound sieve\, with
explicit estimates\nby Harald Andrés Helfgott (Göttingen/CNRS (IMJ)) as
part of Number Theory Web Seminar\n\n\nAbstract\nAt the simplest level\, a
n upper bound sieve of Selberg type is a choice of $\\rho(d)$\, $d\\le D$\
, with $\\rho(1)=1$\, such that\n$$\nS = \\sum_{n\\leq N} \\left(\\sum_{d|
n} \\mu(d) \\rho(d)\\right)^2\n$$\nis as small as possible.\n\nThe optimal
choice of $\\rho(d)$ for given $D$ was found by Selberg. However\, for se
veral applications\, it is better to work with functions $\\rho(d)$ that a
re scalings of a given continuous or monotonic function $\\eta$. The quest
ion is then what is the best function $\\eta$\, and how does $S$ for given
$\\eta$ and $D$ compares to $S$ for Selberg's choice.\n\nThe most common
choice of eta is that of Barban-Vehov (1968)\, which gives an $S$ with the
same main term as Selberg's $S$. We show that Barban and Vehov's choice i
s optimal among all $\\eta$\, not just (as we knew) when it comes to the m
ain term\, but even when it comes to the second-order term\, which is nega
tive and which we determine explicitly.\n\nThis is joint work with Emanuel
Carneiro\, Andrés Chirre and Julian Mejía-Cordero.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Skinner (Princeton University)
DTSTART;VALUE=DATE-TIME:20200820T150000Z
DTEND;VALUE=DATE-TIME:20200820T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/23
DESCRIPTION:Title: Solving diagonal diophantine equations over general $p$
-adic fields\nby Christopher Skinner (Princeton University) as part of Num
ber Theory Web Seminar\n\n\nAbstract\nThis talk will explain a proof that
a system of $r$ diagonal equations\n$$\na_{i\,1}x_1^d + \\cdots +a_{i\,s}
x_s^d = 0 \,\\quad i = 1\,...\,r\n$$\nwith coefficients in a $p$-adic fiel
d $K$ has a non-trivial solution in $K$ if the number of variables $s$ exc
eeds $3r^2d^2$ (if $p > 2$) or $8r^2d^2$ (if $p=2$). This is the first bo
und that holds uniformly for all $p$-adic fields K and that is polynomial
in $r$ or $d$. The methods -- and talk -- are elementary.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hector Pasten (Pontificia Universidad Católica de Chile)
DTSTART;VALUE=DATE-TIME:20200827T150000Z
DTEND;VALUE=DATE-TIME:20200827T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/24
DESCRIPTION:by Hector Pasten (Pontificia Universidad Católica de Chile) a
s part of Number Theory Web Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Özlem Imamoglu (ETH Zürich)
DTSTART;VALUE=DATE-TIME:20200917T150000Z
DTEND;VALUE=DATE-TIME:20200917T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/25
DESCRIPTION:by Özlem Imamoglu (ETH Zürich) as part of Number Theory Web
Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Breuillard (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20200924T150000Z
DTEND;VALUE=DATE-TIME:20200924T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/26
DESCRIPTION:by Emmanuel Breuillard (University of Cambridge) as part of Nu
mber Theory Web Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bianca Viray (University of Washington)
DTSTART;VALUE=DATE-TIME:20200910T150000Z
DTEND;VALUE=DATE-TIME:20200910T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/27
DESCRIPTION:by Bianca Viray (University of Washington) as part of Number T
heory Web Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Pomerance (Dartmouth College)
DTSTART;VALUE=DATE-TIME:20200813T150000Z
DTEND;VALUE=DATE-TIME:20200813T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/28
DESCRIPTION:Title: Practical numbers\nby Carl Pomerance (Dartmouth College
) as part of Number Theory Web Seminar\n\n\nAbstract\nA practical number $
n$ is one where each number up to $n$ can be expressed as a subset sum of
$n$'s positive divisors. It seems that Fibonacci was interested in them si
nce they have the property that all fractions $m/n$ with $m < n$ can be wr
itten as a sum of distinct unit fractions with denominators dividing $n$.
With similar considerations in mind\, Srinivasan in 1948 coined the term
"practical". There has been quite a lot of effort to study their distribut
ion\, effort which has gone hand in hand with the development of the anato
my of integers. After work of Tenenbaum\, Saias\, and Weingartner\, we no
w know the "Practical Number Theorem": the number of practical numbers up
to $x$ is asymptotically $cx/log x$\, where $c= 1.33607...$. In this talk
I'll discuss some recent developments\, including work of Thompson who co
nsidered the allied concept of $\\phi$-practical numbers $n$ (the polynomi
al $t^n-1$ has divisors over the integers of every degree up to $n$) and t
he proof (joint with Weingartner) of a conjecture of Margenstern that each
large odd number can be expressed as a sum of a prime and a practical num
ber.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:René Schoof (Università di Roma “Tor Vergata”)
DTSTART;VALUE=DATE-TIME:20200707T080000Z
DTEND;VALUE=DATE-TIME:20200707T090000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/29
DESCRIPTION:Title: Abelian varieties over ${\\bf Q}(\\sqrt{97})$ with good
reduction everywhere\nby René Schoof (Università di Roma “Tor Vergata
”) as part of Number Theory Web Seminar\n\n\nAbstract\nUnder assumption
of the Generalized Riemann Hypothesis we show that every abelian variety o
ver ${\\bf Q}(\\sqrt{97})$ with good reduction everywhere is isogenous to
a power of a certain $3$-dimensional modular abelian variety.\n\n(joint wi
th Lassina Dembele)\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kannan Soundararajan (Stanford University)
DTSTART;VALUE=DATE-TIME:20200630T000000Z
DTEND;VALUE=DATE-TIME:20200630T010000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/30
DESCRIPTION:Title: Equidistribution from the Chinese Remainder Theorem\nby
Kannan Soundararajan (Stanford University) as part of Number Theory Web S
eminar\n\n\nAbstract\nSuppose for each prime $p$ we are given a set $A_p$
(possibly empty) of residue classes mod $p$. Use these and the Chinese Re
mainder Theorem to form a set $A_q$ of residue classes mod $q$\, for any i
nteger $q$. Under very mild hypotheses\, we show that for a typical integ
er $q$\, the residue classes in $A_q$ will become equidistributed. The pr
ototypical example (which this generalises) is Hooley's theorem that the r
oots of a polynomial congruence mod $n$ are equidistributed on average ove
r $n$. I will also discuss generalisations of such results to higher dime
nsions\, and when restricted to integers with a given number of prime fact
ors. (Joint work with Emmanuel Kowalski.)\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jordan Ellenberg (University of Wisconsin–Madison)
DTSTART;VALUE=DATE-TIME:20200723T150000Z
DTEND;VALUE=DATE-TIME:20200723T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/31
DESCRIPTION:Title: What’s up in arithmetic statistics\nby Jordan Ellenbe
rg (University of Wisconsin–Madison) as part of Number Theory Web Semina
r\n\n\nAbstract\nIf not for a global pandemic\, a bunch of mathematicians
would have gathered in Germany to talk about what’s going on in the geom
etry of arithmetic statistics\, which I would roughly describe as “metho
ds from arithmetic geometry brought to bear on probabilistic questions abo
ut arithmetic objects". What does the maximal unramified extension of a ra
ndom number field look like? What is the probability that a random ellipti
c curve has a $2$-Selmer group of rank 100? How do you count points on a
stack? I’ll give a survey of what’s happening in questions in this are
a\, trying to emphasize open questions.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Ono (University of Virginia)
DTSTART;VALUE=DATE-TIME:20200714T000000Z
DTEND;VALUE=DATE-TIME:20200714T010000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/32
DESCRIPTION:Title: Variants of Lehmer's speculation for newforms\nby Ken O
no (University of Virginia) as part of Number Theory Web Seminar\n\n\nAbst
ract\nIn the spirit of Lehmer's unresolved speculation on the nonvanishing
of Ramanujan's tau-function\, it is natural to ask whether a fixed intege
r is a value of τ(n)\, or is a Fourier coefficient of any given newform.
In joint work with J. Balakrishnan\, W. Craig\, and W.-L. Tsai\, the spea
ker has obtained some results that will be described here. For example\, i
nfinitely many spaces are presented for which the primes ℓ≤37 are not
absolute values of coefficients of any newforms with integer coefficients.
For Ramanujan’s tau-function\, such results imply\, for n>1\, that\n\n
τ(n)∉{±1\,±3\,±5\,±7\,±13\,±17\,−19\,±23\,±37\,±691}.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wadim Zudilin (Radboud University Nijmegen)
DTSTART;VALUE=DATE-TIME:20200721T080000Z
DTEND;VALUE=DATE-TIME:20200721T090000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/33
DESCRIPTION:Title: Irrationality through an irrational time\nby Wadim Zudi
lin (Radboud University Nijmegen) as part of Number Theory Web Seminar\n\n
\nAbstract\nAfter reviewing some recent development and achievements relat
ed to diophantine problems of the values of Riemann's zeta function and ge
neralized polylogarithms (not all coming from myself!)\, I will move the f
ocus to $\\pi=3.1415926\\dots$ and its rational approximations. Specifical
ly\, I will discuss a construction of rational approximations to the numbe
r that leads to the record irrationality measure of $\\pi$. The talk is ba
sed on joint work with Doron Zeilberger.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Ford (University of Illinois at Urbana-Champaign)
DTSTART;VALUE=DATE-TIME:20200903T150000Z
DTEND;VALUE=DATE-TIME:20200903T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/34
DESCRIPTION:by Kevin Ford (University of Illinois at Urbana-Champaign) as
part of Number Theory Web Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Ho (University of Michigan)
DTSTART;VALUE=DATE-TIME:20201001T150000Z
DTEND;VALUE=DATE-TIME:20201001T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/35
DESCRIPTION:by Wei Ho (University of Michigan) as part of Number Theory We
b Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Michel (EPFL)
DTSTART;VALUE=DATE-TIME:20201008T150000Z
DTEND;VALUE=DATE-TIME:20201008T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/36
DESCRIPTION:by Philippe Michel (EPFL) as part of Number Theory Web Seminar
\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umberto Zannier (Scuola Normale Superiore Pisa)
DTSTART;VALUE=DATE-TIME:20200901T080000Z
DTEND;VALUE=DATE-TIME:20200901T090000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/37
DESCRIPTION:by Umberto Zannier (Scuola Normale Superiore Pisa) as part of
Number Theory Web Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cameron L. Stewart (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20201015T150000Z
DTEND;VALUE=DATE-TIME:20201015T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/38
DESCRIPTION:by Cameron L. Stewart (University of Waterloo) as part of Numb
er Theory Web Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Konyagin (Steklov Institute of Mathematics)
DTSTART;VALUE=DATE-TIME:20201022T150000Z
DTEND;VALUE=DATE-TIME:20201022T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042759Z
UID:NTWebSeminar/39
DESCRIPTION:by Sergei Konyagin (Steklov Institute of Mathematics) as part
of Number Theory Web Seminar\n\nAbstract: TBA\n
END:VEVENT
END:VCALENDAR