BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Felipe Voloch (University of Canterbury)
DTSTART:20200603T000000Z
DTEND:20200603T003000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/1/"
 >Sha versus the Volcano</a>\nby Felipe Voloch (University of Canterbury) a
 s part of Number Theory Online Conference 2020\n\n\nAbstract\nWe describe 
 the structure of the Tate-Shafarevich group of constant elliptic curves ov
 er function fields by exploiting the volcano structure of isogeny graphs o
 f elliptic curves over finite fields.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bo-Hae Im (Korea Advanced Institute of Science and Technology)
DTSTART:20200603T010000Z
DTEND:20200603T013000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/2/"
 >Waring’s problem for rational functions in one variable</a>\nby Bo-Hae 
 Im (Korea Advanced Institute of Science and Technology) as part of Number 
 Theory Online Conference 2020\n\n\nAbstract\nLet $f\\in \\mathbb{Q}(x)$ be
  a non-constant rational function.  We consider "Waring's Problem for $f(x
 )$"\, i.e.\, whether every element of $ \\mathbb{Q}  $ can be written as a
  bounded sum of elements of $\\{f(a)\\mid a\\in  \\mathbb{Q} \\}$.  For ra
 tional functions of degree $2$\, we give necessary and sufficient conditio
 ns.  For higher degrees\, we prove that every polynomial of odd degree and
  every odd Laurent polynomial satisfies Waring's Problem.  We also conside
 r the 'Easier Waring's Problem': whether every element of $  \\mathbb{Q} $
  can be  represented as a bounded sum of elements of $\\{\\pm f(a)\\mid a\
 \in \\mathbb{Q}  \\}$. This is a joint work with Michael Larsen.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Shparlinski (UNSW Sydney)
DTSTART:20200603T020000Z
DTEND:20200603T023000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/3/"
 >Denominators of rational numbers in or close to the Cantor set</a>\nby Ig
 or Shparlinski (UNSW Sydney) as part of Number Theory Online Conference 20
 20\n\n\nAbstract\nWe start with a short survey of recent results on the ar
 ithmetic structure of \ndenominators of rational numbers which belong to t
 he Cantor set\, or are very \nclose to one of each elements. We then descr
 ibe how a new point of approach\, using \nclassical bounds of short expone
 ntial sums due to N. Korobov\,  leads to new\nresults and improvements of 
 some existing results.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Trudgian (UNSW Canberra at ADFA)
DTSTART:20200603T040000Z
DTEND:20200603T043000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/4/"
 >Zeta zeroes: mind the gap!</a>\nby Tim Trudgian (UNSW Canberra at ADFA) a
 s part of Number Theory Online Conference 2020\n\n\nAbstract\nI shall pres
 ent some hot-off-the-press work\, with AS and CTB\, on gaps between the ze
 roes of the Riemann zeta-function. I recorded this talk with a document ca
 mera\, and will give commentary as "Current Tim" over the writings of "Pas
 t Tim" --- nothing could go wrong!\n
LOCATION:https://researchseminars.org/talk/NTOC2020/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Morrill (UNSW Canberra)
DTSTART:20200603T050000Z
DTEND:20200603T053000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/5/"
 >Look\, Knave</a>\nby Thomas Morrill (UNSW Canberra) as part of Number The
 ory Online Conference 2020\n\n\nAbstract\nIn this lighthearted tribute to 
 the late John Conway\, we examine a recursive sequence in which $s_n$ is a
  binary string that describes what the previous term $s_{n-1}$ is not. By 
 adapting Conway's approach on the Look-and-Say sequence\, we determine lim
 iting behaviour of $\\{s_n\\}$ and dynamics of a related self-map on the s
 pace of infinite binary sequences. Our main result is the existence and un
 iqueness of a pair of binary sequences\, each the compliment-description o
 f the other.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Wang (Academia Sinica)
DTSTART:20200604T000000Z
DTEND:20200604T005000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/6/"
 >On Pisot’s d-th root conjecture for function fields and related GCD est
 imates</a>\nby Julie Wang (Academia Sinica) as part of Number Theory Onlin
 e Conference 2020\n\n\nAbstract\nLet $B(X)=\\sum_{n=0}^{\\infty}b(n)X^n$ r
 epresent a rational function in $\\mathbb Q(X)$ \n  and suppose that  $b(n
 )$ is a perfect $d$-th power for all large $n\\in\\mathbb N$. Pisot's  $d$
 -th root conjecture states that one can choose a $d$-th root $a(n)$ of $b(
 n)$ such that $A(X):=\\sum a(n)X^n$ is again a rational function. In this 
 talk\,  we propose a function-field analog of Pisot's $d$-th root conjectu
 re  and prove it under some ``non-triviality''\nassumption.  We relate the
  problem to a  result of Pasten-Wang  on Buchi's $d$-th power problem and 
  develop  a function-field analog of an GCD estimate in a recent work of L
 evin-Wang.      This is a joint work with Ji Guo and Chia-Liang Sun.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Grantham (Institute for Defense Analyses)
DTSTART:20200604T010000Z
DTEND:20200604T013000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/7/"
 >Binary and ternary curves of fixed genus and gonality with many points</a
 >\nby Jon Grantham (Institute for Defense Analyses) as part of Number Theo
 ry Online Conference 2020\n\n\nAbstract\nWe determine the maximum number o
 f rational points on curves over $\\mathbb{F}_2$ and $\\mathbb{F}_3$ with 
 fixed gonality and small genus.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisa Bellah (University of Oregon)
DTSTART:20200604T020000Z
DTEND:20200604T023000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/8/"
 >Norm form equations and linear divisibility sequences</a>\nby Elisa Bella
 h (University of Oregon) as part of Number Theory Online Conference 2020\n
 \n\nAbstract\nFinding integer solutions to norm form equations is a classi
 c Diophantine problem. Using the units of the associated coefficient ring\
 , we can produce sequences of solutions to these equations. It turns out t
 hat such a sequence can be written as a tuple of integer linear recurrence
  sequences\, each with characteristic polynomial equal to the minimal poly
 nomial of our unit. We show that in some cases\, these sequences are linea
 r divisibility sequences.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Bordignon (UNSW Canberra)
DTSTART:20200604T040000Z
DTEND:20200604T043000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/9/"
 >Partial Gaussian sums and Polya–Vinogradov inequality for primitive cha
 racters</a>\nby Matteo Bordignon (UNSW Canberra) as part of Number Theory 
 Online Conference 2020\n\n\nAbstract\nWe will improve\, for large moduli\,
  on the best explicit version of the Polya--Vinogradov inequality for prim
 itive characters\, due to Frolenkov and Soudararajan\, drawing inspiration
  from a paper by Hildebrand.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Delbourgo (University of Waikato)
DTSTART:20200605T000000Z
DTEND:20200605T005000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/10/
 ">Variation of Iwasawa invariants over number fields</a>\nby Daniel Delbou
 rgo (University of Waikato) as part of Number Theory Online Conference 202
 0\n\n\nAbstract\nIwasawa theory provides an intriguing $p$-adic link betwe
 en the algebraic world and the analytic world.\nA key quantity is the lamb
 da-invariant\, which counts the number of zeroes of the $p$-adic L-functio
 n.\nWe shall carefully explain how this invariant (both the algebraic and 
 analytic version) behaves over a non-abelian extension $K/\\mathbb{Q}$\, a
 s one moves around a Hida family of modular forms.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fu-Tsun Wei (National Tsing Hua University)
DTSTART:20200605T010000Z
DTEND:20200605T013000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/11/
 ">On class number relations and intersections over function fields</a>\nby
  Fu-Tsun Wei (National Tsing Hua University) as part of Number Theory Onli
 ne Conference 2020\n\n\nAbstract\nIn this talk\, we shall discuss a functi
 on field analogue of the Hirzebrush-Zagier class number formula. More prec
 isely\, we establish a connection between class numbers of "imaginary" qua
 dratic function fields and the corresponding intersections of "Heegner-typ
 e" divisors on the Drinfeld-Stuhler modular surfaces. The main bridge is t
 he theta series associated to anisotropic quadratic spaces of dimension 4.
  The connection directly comes from two different expressions of the Fouri
 er coefficients of the theta series\, which can be viewed as a geometric S
 iegel-Weil formula in this particular case. This is a joint work with Jia-
 Wei Guo.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peng-Jie Wong (University of Lethbridge)
DTSTART:20200605T020000Z
DTEND:20200605T023000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/12/
 ">Refinements of Strong Multiplicity One for GL(2)</a>\nby Peng-Jie Wong (
 University of Lethbridge) as part of Number Theory Online Conference 2020\
 n\n\nAbstract\nLet $f_1$ and $f_2$ be holomorphic newforms of same weight 
 and with same nebentypus\, and let  $a_{f_1}(n)$ and $a_{f_2}(n)$ denote t
 he Fourier coefficients of $f_1$ and $f_2$\, respectively. By the strong m
 ultiplicity one theorem\, it is known that if $a_{f_1}(p)=a_{f_2}(p)$ for 
 almost all primes $p$\, then  $f_1$ and $f_2$ are equivalent. Furthermore\
 , a result of Ramakrishnan states that if $a_{f_1}(p)^2=a_{f_2}(p)^2$ outs
 ide a set of primes $p$ of density less than $\\frac{1}{18}$\, then $f_1$ 
 and $f_2$ are twist-equivalent.\n\nIn this talk\, we will discuss some ref
 inements and variants of the strong multiplicity one theorem and Ramakrish
 nan's result for general $\\rm{GL}(2)$-forms. In particular\, we will anal
 yse the set of primes $p$ for which $|a_{f_1}(p)| \\neq |a_{f_2}(p)|$ for 
 non-twist-equivalent $f_1$ and $f_2$.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mumtaz Hussain (La Trobe University)
DTSTART:20200605T040000Z
DTEND:20200605T043000Z
DTSTAMP:20260415T053509Z
UID:NTOC2020/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/13/
 ">Uniform Diophantine approximation: improving Dirichlet’s theorem</a>\n
 by Mumtaz Hussain (La Trobe University) as part of Number Theory Online Co
 nference 2020\n\n\nAbstract\nIn this talk\, I will discuss the metrical th
 eory associated with the set of Dirichlet non-improvable numbers. \n\nLet 
 $\\Psi :[1\,\\infty )\\rightarrow \\mathbb{R}_{+}$ be a non-decreasing fun
 ction\, $a_{n}(x)$ the $n$'th partial quotient of $x$ and $q_{n}(x)$ the d
 enominator of the $n$'th convergent. The set of $\\Psi $-Dirichlet non-imp
 rovable numbers \n$$\nG(\\Psi):=\\Big\\{x\\in \\lbrack 0\,1):a_{n}(x)a_{n+
 1}(x)\\\,>\\\,\\Psi \\big(q_{n}(x)\n\\big)\\ \\mathrm{for\\ infinitely\\ m
 any}\\ n\\in \\mathbb{N}\\Big\\}\,\n$$\nis related with the classical set 
 of $1/q^{2}\\Psi (q)$-approximable numbers \n\n$$\n\\mathcal{K}(\\Psi):=\\
 left\\{x\\in[0\,1): \\left|x-\\frac pq\\right|<\\frac{1}{\nq^2\\Psi(q)} \\
  \\mathrm{for \\ infinitely \\ many \\ } (p\, q)\\in \\mathbb{Z}\\times \\
 mathbb{N }\n\\right\\}\,\n$$\n in the sense that $\\mathcal{K}(3\\Psi )\\s
 ubset G(\\Psi )$. In this talk\, I will explain that the Hausdorff measure
  of the set  $G(\\Psi)$ obeys a zero-infinity law for a large class of dim
 ension functions.  Together with the Lebesgue measure-theoretic results es
 tablished by Kleinbock \\& Wadleigh (2016)\, our results contribute to bui
 lding a complete metric theory for the set of Dirichlet non-improvable num
 bers.\n\nAnother recent result that I will discuss will be the Hausdorff d
 imension of the set  $G(\\Psi)\\setminus \\mathcal{K}(3\\Psi )$.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/13/
END:VEVENT
END:VCALENDAR