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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Shalom Eliahou (Universite du Littoral Cote d'Opale)
DTSTART:20200710T150000Z
DTEND:20200710T160000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/1/">Iterated sumsets and Hilbert functions</a>\n
 by Shalom Eliahou (Universite du Littoral Cote d'Opale) as part of New Yor
 k Number Theory Seminar\n\n\nAbstract\nLet $A\,B \\subset \\Z$. Denote $A+
 B=\\{a+b \\mid a \\in A\, b \\in B\\}$\, the \\emph{sumset} of $A\,B$. For
  $A=B$\, denote $2A=A+A$. More generally\, for $h \\ge 2$\, denote $hA=A+(
 h-1)A$\, the $h$-fold \\emph{iterated sumset} of $A$. If $A$ is finite\, h
 ow does the sequence $|hA|$ behave as $h$ grows? This is a typical problem
  in additive combinatorics. In this talk\, we focus on the following speci
 fic question: if $|hA|$ is known\, what can one say about $|(h-1)A|$ and $
 |(h+1)A|$? It is known that $$|(h-1)A| \\ge |hA|^{(h-1)/h}\,$$ a consequen
 ce of Pl\\"unnecke's inequality derived from graph theory. Here we propose
  a new approach\, by modeling the sequence $|hA|$ with the Hilbert functio
 n of a suitable standard graded algebra $R(A)$. We then apply Macaulay's 1
 927 theorem on the growth of Hilbert functions. This allows us to recover 
 and strengthen Pl\\"unnecke's  estimate on $|(h-1)A|$. This is joint work 
 with Eshita Mazumdar.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20200903T190000Z
DTEND:20200903T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/2/">Sums of finite sets of integers\, II</a>\nby
  Mel Nathanson (CUNY) as part of New York Number Theory Seminar\n\nAbstrac
 t: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20200910T190000Z
DTEND:20200910T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/3/">Chromatic sumsets</a>\nby Mel Nathanson (CUN
 Y) as part of New York Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20200917T190000Z
DTEND:20200917T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/4/">A curious convergent series of integers with
  missing digits</a>\nby Mel Nathanson (CUNY) as part of New York Number Th
 eory Seminar\n\n\nAbstract\nBy a classical theorem of Kempner\, the sum of
  the reciprocals of integers with missing digits converges.  This result i
 s extended to a much larger family of ``missing digits'' sets of positive 
 integers  with convergent harmonic series. Related sets with divergent har
 monic series are also constructed.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harald Helfgott (Gottigen)
DTSTART:20200924T190000Z
DTEND:20200924T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/5/">Expansion in a prime divisibility graph</a>\
 nby Harald Helfgott (Gottigen) as part of New York Number Theory Seminar\n
 \n\nAbstract\n(Joint with M. Radziwill.)\nLet $\\mathbf{N} = \\mathbb{Z} \
 \cap (N\, 2N]$ and $\\mathbf{P} \\subset [1\,H]$ a set of primes\n    with
  $H \\leq \\exp(\\sqrt{\\log N}/2)$. Given any subset $\\mathcal{X} \\subs
 et \\mathbf{N}$\,\ndefine the linear operator\n  $$\n (A_{|\\mathcal{X}} f
 )(n) = \\sum_{\\substack{p \\in \\mathbf{P} : p | n \\\\ n\, n \\pm p \\in
  \\mathcal{X}}} f(n \\pm p) - \\sum_{\\substack{p \\in \\mathbf{P} \\\\ n\
 , n \\pm p \\in \\mathcal{X}}} \\frac{f(n \\pm p)}{p}\n  $$\non functions 
 $f:\\mathbf{N}\\to \\mathbb{C}$. Let $\\mathcal{L} = \\sum_{p \\in \\mathb
 f{P}} \\frac{1}{p}$.\n\nWe prove that\, for any $C > 0$\, there exists a s
 ubset $\\mathcal{X} \\subset \\mathbf{N}$ of density $1 - O(e^{-C \\mathca
 l{L}})$ in $\\mathbf{N}$ such that\n$A_{|\\mathcal{X}}$ has a strong expan
 der property:\nevery eigenvalue of $A_{|\\mathcal{X}}$ is $O(\\sqrt{\\math
 cal{L}})$.\nIt follows immediately that\,  for any bounded\n  $f\,g:\\math
 bf{N}\\to \\mathbb{C}$\,\n  \\begin{equation}\\label{eq:bamidyar}\n    \\f
 rac{1}{N \\mathcal{L}} \\Big|\n  \\sum_{\\substack{n \\in \\mathbf{N} \\\\
  p \\in \\mathbf{P} : p | n}} f(n) \\overline{g(n\\pm p)} -\n  \\sum_{\\su
 bstack{n \\in \\mathbf{N} \\\\ p \\in \\mathbf{P}}} \\frac{f(n)\\overline{
 g(n\\pm p)}}{p} \\Big| =\n  O\\Big(\\frac{1}{\\sqrt{\\mathcal{L}}}\\Big).\
 n  \\end{equation}\n  This bound is sharp up to constant factors.\n\n  Spe
 cializing the above bound to $f(n) = g(n) = \\lambda(n)$ with $\\lambda(n)
 $ the Liouville function\, and using a result in (Matom\\"aki-Radziwi\\l\\
 l-Tao\, 2015)\,\n  we obtain\n  \\begin{equation}\\label{eq:cruciator}\n  
   \\frac{1}{\\log x} \\sum_{n\\leq x} \\frac{\\lambda(n) \\lambda(n+1)}{n}
  =\n    O\\left(\\frac{1}{\\sqrt{\\log \\log x}}\\right)\,\n    \\end{equa
 tion}\n  improving on a result of Tao's. Tao's result relied on a differen
 t\n  approach (entropy decrement)\, requiring $H\\leq (\\log N)^{o(1)}$\n 
  and leading to weaker bounds.\n\n  We also prove the stronger statement\n
   that Chowla's conjecture is true at almost all scales\n  with an error t
 erm as in (\\ref{eq:cruciator})\,\n  improving on a result by Tao and Tera
 v\\"ainen.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20201001T190000Z
DTEND:20201001T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/6/">Convergent and divergent series of integers 
 with missing digits</a>\nby Mel Nathanson (CUNY) as part of New York Numbe
 r Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Hopkins (Saint Peter's University)
DTSTART:20201008T190000Z
DTEND:20201008T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/8/">Rank\, crank\, and mex: New connections betw
 een partition statistics</a>\nby Brian Hopkins (Saint Peter's University) 
 as part of New York Number Theory Seminar\n\n\nAbstract\nAbout 100 years a
 go\, Ramanujan proved certain patterns in the counts of integer partitions
 \, but not in a way that fully ``explained'' them.   A young Freeman Dyson
  wrote in a somewhat cheeky 1944 article that a new notion he called the r
 ank of a partition explained some of the patterns of partition counts---wi
 thout proving it---and that something called the crank should explain the 
 rest---without defining crank!  Everything he proposed was eventually prov
 en by others to be correct.  The new part of the story is recent work of t
 he speaker and James Sellers that explains crank\, whose definition is som
 ewhat tricky\, in terms of the minimal excluded part (``mex'') of integer 
 partitions. This allows us to improve and simplify a recent result in the 
 Ramanujan Journal.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20201015T190000Z
DTEND:20201015T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/9/">Dirichlet series of integers with missing di
 gits</a>\nby Mel Nathanson (CUNY) as part of New York Number Theory Semina
 r\n\n\nAbstract\nFor certain sequences $A$ of positive integers with missi
 ng $g$-adic digits\, the Dirichlet series $F_A(s) = \\sum_{a\\in A} a^{-s}
 $ has abscissa of convergence $\\sigma_c < 1$.  The number $\\sigma_c$ is 
 computed.  This generalizes and strengthens a classical theorem  of Kempne
 r on the convergence of the sum of the reciprocals of a sequence of intege
 rs with missing decimal digits.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Beck (San Francisco State University)
DTSTART:20201029T190000Z
DTEND:20201029T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/10
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/10/">The arithmetic of Coxeter permutahedra</a>\
 nby Matthias Beck (San Francisco State University) as part of New York Num
 ber Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Beck (San Francisco State University)
DTSTART:20201029T190000Z
DTEND:20201029T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/11/">The arithmetic of Coxeter permutahedra</a>\
 nby Matthias Beck (San Francisco State University) as part of New York Num
 ber Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Beck (San Francisco State University)
DTSTART:20201029T190000Z
DTEND:20201029T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/12/">The arithmetic of Coxeter permutahedra</a>\
 nby Matthias Beck (San Francisco State University) as part of New York Num
 ber Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Beck (San Francisco State University)
DTSTART:20201029T190000Z
DTEND:20201029T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/13
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/13/">The arithmetic of Coxeter permutahedra</a>\
 nby Matthias Beck (San Francisco State University) as part of New York Num
 ber Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emma Bailey (CUNY Graduate Center)
DTSTART:20201112T200000Z
DTEND:20201112T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/14
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/14/">L-functions and random matrix theory</a>\nb
 y Emma Bailey (CUNY Graduate Center) as part of New York Number Theory Sem
 inar\n\n\nAbstract\nI will review the (conjectured but well evidenced) con
 nection between families of $L$-functions and characteristic polynomials o
 f random matrices. The canonical example connects the Riemann zeta functio
 n with unitary matrices. I will then explain some recent results pertainin
 g to various moments of interest (both of characteristic polynomials and o
 f $L$-functions).  Our work has further connections to log-correlated fiel
 ds and combinatorics.   This is joint work with Jon Keating and Theo Assio
 tis.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Iosevich (University of Rochester)
DTSTART:20201105T200000Z
DTEND:20201105T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/15
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/15/">Discrete energy and applications to Erdos t
 ype problems</a>\nby Alex Iosevich (University of Rochester) as part of Ne
 w York Number Theory Seminar\n\n\nAbstract\nWe are going to survey a simpl
 e conversion mechanism that allows one to deduce certain quantitative disc
 rete results from their continuous analogs.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNYMinimal bases in additive number theory)
DTSTART:20201119T200000Z
DTEND:20201119T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/16
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/16/">Minimal bases in additive number theory</a>
 \nby Mel Nathanson (CUNYMinimal bases in additive number theory) as part o
 f New York Number Theory Seminar\n\n\nAbstract\nThe set $A$ of nonnegative
  integers is an \\emph{asymptotic basis of order $h$} if every \n sufficie
 ntly large integer can be represented as the sum of $h$ elements of $A$.  
 \n An asymptotic basis of order $h$ is \\emph{minimal} if no proper subset
  of $A$ \n is an asymptotic basis of order $h$.  Minimal asymptotic bases 
 are extremal objects \n in additive number theory\, and related to the con
 jecture of Erd\\H os and Tur\\' an that \n the representation function of 
 an asymptotic basis must be unbounded.  \n This talk describes the constru
 ction of a new class of minimal asymptotic bases.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20201203T200000Z
DTEND:20201203T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/17
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/17/">Sidon sets and perturbations</a>\nby Mel Na
 thanson (CUNY) as part of New York Number Theory Seminar\n\n\nAbstract\nA 
 subset $A$ of an additive abelian group is an $h$-Sidon set if every eleme
 nt in the $h$-fold sumset \n$hA$ has a unique representation as the sum of
  $h$ not necessarily distinct elements of $A$.   \nLet $\\mathbf{F}$ be a 
 field of characteristic 0 with a nontrivial absolute value\, \nand let $A 
 = \\{a_i :i \\in \\mathbf{N} \\}$ and $B = \\{b_i :i \\in \\mathbf{N} \\}$
  be subsets of $\\mathbf{F}$.\nLet $\\varepsilon =  \\{  \\varepsilon_i:i 
 \\in \\mathbf{N} \\}$\,  where $\\varepsilon_i > 0$ for all $i \\in \\math
 bf{N}$.\nThe set $B$ is an $\\varepsilon$-perturbation of  $A$ \nif $|b_i-
 a_i| < \\varepsilon_i$ for all $i \\in \\mathbf{N}$.\nIt is proved that\, 
 for every $\\varepsilon =   \\{  \\varepsilon_i:i \\in \\mathbf{N} \\}$ wi
 th $\\varepsilon_i > 0$\,   \nevery set $A = \\{a_i :i \\in \\mathbf{N} \\
 }$  has an $\\varepsilon$-perturbation $B$ \nthat is an $h$-Sidon set.  Th
 is result extends to sets of vectors \nin $\\mbF^n$.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20201210T200000Z
DTEND:20201210T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/18
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/18/">Multiplicative representations of integers 
 and Ramsey's theorem</a>\nby Mel Nathanson (CUNY) as part of New York Numb
 er Theory Seminar\n\n\nAbstract\nLet $\\mathcal{B} = (B_1\,\\ldots\, B_h)$
  be an $h$-tuple of sets of positive integers.  \nLet $g_{\\mathcal{B}}(n)
 $ count the number of multiplicative representations of $n$ \nin the form 
 $n = b_1\\cdots b_h$\, \nwhere $b_i \\in B_i$ for all $i \\in \\{1\,\\ldot
 s\, h\\}$.  \nIt is proved that $\\liminf_{n\\rightarrow \\infty} g_{\\mat
 hcal{B}}(n) \\geq 2$ \nimplies $\\limsup_{n\\rightarrow \\infty} g_{\\math
 cal{B}}(n) = \\infty$.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arindam Biswas (Technion\, Israel)
DTSTART:20201217T200000Z
DTEND:20201217T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/19
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/19/">Direct and inverse problems related to mini
 mal complements</a>\nby Arindam Biswas (Technion\, Israel) as part of New 
 York Number Theory Seminar\n\n\nAbstract\nMinimal complements of subsets o
 f groups have been popular objects of study in recent times. The notion wa
 s introduced by Nathanson in 2011.  The past few years have seen a flurry 
 of activities  focussing on the existence and nonexistence of minimal  com
 plements. In this talk\, we shall speak about the direct and the inverse p
 roblems elated to minimal complements and discuss some  of the recent resu
 lts addressing some of these problems.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Kaplan (University of California\, Irvine)
DTSTART:20210128T200000Z
DTEND:20210128T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/20
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/20/">Counting subrings of Z^n</a>\nby Nathan Kap
 lan (University of California\, Irvine) as part of New York Number Theory 
 Seminar\n\n\nAbstract\nHow many subgroups of $\\mathbb{Z}^n$ have index at
  most $X$?  How many of these subgroups are also subrings?  We can give an
  asymptotic answer to the first question by computing the ‘subgroup zeta
  function’ of $\\mathbb{Z}^n$.  For the second question\, we only know a
 n asymptotic answer for small $n$ because the ‘subring zeta function’ 
 of $\\mathbb{Z}^n$ is much harder to compute.  It is not difficult to show
  that it is enough to understand the number of subrings of prime power ind
 ex.  Let $f_n(p^e)$ be the number of subrings of $\\mathbb{Z}^n$ with inde
 x $p^e$.  When $n$ and $e$ are fixed\, how does $f_n(p^e)$ vary as a funct
 ion of p?  We will discuss the quotient $\\mathbb{Z}^n/L$ where $L$ is a `
 random’ subgroup or subring of $\\mathbb{Z}^n$.  We will also see connec
 tions to counting orders in number fields.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshiharu Kohayakawa (University of Sao Paulo\, Brazil)
DTSTART:20200204T200000Z
DTEND:20200204T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/21
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/21/">The number of Sidon sets and an application
  to an extremal problem for random sets of integers</a>\nby Yoshiharu Koha
 yakawa (University of Sao Paulo\, Brazil) as part of New York Number Theor
 y Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshiharu Kohayakawa (University of Sao Paulo\, Brazil)
DTSTART:20200204T200000Z
DTEND:20200204T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/22
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/22/">The number of Sidon sets and an application
  to an extremal problem for random sets of integers</a>\nby Yoshiharu Koha
 yakawa (University of Sao Paulo\, Brazil) as part of New York Number Theor
 y Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshiharu Kohayakawa (University of Sao Paulo\, Brazil)
DTSTART:20200204T200000Z
DTEND:20200204T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/23
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/23/">The number of Sidon sets and an application
  to an extremal problem for random sets of integers</a>\nby Yoshiharu Koha
 yakawa (University of Sao Paulo\, Brazil) as part of New York Number Theor
 y Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshiharu Kohayakawa (University of Sao Paulo\, Brazil)
DTSTART:20210204T200000Z
DTEND:20210204T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/24
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/24/">The number of Sidon sets and an extremal pr
 oblem for random sets of integers</a>\nby Yoshiharu Kohayakawa (University
  of Sao Paulo\, Brazil) as part of New York Number Theory Seminar\n\n\nAbs
 tract\nA set of integers is a Sidon set if the pairwise sums of its elemen
 ts are all distinct. We discuss the number of Sidon sets contained in $[n]
 =\\{1\,\\dots\,n\\}$.  As an application\, we investigate random sets of i
 ntegers $R\\subset[n]$ of a given\ncardinality $m=m(n)$ and study $F(R)$\,
  the typical maximal cardinality of a Sidon set contained in $R$.  The beh
 aviour of $F(R)$ as $m=m(n)$ varies is somewhat unexpected\,  presenting t
 wo points of ``phase transition.'' We shall also briefly discuss the case 
 in which the random set $R$ is\nan infinite random subset of the set of na
 tural numbers\, according to\na natural model\; that is\, we shall discuss
  infinite Sidon sets\ncontained in certain infinite random sets of integer
 s.  Finally\, we shall mention extensions to $B_h$-sets. Joint work with D
 . Dellamonica Jr.\,  S. J. Lee\, C. G. Moreira\, V. R\\"odl\, and W. Samot
 ij.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20210211T200000Z
DTEND:20210211T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/25
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/25/">Sidon sets for linear forms</a>\nby Mel Nat
 hanson (CUNY) as part of New York Number Theory Seminar\n\n\nAbstract\nLet
  $\\varphi(x_1\,\\ldots\, x_h) =  c_1 x_1 + \\cdots + c_h x_h $ be a linea
 r form \nwith coefficients in a field $\\mathbf{F}$\, and let $V$ be a vec
 tor space over $\\mathbf{F}$.  \nA nonempty subset $A$  of $V$ is a \n$\\v
 arphi$-Sidon set if\, \nfor all $h$-tuples $(a_1\,\\ldots\, a_h) \\in A^h$
  and $ (a'_1\,\\ldots\, a'_h) \\in A^h$\,   \nthe relation  \n$\\varphi(a_
 1\,\\ldots\, a_h) = \\varphi(a'_1\,\\ldots\, a'_h) \n$ implies $(a_1\,\\ld
 ots\, a_h) = (a'_1\,\\ldots\, a'_h)$.  \nThere exist infinite Sidon sets f
 or the linear form $\\varphi$ if and only if the set of coefficients of $\
 \varphi$ has distinct subset sums.  \nIn a normed vector space with $\\var
 phi$-Sidon sets\, \nevery infinite sequence of vectors is \nasymptotic to 
 a $\\varphi$-Sidon set of vectors.\nResults on $p$-adic perturbations of $
 \\varphi$-Sidon sets of integers and bounds on the growth \nof $\\varphi$-
 Sidon sets of  integers are also obtained.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Miller (Williams College)
DTSTART:20210218T200000Z
DTEND:20210218T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/26
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/26/">How low can we go? Understanding zeros of L
 -functions near the central point</a>\nby Steve Miller (Williams College) 
 as part of New York Number Theory Seminar\n\n\nAbstract\nSpacings between 
 zeros of $L$-functions occur throughout modern number theory\, \n  such as
  in Chebyshev's bias and the class number problem.  Montgomery and Dyson \
 n  discovered in the 1970's that random matrix theory models these spacing
 s. \n  The initial models are insensitive to finitely many zeros\, and thu
 s miss the behavior \n  near the central point. This is the most arithmeti
 cally interesting place\; for example\, \n  the Birch and Swinnerton-Dyer 
 conjecture states that the rank of the Mordell-Weil group \n  equals the o
 rder of vanishing of the associated $L$-function there. To investigate the
  zeros \n  near the central point\, Katz and Sarnak developed a new statis
 tic\, the $n$-level density\; \n  one application is to bound the average 
 order of vanishing at the central point for a given \n  family of $L$-func
 tions by an integral of a weight against some test function $\\phi$. After
  \n  reviewing early results in the subject and describing how these stati
 stics are computed\, \n  we discuss as time permits recent progress and on
 going work on several questions. \n  We describe the Excised Orthogonal En
 sembles and their success in explaining the \n  observed repulsion of zero
 s near the central point for families of $L$-functions\, \n  and efforts t
 o extend to other families. We discuss an alternative to the Katz-Sarnak \
 n  expansion for the $n$-level density which facilitate comparisons with r
 andom matrix theory\,\n  and applications to improving the bounds on high 
 vanishing at the central point. \n This work is joint with numerous summer
  REU students.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillermo Mantilla Soler (Universidad Konrad Lorenz\, Bogota\, Col
 ombia)
DTSTART:20210304T200000Z
DTEND:20210304T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/27
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/27/">Arithmetic equivalence and classification o
 f number fields  via the integral trace</a>\nby Guillermo Mantilla Soler (
 Universidad Konrad Lorenz\, Bogota\, Colombia) as part of New York Number 
 Theory Seminar\n\n\nAbstract\nTwo number fields are called arithmetically 
 equivalent if their Dedekind zeta functions coincide. Thanks to the work o
 f R. Perlis\, we know that much of the arithmetic information of a number 
 field is encoded in its zeta function. By interpreting the Dedekind zeta f
 unction as the Artin $L$-function attached  to a certain Galois representa
 tion of $G_{\\mathbb{Q}}$\, we see how all the information mentioned above
  can be recovered in a very natural way.  Moreover\, we will show how this
  approach leads to new results. Going further\, we will see how from zeta 
 functions we can connect with trace forms and we will explore the classifi
 cation power of integral trace forms.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thai Hoang Le (University of Mississippi)
DTSTART:20210311T200000Z
DTEND:20210311T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/28
DESCRIPTION:by Thai Hoang Le (University of Mississippi) as part of New Yo
 rk Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Bienvenue (Universite Claude Bernard Lyon)
DTSTART:20210318T190000Z
DTEND:20210318T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/29
DESCRIPTION:by Pierre Bienvenue (Universite Claude Bernard Lyon) as part o
 f New York Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brandon Hanson (University of Georgia)
DTSTART:20210325T190000Z
DTEND:20210325T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/30
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/30/">Sum-product and convexity</a>\nby Brandon H
 anson (University of Georgia) as part of New York Number Theory Seminar\n\
 n\nAbstract\nA recurring theme in number theory is that addition and multi
 plication do not mix well. \n  A combinatorial take on this theme is the E
 rdos-Szemeredi sum-product problem\, \n  which says that a finite set of n
 umbers (in an appropriate field) must have either a large \n sumset or a l
 arge product set.  Depending  on  the  field  one  is  working  in\,  ther
 e  are  \n different  tools  which  are useful for attacking this problem.
   Over the real numbers\, \n convexity is one such tool.  In this talk\, I
  will discuss the sum-product problem and its\n  variants\, and progress t
 hat has been made on it.  I will then discuss some elementary \n methods o
 f using convexity to obtain some new results.  This will all be based on r
 ecent \n and ongoing work with P. Bradshaw\, O. Roche-Newton\, and M. Rudn
 ev.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgis Petridis (University of Georgia)
DTSTART:20210225T200000Z
DTEND:20210225T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/31
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/31/">Almost eventowns</a>\nby Giorgis Petridis (
 University of Georgia) as part of New York Number Theory Seminar\n\n\nAbst
 ract\nLet $n$ be an even positive integer. An eventown is a collection of 
 subsets of $\\{1\,\\ldots\,n\\}$ \n with the property that every two not n
 ecessarily distinct elements have even intersection. \n Berlekamp determin
 ed the largest size of an even town in the 1960s\,  answering \n a questio
 n of Erd\\H{o}s. In line with other Erd\\H{o}s questions\, Ahmadi and Moha
 mmadian \n made a conjecture on the size of the largest size of an almost 
 eventown: \n a family of subsets of $\\{1\, …\,n\\}$ with the property t
 hat among any three elements \n there are two with even intersection. In t
 his talk we will prove the conjecture and \n mention other related results
  proved in joint work with Ali Mohammadi.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Trudgian (UNSW Canberra at the Australian Defense Force Academ
 y)
DTSTART:20210401T190000Z
DTEND:20210401T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/32
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/32/">Verifying the Riemann hypothesis to a new h
 eight</a>\nby Tim Trudgian (UNSW Canberra at the Australian Defense Force 
 Academy) as part of New York Number Theory Seminar\n\n\nAbstract\nSadly\, 
 I won't have time to prove the Riemann hypothesis in this talk. However\, 
 I do hope to outline recent work in a record partial-verification of RH. T
 his is joint work with Dave Platt\, in Bristol\, UK.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (Lehman College (CUNY))
DTSTART:20210408T190000Z
DTEND:20210408T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/33
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/33/">Inverse problems for Sidon sets</a>\nby Mel
  Nathanson (Lehman College (CUNY)) as part of New York Number Theory Semin
 ar\n\n\nAbstract\nThe Riemann zeta function is an important function in nu
 mber theory.  It captures \n arithmetic properties of the integers.  Riema
 nn zeta values and multiple zeta values\, \n defined by Euler and Zagier\,
  can be expressed in terms of iterated path integrals. \n Those iterated i
 ntegrals a quite special. They have a very good meaning in terms \n of alg
 ebraic geometry. More precisely\, the underlying algebraic variety is the 
 Deligne-Mumford  comactification of the moduli space of curves of genus ze
 ro. I will explain intuitively what  that means. \n\n If we adjoin $\\sqrt
 {2}$ or $i$ to the integers\, then the corresponding zeta functions are ca
 lled Dedekind zeta functions.  My main interest in this area is related to
  the Dedekind \n zeta functions. I express them in terms of a higher dimen
 sional iterated integrals\, \n which I call iterated integrals on membrane
 s. Using this tool\, one can define multiple \n Dedekind zeta values as a 
 number theoretic  analogue of multiple zeta values and \n relate them to a
 lgebraic geometry and motives.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (Lehman College (CUNY))
DTSTART:20210930T190000Z
DTEND:20210930T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/34
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/34/">Egyptian fractions and the Muirhead-Rado in
 equality</a>\nby Mel Nathanson (Lehman College (CUNY)) as part of New York
  Number Theory Seminar\n\n\nAbstract\nFibonacci proved that a greedy algor
 ithm constructs a representation of a positive rational number as the sum 
 of a finite number of Egyptian fractions.   Sylvester used a greedy approx
 imation algorithm to construct an increasing sequence of positive integers
  $a_1\, a_2\, \\ldots$ such that $\\sum_{i=1}^n 1/a_i < 1$ and\, if $b_1\,
  \\ldots\, b_n$ is any increasing sequence of positive integers  such that
  $\\sum_{i=1}^n 1/a_i \\leq \\sum_{i=1}^n 1/b_i < 1$\, then $a_i = b_i$ fo
 r all $i = 1\,\\ldots\, n$.  This result (conjectured by Kellogg and prove
 d\, or believed to have been proved\, by several mathematicians) extends t
 o Egyptian fraction approximations of other positive rational numbers.  Th
 e proof uses an application of the Muirhead inequality first observed by S
 oundararajan.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (Lehman College (CUNY))
DTSTART:20211007T190000Z
DTEND:20211007T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/35
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/35/">Problems and results on Egyptian fractions<
 /a>\nby Mel Nathanson (Lehman College (CUNY)) as part of New York Number T
 heory Seminar\n\n\nAbstract\nSome problems related to the theorem that Syl
 vester's sequence (defined recursively by $a_0=1$\, $a_{n+1} =  1 +\\prod_
 {i=1}^n a_i $) gives the best underapproximation to 1.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Lebowitz-Lockard (Philadelphia)
DTSTART:20211014T190000Z
DTEND:20211014T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/36
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/36/">Binary Egyptian fractions</a>\nby Noah Lebo
 witz-Lockard (Philadelphia) as part of New York Number Theory Seminar\n\n\
 nAbstract\nDefine a ``unit fraction" as a fraction with numerator $1$. We 
 say that an ``Egyptian fraction representation" of a number is a sum of di
 stinct unit fractions. In this talk\, we discuss the history of these repr
 esentations\, starting with their origins on an ancient Egyptian papyrus. 
 In particular\, we look at several recent results related to binary Egypti
 an fractions\, which are sums of two unit fractions. Most of these results
  relate to how often a given rational number has a binary Egyptian fractio
 n representation.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Russell Jay Hendel (Towson University)
DTSTART:20211021T190000Z
DTEND:20211021T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/37
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/37/">Limiting behavior of resistances in triangu
 lar graphs</a>\nby Russell Jay Hendel (Towson University) as part of New Y
 ork Number Theory Seminar\n\n\nAbstract\nCertain electric circuit can be p
 erceived as   undirected graphs whose edges are 1-ohm resistances. \nOhm's
  law allows calculation of equivalent single resistances   \nbetween     t
 wo arbitrary points on the electric circuit. \nFor graphs embeddable in th
 e plane\,      there are four functions that allow the implementation of O
 hm's law and \ncalculation     of equivalent resistances.   \nConsequently
 \, no knowledge of electrical engineering is needed   for this talk. \nIt 
 is a talk about interesting properties of graphs \nwhose edges have specif
 ic     resistances and \nwhich allow reduction to other graphs. \nInterest
 ing results are possible    when the underlying graph \nbelongs to certain
  families. For example  \nthe resistance  between two corners \n(degree-tw
 o vertices) of a graph on $n$\nedges consisting of $n-2$ triangles    arra
 nged in a line is \n$\\frac{n-1}{5}+ \\frac{4}{5} \\frac{F_{n-1}}{L_{n-1}}
 $\nwith $F$ and $L$ representing the Fibonacci and Lucas   numbers respect
 ively\n\nThis presentation explores \ntriangular graphs of $n$ rows of equ
 ilateral triangles. \nThese triangular graphs were mentioned in passing \n
 in one paper with a conjecture on the equivalent resistance between \ntwo 
 corners. In this presentation we present new computation methods\, \nallow
 ing reviewing more data. It turns out that the \nlimiting behavior of thes
 e $n$-row triangular grids \n(as $n$ goes to infinity) has unexpected simp
 ly described behavior: \nThe  sides of individual triangles are conjecture
 d to \nasymptotically equal products of basically \nfractional linear tran
 sformations and $e^{-1}.$ \nWe also introduce new proof methods based on a
  simple \n$verification$ method.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20211028T190000Z
DTEND:20211028T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/38
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/38/">Some results in elementary number theory</a
 >\nby Mel Nathanson (CUNY) as part of New York Number Theory Seminar\n\n\n
 Abstract\nVariations on Euler's totient function and associated arithmetic
  identities.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ajmain Yamin (CUNY Graduate Center)
DTSTART:20211104T190000Z
DTEND:20211104T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/39
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/39/">Complete regular dessins</a>\nby Ajmain Yam
 in (CUNY Graduate Center) as part of New York Number Theory Seminar\n\n\nA
 bstract\nA map is an embedding of a graph into a topological surface such 
 that the complement of the image is a union of topological disks.  A regul
 ar map is one that exhibits the maximal amount of symmetry\, that is\, the
  automorphism group of the map acts transitively on flags. In 1985\, James
  and Jones classified complete regular maps\, i.e. regular maps where the 
 underlying graph is complete. The first goal of my talk is to give a brief
  overview of this story and in particular review Biggs' construction of co
 mplete regular maps as Cayley maps associated to finite fields. \n\n Given
  any map\, one obtains a dessin by taking the bipartification of the under
 lying graph and embedding that into the surface. Dessins associated to com
 plete regular maps will be called \\emph{complete regular dessins} in my t
 alk. After reviewing the basic theory of dessins\, I will introduce the ma
 in question of my talk: can one obtain an explicit model for the Riemann s
 urface underlying a complete regular dessin as an algebraic curve over $\\
 mathbb{\\overline{Q}}$? What about the its Belyi function as a rational ma
 p down to $\\mathbb{P}^1(\\mathbb{C})$? In this talk I will explain how to
  obtain such an affine model for the complete regular dessin $K_5$ embedde
 d in the torus.  In the process\, we will be led to consider airithmetic i
 n the Gaussian integers\, uniformization of elliptic curves\, Galois theor
 y of function fields and Weierstrass $\\wp$ functions.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laszlo Toth (University of  Pecs\, Hungary)
DTSTART:20211111T200000Z
DTEND:20211111T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/40
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/40/">Menon's identity: proofs\, generalizations 
 and analogs</a>\nby Laszlo Toth (University of  Pecs\, Hungary) as part of
  New York Number Theory Seminar\n\n\nAbstract\nMenon's identity states tha
 t for every positive integer $n$ one has \n$\\sum (a-1\,n) = \\varphi(n) \
 \tau(n)$\, where $a$ runs through a reduced residue system (mod $n$)\, \n$
 (a-1\,n)$ stands for the greatest common divisor of $a-1$ and $n$\,\n$\\va
 rphi(n)$ is Euler's totient function and $\\tau(n)$ is the number of divis
 ors of $n$. It is named after Puliyakot Kesava Menon\, \nwho proved it in 
 1965. Menon's identity has been the subject of many research papers\, also
  in the last years.\n\nIn this talk I will present different methods to pr
 ove this identity\, and will point out those that I could not identify in 
 the literature. \nThen I will survey the directions to obtain generalizati
 ons and analogs. I will also present some of my own general identities.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Cohen (MIT)
DTSTART:20211202T200000Z
DTEND:20211202T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/41
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/41/">An optimal inverse theorem for tensors over
  large fields</a>\nby Alex Cohen (MIT) as part of New York Number Theory S
 eminar\n\n\nAbstract\nA degree $k$ tensor $T$ over a finite field $\\mathb
 f{F}_q$ can be viewed as a multilinear function  $\\mathbf{F}_q^n \\times 
 \\dots \\times \\mathbf{F}_q^n \\to \\mathbf{F}_q.$\n The analytic rank of
  $T$ takes a value between $0$ and $n$\, and is small if the output distri
 bution is far from uniform---in some sense\, it is a measure of how random
 ly $T$ behaves. On the other hand\, the partition rank of $T$ is small if 
 $T$ can be decomposed into a few highly structured pieces. It is not hard 
 to show that the analytic rank is less than the partition rank---or in oth
 er words\, if $T$ is highly structured\, then it does not \n  behave rando
 mly. In 2008 Green and Tao proved a qualitative inverse theorem stating th
 at  the partition rank is bounded by some (large) function of the analytic
  rank. We prove an \n  optimal inverse theorem: Analytic rank and partitio
 n rank are equivalent up to linear factors  (over large enough fields). Th
 is theorem allows us to explain any lack of randomness in $T$  by the pres
 ence of structure. Our techniques are very different from the usual method
 s  in this area.  We rely on algebraic geometry rather than additive combi
 natorics. This is joint work with Guy Moshkovitz.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunping Jiang (Queens College (CUNY))
DTSTART:20211209T200000Z
DTEND:20211209T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/42
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/42/">Ergodic theory motivated by Sarnak's conjec
 ture in number theory</a>\nby Yunping Jiang (Queens College (CUNY)) as par
 t of New York Number Theory Seminar\n\n\nAbstract\nSarnak's conjecture bri
 ngs together number theory\, ergodic theory\, and dynamical systems. \n Mo
 tivated by this conjecture\, we started a study in ergodic theory about or
 ders of oscillating \n sequences and minimally mean attractable (MMA) and 
 minimally mean-L-stable (MMLS) flows. \n The Mobius function in number the
 ory gives an example of oscillating sequences of order $d$ \n for all $d>0
 $. From the dynamical systems point of view\, we found another class of ex
 amples \n of oscillating sequences of order  $d$ for all $d>0$. All equico
 ntinuous flows are MMA and MMLA. \n I will talk about two non-trivial exam
 ples of MMA and MMLS flows that are not equicontinuous. \n One is a Denjoy
  counterexample in circle homeomorphisms and the other is an infinitely \n
  renormalizable one-dimensional map. I will show that all oscillation sequ
 ences of order  1\n are linearly disjoint with (or meanly orthogonal to) M
 MA and MMLA flows. Thus\, we confirm \n Sarnak's conjecture for a large cl
 ass of zero topological entropy flows. For oscillating sequences \n of ord
 er $d>1$\, I will show that they are linearly disjoint from all affine dis
 tal flows on the \n $d$-torus. One of the consequences is that Sarnak's co
 njecture holds for all zero topological \n entropy affine flows on the $d$
 -torus and some nonlinear zero topological entropy flows \n on the $d$-tor
 us. I will also review some current developments after our work on this to
 pic \n about flows with the quasi-discrete spectrum and the Thue-Morse seq
 uence\, which has zero \n topological entropy and small Gowers norms and t
 hus is a higher-order oscillating sequence.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guy Moshkovitz (Baruch College (CUNY))
DTSTART:20211216T200000Z
DTEND:20211216T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/43
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/43/">An optimal inverse theorem for tensors over
  large fields II</a>\nby Guy Moshkovitz (Baruch College (CUNY)) as part of
  New York Number Theory Seminar\n\n\nAbstract\nWe will give more details a
 bout our recent proof\, joint with Alex Cohen\, showing that the partition
  rank and the analytic rank of tensors are equal up to a constant\, over f
 inite fields of every characteristic and of mildly large size (independent
  of the number of variables). Proving the equivalence between these two qu
 antities is a central question in additive combinatorics\, the main questi
 on in the "bias implies low rank" line of work\, and corresponds to the fi
 rst non-trivial case of the Polynomial Gowers Inverse conjecture.\n\nThe t
 alk will be a continuation of Alex Cohen's talk from December 2nd\, though
  I will aim for it to be mostly self-contained.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220203T200000Z
DTEND:20220203T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/44
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/44/">Best underapproximation by Egyptian fractio
 ns</a>\nby Mel Nathanson (CUNY) as part of New York Number Theory Seminar\
 n\n\nAbstract\nAn increasing sequence $(x_i)_{i=1}^n$ of positive integers
  is an  $n$-term Egyptian \nunderapproximation of $\\theta \\in (0\,1]$ if
  $\\sum_{i=1}^n \\frac{1}{x_i}  < \\theta$.\nA greedy algorithm constructs
  an $n$-term underapproximation of $\\theta$. For some but not all  number
 s $\\theta$\, the greedy algorithm gives a unique best $n$-term  underappr
 oximation for all $n \\geq 1$.  An infinite set of rational numbers is con
 structed  for which the greedy underapproximations are best\, and numbers 
 for which the greedy algorithm is not best are also studied.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220210T200000Z
DTEND:20220210T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/45
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/45/">A chapter on the theory of equations: Desca
 rtes\, Budan-Fourier\, and Sturm</a>\nby Mel Nathanson (CUNY) as part of N
 ew York Number Theory Seminar\n\n\nAbstract\nA discussion of the theorems 
 of Descartes\, Budan-Fourier\, and Sturm on the number of positive solutio
 ns a polynomials equation  in an interval $(a\,b]$.  This is in preparatio
 n for a discussion of Tarski's extension of Sturm's theorem and the Tarski
 -Seidenberg decidability result.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josiah Sugarman (CUNY Graduate Center)
DTSTART:20220217T200000Z
DTEND:20220217T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/46
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/46/">The spectrum of the quaquaversal operator i
 s real</a>\nby Josiah Sugarman (CUNY Graduate Center) as part of New York 
 Number Theory Seminar\n\n\nAbstract\nIn the mid 90s Conway and Radin intro
 duced the Quaquaversal Tiling. It is a hierarchical tiling of three dimens
 ional space that exhibits statistical rotational symmetry\, in the sense t
 hat the distribution of tiles chosen uniformly at random from a large sphe
 re has a nearly uniform distribution of orientations. Any hierarchical til
 ing has an associated operator whose spectrum can be analyzed to study the
  distribution of orientations in a large sample. Radin and Conway showed t
 hat 1 has multiplicity 1 in the spectrum of this operator to show that the
  operator exhibited statistical rotational symmetry. By numerically analyz
 ing the spectrum of this operator Draco\, Sadun\, and Wieren found eigenva
 lues very close to 1 and concluded that the rate with which the distributi
 on approaches uniformity is fairly slow\, mentioning that a galactic scale
  sample of a material with this crystal structure at the molecular level w
 ould exhibit noticeable anisotropy. Bourgain and Gamburd proved\, on the o
 ther hand\, that a certain class of operators including this one have a no
 nzero gap between 1 and the second largest eigenvalue\, concluding that th
 e distribution must approach uniformity at an exponential rate.\n\nIn this
  talk I will introduce hierarchical tilings\, discuss results similar to t
 hose above\, and prove that the spectrum of this operator is real. Answeri
 ng a question of Draco\, Sadun\, and Wieren.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220224T200000Z
DTEND:20220224T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/47
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/47/">The Budan-Fourier theorem and multiplicity 
 matrices of polynomials</a>\nby Mel Nathanson (CUNY) as part of New York N
 umber Theory Seminar\n\n\nAbstract\nThe Budan-Fourier theorem gives an upp
 er bound for the number of zeros \n (with multiplicity) of a polynomial $f
 (x)$ of degree $n$  in the interval $(a\,b]$ \n in terms of the number of 
 sign variations in the vector of derivatives  \n$D_f(\\lambda) = \\left( f
 (\\lambda)\, f'(\\lambda)\, f''(\\lambda)\,\\ldots\, f^{(n)}(\\lambda) \\r
 ight)$ \n  at $\\lambda=a$ and $\\lambda=b$. \n One proof of the Budan-Fou
 rier theorem considers the multiplicity vector \n $M_f(\\lambda) = \\left(
   \\mu_0(\\lambda)\, \\mu_1(\\lambda)\, \\ldots\, \\mu_n(\\lambda) \\right
 )$\, \nwhere $\\mu_j(\\lambda)$ is the multiplicity of $\\lambda$ as a roo
 t \n of the $j$th derivative $f^{(j)}(x)$. \n The inverse problem asks: Wh
 at vectors are the multiplicity vectors of polynomials\, \n and\, given a 
 multiplicity vector\, what are the associated polynomials?  \n The simulta
 neous study of multiplicities of real numbers $\\lambda_1\,\\ldots\, \\lam
 bda_m$   leads to \n multiplicity matrices and their associated polynomial
 s.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220303T200000Z
DTEND:20220303T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/48
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/48/">Multiplicity matrices for polynomials</a>\n
 by Mel Nathanson (CUNY) as part of New York Number Theory Seminar\n\n\nAbs
 tract\nLet $f(x)$ be a polynomial of degree $n$ and let $f^{(j)}(x)$ be th
 e $j$th derivative of $f(x)$.\n Let $\\Lambda = (\\lambda_1\,\\ldots\, \\l
 ambda_m)$ be a strictly increasing sequence of real numbers.  \n For $i \\
 in \\{1\,\\ldots\, m\\}$ and  $j \\in \\{0\,1\,\\ldots\, n\\}$\, \nlet $ \
 \mu_{i\,j}$ be the multiplicity of $\\lambda_i$ as a root \n of the polyno
 mial $f^{(j)}(x)$. For $i \\in \\{1\,\\ldots\, m\\}$ and  $j \\in \\{0\,1\
 ,\\ldots\, n\\}$\, \nlet $ \\mu_{i\,j}$ be the   \n multiplicity of $\\lam
 bda_i$ as a root of the polynomial $f^{(j)}(x)$. \nThe multiplicity matrix
  of $f$  \n with respect to $\\lambda_1\,\\ldots\, \\lambda_m$\nis the $m 
 \\times (n+1)$ matrix  \n$\nM_f(\\Lambda) = \n\\begin{matrix} \\mu_{i\,j} 
   \n\\end{matrix}.\n$\n The problem is to describe the matrices are multip
 licity matrices of polynomials.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Kravitz (Princeton University)
DTSTART:20220310T200000Z
DTEND:20220310T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/49
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/49/">Multiplicity matrices and zeros of polynomi
 als</a>\nby Noah Kravitz (Princeton University) as part of New York Number
  Theory Seminar\n\n\nAbstract\nEarlier this week\, Nathanson introduced th
 e notion of the derivative matrix associated with a polynomial and a finit
 e tuple of points.  He established several properties of derivative matric
 es and proposed a number of appealing open problems.  I will discuss Natha
 nson's setup\, the solutions to a few of his problems\, and partial progre
 ss on natural follow-up questions.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David and Gregory Chudnovsky (NYU  Tandon School of Engineering)
DTSTART:20220317T190000Z
DTEND:20220317T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/50
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/50/">How to break step</a>\nby David and Gregory
  Chudnovsky (NYU  Tandon School of Engineering) as part of New York Number
  Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Itay Londner (Weizmann Institute of Science\, Israel)
DTSTART:20220324T190000Z
DTEND:20220324T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/51
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/51/">Tiling the integers with translates of one 
 tile: the Coven-Meyerowitz tiling conditions</a>\nby Itay Londner (Weizman
 n Institute of Science\, Israel) as part of New York Number Theory Seminar
 \n\n\nAbstract\nIt is well known that if a finite set of integers A tiles 
 the integers by translations\,  then the translation set must be periodic\
 , so that the tiling is equivalent to a factorization  $A+B=Z_M$ of a fini
 te cyclic group. Coven and Meyerowitz (1998) proved that when the tiling p
 eriod $M$ has at most two distinct prime factors\, each of the sets A and 
 B can be replaced by a highly ordered "standard" tiling complement. It is 
 not known whether this behavior persists for all tilings with no restricti
 ons on the number of prime factors of $M$.  In joint work with Izabella La
 ba (UBC)\, we proved that this is true for all sets tiling the integers wi
 th period $M=(pqr)^2$. In my talk I will discuss this problem and introduc
 e  some ideas from the proof.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darij Grinberg (Drexel University)
DTSTART:20220331T190000Z
DTEND:20220331T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/52
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/52/">From the Vandermonde determinant to general
 ized factorials to greedoids and back</a>\nby Darij Grinberg (Drexel Unive
 rsity) as part of New York Number Theory Seminar\n\n\nAbstract\nA classica
 l result in elementary number theory says that the\nproduct of the pairwis
 e \n differences between any given $n + 1$ integers\nis divisible by the p
 roduct of the pairwise \n differences between $0\, 1\,\n...\, n$. In the l
 ate 90s\, Manjul Bhargava developed this much further\n into a theory of "
 generalized factorials\," in particular giving a\nquasi-algorithm for find
 ing \n  the gcd of the products of the pairwise\ndifferences between any $
 n + 1$ integers in $S$\, \n where $n$ is a given number\nand $S$ is a give
 n set of integers.\nIn this talk\, I will explain \n why this is actually 
 a combinatorial\nquestion in disguise\, and how to answer it in full \n ge
 nerality (joint\nwork with Fedor Petrov). The general setting is a finite 
 set $E$\nequipped \n with weights (every element of $E$ has a weight) and 
 distances\n(any two distinct elements \n of $E$ have a distance)\, where t
 he distances\nsatisfy the ultrametric triangle inequality. \n The question
  is then to\nfind a subset of $E$ of given size that has maximum perimeter
  \n (i.e.\, sum\nof weights of elements plus their pairwise distances). It
  turns out\nthat all such \n subsets form a "strong greedoid" -- a type of
  set system\nparticularly adapted to optimization. \n Even better\, this g
 reedoid is a\n"Gaussian elimination greedoid" -- which\, roughly speaking\
 , \n means that\nthe problem reduces to linear algebra.\nIf time allows\, 
 I will briefly discuss \n another closely related\ngreedoid coming from a 
 rather similar problem in phylogenetics. \n (This\nis mostly due to Manson
 \, Moulton\, Semple and Steel.)\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgis Petridis (University of Georgia)
DTSTART:20220414T190000Z
DTEND:20220414T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/54
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/54/">On a question of Yufei Zhao on the interfac
 e of combinatorial geometry</a>\nby Giorgis Petridis (University of Georgi
 a) as part of New York Number Theory Seminar\n\n\nAbstract\nLet $A$ be a f
 inite set of integers and consider the lines determined by pairs of points
  of $P = \\{(a\,a^2) : a \\in A\\}$. The sum set of $A$ is the set of slop
 es of these lines and the product set of $A$ is the set of $y$-intercepts.
  We know from the celebrated sum-product theorem of Erd\\H{o}s and Szemer\
 \'edi that at least one of these sets is much larger than $|A|$. Geometric
 ally\, this observation can be phrased as follows:  infinity cannot both b
 e close to the minimum. Motivated by this observation\, Yufei Zhao asked i
 f this is a manifestation of a more general phenomenon. The goal of the ta
 lk is to answer this in the affirmative.  Joint work with O. Roche-Newton\
 , M. Rudnev and A. Warren.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220407T190000Z
DTEND:20220407T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/55
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/55/">Exponential automorphisms and a problem of 
 Mycielski</a>\nby Mel Nathanson (CUNY) as part of New York Number Theory S
 eminar\n\n\nAbstract\nAn exponential automorphism of $\\mathbf{C}$ is a fu
 nction $\\alpha: \\mathbf{C} \\rightarrow \\mathbf{C}$  such that \n$\\alp
 ha(z + w) = \\alpha(z) + \\alpha(w)$\nand\n$\\alpha\\left( e^z \\right) = 
 e^{\\alpha(z)}$\nfor all $z\, w \\in \\C$. \nMycielski asked if $\\alpha(\
 \log 2) = \\log 2$ and if $\\alpha(2^{1/k}) = 2^{1/k}$ for $k = 2\, 3\, 4$
 .\nThis paper solves these problems.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220428T190000Z
DTEND:20220428T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/56
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/56/">Multiplicity interpolation and the theorems
  of Descartes and Budan-Fourier</a>\nby Mel Nathanson (CUNY) as part of Ne
 w York Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220505T190000Z
DTEND:20220505T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/57
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/57/">Polynomials and the Budan-Fourier theorem</
 a>\nby Mel Nathanson (CUNY) as part of New York Number Theory Seminar\n\nA
 bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220512T190000Z
DTEND:20220512T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/58
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/58/">van der Waerden's proof of Sturm's theorem<
 /a>\nby Mel Nathanson (CUNY) as part of New York Number Theory Seminar\n\n
 \nAbstract\nContinuation of series of talks on classical results for count
 ing the number of real roots of polynomials with real coefficients.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven J. Miller (Williams College)
DTSTART:20220616T190000Z
DTEND:20220616T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/59
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/59/">Benford's Law: Why the IRS might care about
  the 3x+1 problem and zeta(s)</a>\nby Steven J. Miller (Williams College) 
 as part of New York Number Theory Seminar\n\n\nAbstract\nMany systems exhi
 bit a digit bias. For example\, the first digit base 10 of the \n Fibonacc
 i numbers or of $2^n$ equals 1 about 30\\% of the time\; the IRS uses this
  digit bias to detect fraudulent corporate tax returns. This phenomenon\, 
 \n known as Benford's Law\, was first noticed by observing which pages of 
 log tables \n were most worn from age -- it's a good thing there were no c
 alculators 100 years ago!  \n We'll discuss the general theory and applica
 tion\, talk about some fun examples \n (ranging from the $3x+1$ problem to
  the Riemann zeta function to fragmentation \n problems\, as time permits)
 \, and see how the irrationality type of numbers often \n enter into the a
 nalysis (through error terms in equidistribution theorems).\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220623T190000Z
DTEND:20220623T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/60
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/60/">Arithmetic functions and fixed points of po
 wers of permutations</a>\nby Mel Nathanson (CUNY) as part of New York Numb
 er Theory Seminar\n\n\nAbstract\nLet $\\sigma$ be a permutation of a finit
 e or  infinite set $X$\, \nand let $F_X\\left( \\sigma^k\\right)$ count th
 e number of fixed points of \nthe $k$th power of $\\sigma$.\nThis paper de
 scribes how the sequence $\\left(F_X\\left( \\sigma^k\\right) \\right)_{k=
 1}^{\\infty}$ \ndetermines the conjugacy class of the permutation $\\sigma
 $.   \nWe also describe the arithmetic functions that are fixed point sequ
 ences of permutations.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220630T190000Z
DTEND:20220630T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/61
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/61/">Continuity of the roots of a polynomial</a>
 \nby Mel Nathanson (CUNY) as part of New York Number Theory Seminar\n\n\nA
 bstract\nLet $K$ be an algebraically closed field with an absolute value. 
  We give an elementary \n (high school algebra) proof of the classical res
 ult that the roots  of a polynomial \n with coefficients in $K$ are contin
 uous functions  of the coefficients of the polynomial. \n \n Joint work wi
 th David Ross.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David A. Ross (University of Hawaii)
DTSTART:20220707T190000Z
DTEND:20220707T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/62
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/62/">Yet another proof that the roots of a polyn
 omial depend continuously on the coefficients</a>\nby David A. Ross (Unive
 rsity of Hawaii) as part of New York Number Theory Seminar\n\n\nAbstract\n
 The roots of a complex polynomial depend continuously on the coefficients\
 ; that is\, an infinitesimal perturbation of the coefficients results in a
 n infinitesimal  perturbation of the roots.  I'll give a short\, straightf
 orward proof of this using infinitesimals.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220714T190000Z
DTEND:20220714T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/63
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/63/">A nonstandard proof of continuity of affine
  varieties</a>\nby Mel Nathanson (CUNY) as part of New York Number Theory 
 Seminar\n\n\nAbstract\nExtending the classical result \nthat the roots of 
 a polynomial with coefficients in $\\mathbf{C}$ are continuous functions \
 nof the coefficients of the polynomial\, nonstandard analysis is used to p
 rove that  \nif $\\mathcal{F} = \\{f_{\\lambda}  :\\lambda \\in \\Lambda\\
 }$ \nis a set of polynomials in $\\C[t_1\,\\ldots\, t_n]$ and if \n $^*\\m
 athcal{G} = \\{g_{\\lambda}  :\\lambda \\in \\Lambda\\}$ \n is a set of po
 lynomials in $^*\\mathbf{C}_0[t_1\,\\ldots\, t_n]$ \n such that $g_{\\lamb
 da}$ is an infinitesimal deformation of $f_{\\lambda}$ \n for all $\\lambd
 a \\in \\Lambda$\,  \n then the nonstandard affine variety $^*V_0(\\mathca
 l{G})$ \n is an infinitesimal deformation of the affine variety $V(\\mathc
 al{F})$.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O'Bryant (College of Staten Island (CUNY))
DTSTART:20220721T190000Z
DTEND:20220721T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/64
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/64/">On the size of finite Sidon sets</a>\nby Ke
 vin O'Bryant (College of Staten Island (CUNY)) as part of New York Number 
 Theory Seminar\n\n\nAbstract\nIn 2021\, Balogh-Furedi-Roy proved that any 
 Sidon set with $k$ elements has diameter at least $k^2-1.996 k^{3/2}$\, pr
 ovided that $k$ is sufficiently large. We give a method   logically simple
 r than the BFR one\, though trading on the same phenomena\, but substantiv
 ely more involved computationally. The diameter of a $k$ element Sidon set
  is at least $k^2 - 1.99405 k^{3/2}$.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Khan (Johns Hopkins University)
DTSTART:20220728T190000Z
DTEND:20220728T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/65
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/65/">Optimal chaotic dynamics\, the checkmap and
  the 2-sector RSS model</a>\nby Ali Khan (Johns Hopkins University) as par
 t of New York Number Theory Seminar\n\n\nAbstract\nThis talk reports on jo
 int work with Deng\, Fujio and Rajan on optimal chaotic dynamics in mathem
 atical economics revolving around the check-map and a model due to Robinso
 n-Srinivasan-Solow – the RSS model. I hope to emphasize number-theoretic
  considerations\, and touch on earlier work of Nathanson (1976 PAMS)\, and
  more conjecturally with two papers of Lagarias and co-authors (J. London 
 Math. Soc. 1993\; Ill. J. Math.  1994) on the asymmetric tent map.  Geomet
 ry as an engine of analysis will also be emphasized.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220804T190000Z
DTEND:20220804T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/66
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/66/">Patterns in the iteration of an arithmetic 
 function</a>\nby Mel Nathanson (CUNY) as part of New York Number Theory Se
 minar\n\n\nAbstract\nLet $\\Omega$ be a set of positive integers and let $
 S:\\Omega \\rightarrow \\Omega$\n be an arithmetic function.  Let $V = (v_
 i)_{i=1}^n$ be a finite sequence of positive integers.  \nAn integer $m \\
 in \\Omega$ has increasing-decreasing pattern $V$ with respect to $S$ if\,
   \nfor odd integers $i \\in \\{1\,\\ldots\, n\\}$\,  \n\\[\nS^{v_1+ \\cdo
 ts + v_{i-1}}(m) < S^{v_1+ \\cdots + v_{i-1}+1}(m) < \\cdots < S^{v_1+ \\c
 dots + v_{i-1}+v_{i}}(m)\n\\]\nand\, for even  integers $i \\in \\{2\,\\ld
 ots\, n\\}$\, \n\\[\nS^{v_1+ \\cdots + v_{i-1}}(m) > S^{v_1+ \\cdots  +v_{
 i-1}+1}(m) > \\cdots > S^{v_1+ \\cdots  +v_{i-1}+v_i}(m).\n\\]\nThe arithm
 etic function $S$ is wildly increasing-decreasing if\,  \nfor every finite
  sequence $V$ of positive integers\, there exists an integer $m  \\in \\Om
 ega$ \nsuch that $m$ has increasing-decreasing pattern $V$ with respect to
  $S$.  \nThis paper gives a new proof that the Collatz function \nis wildl
 y increasing-decreasing.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20220929T190000Z
DTEND:20220929T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/67
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/67/">Poincare's Positivstellensatz</a>\nby Mel N
 athanson (CUNY) as part of New York Number Theory Seminar\n\n\nAbstract\nP
 oincare's  proof of Poincare's  theorem (H. Poincare\, Sur les equations a
 lgebriques\, Comptes Rendus 97 (1883)\, 1418--1419).\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O'Bryant (CUNY\, College of Staten Island and The Graduate C
 enter)
DTSTART:20221027T190000Z
DTEND:20221027T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/68
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/68/">Finite Sidon sets</a>\nby Kevin O'Bryant (C
 UNY\, College of Staten Island and The Graduate Center) as part of New Yor
 k Number Theory Seminar\n\n\nAbstract\nA finite Sidon set is a set $A = \\
 { a_1 < a_2 < ... < a_k \\}$ with all the sums $a_i+a_j$ with $i \\leq j$ 
 different. We will review the history of Sidon sets before turning \n our 
 attention to recent progress bounding the diameter of $A$ in terms of the 
 size\n of $A$. This talk is suitable for tourists and newcomers to additiv
 e number theory.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20221117T200000Z
DTEND:20221117T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/69
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/69/">Von Neumann's decomposition of intervals in
 to countably infinitely many pairwise disjoint and congruent subsets</a>\n
 by Mel Nathanson (CUNY) as part of New York Number Theory Seminar\n\n\nAbs
 tract\nAn exposition of von Neumann's paper\,  ``Die Zerlegung eines Inter
 valles in abzahlbar viele kongruente Teilmengen'' (Fund. Math. 11 (1928)\,
  230--238)\, of which Freeman Dyson wrote\, ``In another corner of [Johnny
  von Neumann's] garden\, there is a little flower all by itself\, a short 
 paper ... [that] solves a problem raised by the Polish mathematician Hugo 
 Steinhaus....''\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Iosevich (University of Rochester)
DTSTART:20230209T200000Z
DTEND:20230209T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/71
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/71/">Finite point configurations and complexity<
 /a>\nby Alex Iosevich (University of Rochester) as part of New York Number
  Theory Seminar\n\n\nAbstract\nWe are going to discuss connections between
  the notion of the Vapnik-Chervonenkis dimension  and some classical Erdos
 -type problems.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhi-Wei Sun (Nanjing University\, P. R. China)
DTSTART:20230216T200000Z
DTEND:20230216T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/72
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/72/">New results on power residues modulo primes
 </a>\nby Zhi-Wei Sun (Nanjing University\, P. R. China) as part of New Yor
 k Number Theory Seminar\n\n\nAbstract\nIn this talk we introduce some new 
 results on power residues modulo primes.\n\nLet $p$ be an odd prime\, and 
 let $a$ be an integer not divisible by $p$.\nWhen $m$ is a positive intege
 r with $p\\equiv 1\\pmod{2m}$ and $2$ is an $m$th power residue modulo $p$
 \,\nthe speaker determines the value of the product $\\prod_{k\\in R_m(p)}
 (1+\\tan\\pi\\frac{ak}p)$\, where\n$R_m(p)=\\{0<k<p:\\ k\\in\\mathbb Z\\ \
 \text{is an}\\ m\\text{th power residue modulo}\\ p\\}.$\n\nLet $p>3$ be a
  prime.\nLet $b\\in\\mathbb Z$ and $\\varepsilon\\in\\{\\pm1\\}$.\nJoint w
 ith Q.-.H. Hou and H. Pan\, we prove that\n$\\left|\\left\\{N_p(a\,b):\\ 1
 <a<p\\ \\text{and}\\ \\left(\\frac ap\\right)=\\varepsilon\\right\\}\\righ
 t|=\\frac{3-(\\frac{-1}p)}2\,$\nwhere $N_p(a\,b)$ is the number of positiv
 e integers $x<p/2$ with $\\{x^2+b\\}_p>\\{ax^2+b\\}_p$\, and\n$\\{m\\}_p$ 
 with $m\\in\\mathbb Z$ is the least nonnegative residue of $m$ modulo $p$.
 \n\nWe will also mention some open conjectures.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hung Viet Chu (University of Illinois)
DTSTART:20230223T200000Z
DTEND:20230223T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/73
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/73/">Underapproximation by Egyptian fractions an
 d the weak greedy algorithm</a>\nby Hung Viet Chu (University of Illinois)
  as part of New York Number Theory Seminar\n\n\nAbstract\nNathanson recent
 ly studied the greedy underapproximation algorithm which\, given $\\theta\
 \in (0\,1]$\, produces a sequence of positive integers $(a_n)_{n=1}^\\inft
 y$ such that $\\sum_{n=1}^\\infty 1/a_n = \\theta$. The algorithm is ``gre
 edy" in the sense that at each step\, $a_n$ is chosen to be the smallest p
 ositive integer such that \n$$\\frac{1}{a_n} \\ <\\ \\theta-\\sum_{i=1}^{n
 -1}\\frac{1}{a_i}.$$\n\n\nWe introduce the weak greedy underapproximation 
 algorithm (WGUA)\, which follows the ``greedy choice up to a constant." In
  particular\, for each $\\theta$\, the WGUA produces two sequences of posi
 tive integers $(a_n)$ and $(b_n)$ such that \n\na) $\\sum_{n=1}^\\infty 1/
 b_n = \\theta$\;\n\nb) $1/a_{n+1} < \\theta - \\sum_{i=1}^{n}1/b_i < 1/(a_
 {n+1}-1)$ for all $n\\geqslant 1$\;\n\nc) there exists $t\\geqslant 1$ suc
 h that $b_n/a_n \\leqslant t$ infinitely often.\n\nA sequence of positive 
 integers $(b_n)_{n=1}^\\infty$ is called a weak greedy underapproximation 
 of $\\theta$ if $\\sum_{n=1}^{\\infty}1/b_n = \\theta$.\nWe investigate wh
 en a given weak greedy underapproximation $(b_n)$ can be produced by the W
 GUA. Furthermore\, we show that for any increasing $(a_n)$ with $a_1\\geqs
 lant 2$ and $a_n\\rightarrow\\infty$\, there exist $\\theta$ and $(b_n)$ s
 uch that a) and b) are satisfied\; whether c) is also satisfied depends on
  the sequence $(a_n)$. Finally\, we address the uniqueness of $\\theta$ an
 d $(b_n)$ and apply our framework to specific sequences.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20230302T200000Z
DTEND:20230302T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/74
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/74/">Sinkhorn limits for  generalized doubly sto
 chastic matrices and tensors</a>\nby Mel Nathanson (CUNY) as part of New Y
 ork Number Theory Seminar\n\n\nAbstract\nSinkhorn's theorem asserts that i
 f $A$ is a square matrix with positive coordinates\, then there \nexist (e
 ssentially unique) positive diagonal matrices $X$ and $Y$ such that $XAY$ 
 is doubly stochastic.  \nMenon applied Brouwer's fixed point theorem to pr
 ove this result.  This talk will describe Menon's method and an extension 
 to higher dimensional tensors.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Glaudo (Institute for Advanced Study)
DTSTART:20230330T190000Z
DTEND:20230330T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/75
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/75/">Can you determine a set from its subset sum
 s?</a>\nby Federico Glaudo (Institute for Advanced Study) as part of New Y
 ork Number Theory Seminar\n\n\nAbstract\nLet $A$ be a multiset with elemen
 ts in an abelian group. \nLet $FS(A)$ be its subset sums \n multiset\,  i.
 e.\, the multiset containing the $2^{|A|}$ sums of all subsets of $A$.  \n
  Given $FS(A)$\, can you determine $A$? \n\n\n   If the abelian group is $
 \\Z$\, one can see that the two multisets $A=\\{-2\, 1\, 1\\}$ \n and $A'=
 \\{-1\,-1\,2\\}$ satisfy $FS(A)=FS(A')$\; notice that one is obtained from
  the other \n by changing signs to the elements. We will see that this is 
 the only obstruction and so\, \n up to the sign of the elements\, $FS(A)$ 
 determines $A$ in $\\Z$.\n\nIn a general abelian group the situation is mu
 ch more involved and we will see that the  \n  answer depends intimately o
 n the orders of the torsion elements of the group.\n        \n    The core
  of the proof relies on a delicate study of the structure of cyclotomic un
 its  \n   and on an inversion formula for a novel discrete Radon transform
  on finite abelian groups.\n    \n    This is a joint work with Andrea Cip
 rietti.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Russell Jay Hendel (Towson University)
DTSTART:20230309T200000Z
DTEND:20230309T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/76
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/76/">Recursions\, closed forms\, and characteris
 tic polynomials of the circuit array</a>\nby Russell Jay Hendel (Towson Un
 iversity) as part of New York Number Theory Seminar\n\n\nAbstract\nOne mod
 ern graph metric represents an electrical circuit with a graph whose  edge
 s are replaced with resistors and the so-called resistance distance betwee
 n the nodes is determined by calculating the electrical resistance in the 
 circuit. Electrical circuit theory provides functions that allow ``reducti
 on'' of one circuit to another circuit where the resistance distance betwe
 en certain vertices is preserved. Recently there has been study of a graph
 \, representable in the Cartesian plan as an n-grid\, n rows of upright eq
 uilateral triangles\, all of whose edges are labeled one. It is possible t
 o reduce the n-grid to an (n-1)-grid with resistance preserving operations
 . The collections of successive reductions has many interesting properties
 . In this talk we continue to study a ``slice'' of this collection of grid
 s represented by the Circuit Array\, an infinite array of rational functio
 ns. We show that certain closed forms\, recursions\, and characteristic po
 lynomials (annihilators) emerge. One surprising result is that the annihil
 ators of the numerators and denominators of the underlying rational functi
 ons exclusively have roots which are integral powers of 9.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashvin Rajan
DTSTART:20230420T190000Z
DTEND:20230420T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/77
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/77/">A diophantine problem on products of three 
 consecutive integers</a>\nby Ashvin Rajan as part of New York Number Theor
 y Seminar\n\n\nAbstract\nWe prove that (3\,4\,5) is the only triple of con
 secutive positive integers whose product when doubled also factors as a pr
 oduct of three consecutive integers.  Joint work with Francois Ramaroson.\
 n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sayak Sengupta (SUNY-Binghamton)
DTSTART:20230504T190000Z
DTEND:20230504T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/78
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/78/">Locally nilpotent polynomials over Z</a>\nb
 y Sayak Sengupta (SUNY-Binghamton) as part of New York Number Theory Semin
 ar\n\n\nAbstract\nLet $K$ be a number field and $\\mathcal{O}_K$ be the ri
 ng of integers of $K$. For a polynomial $u(x)$ in $\\mathcal{O}_K[x]$ and 
 $r\\in\\mathcal{O}_K$\, we can construct a dynamical sequence $u(r)\,u^{(2
 )}(r)\,\\ldots$. Let $P(u^{(n)}(r)):=\\{\\mathfrak{p}\\in \\text{MSpec}(\\
 mathcal{O}_K)~|~u^{(n)}(r)\\in \\mathfrak{p}\,\\text{for some }n\\in\\math
 bb{N} \\}$. For which polynomials $u(x)$ and $r\\in \\mathcal{O}_K$ do we 
 expect to have $P(u^{(n)}(r))=\\text{MSpec}(\\mathcal{O}_K)$? If we hit 0 
 somewhere in the above sequence\, then we obviously have the equality. If 
 we do not hit zero for any iteration then the question becomes very intere
 sting. In this talk\, we will define such polynomials for a general number
  field $K$ and then we will look at some results in the particular case of
  $K=\\mathbb{Q}.$ This talk is based on a preprint of my ongoing work\, wh
 ich is available in arXiv under the same name as the title.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Shallit (University of Waterloo)
DTSTART:20230427T190000Z
DTEND:20230427T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/79
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/79/">Doing additive number theory with logic and
  automata</a>\nby Jeffrey Shallit (University of Waterloo) as part of New 
 York Number Theory Seminar\n\n\nAbstract\nThe classical tools of the addit
 ive number theorist include analytic\nand combinatorial methods\, such as 
 the circle method and the sieve method.\nIn this talk I will present anoth
 er method\, based on logic and automata\ntheory\, that can sometimes be us
 ed to prove results in additive number\ntheory in relatively simple ways. 
  No experience with finite automata is \nassumed.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20240201T200000Z
DTEND:20240201T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/80
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/80/">Finitely many implies infinitely many  (for
  polynomials in infinitely many variables)</a>\nby Mel Nathanson (CUNY) as
  part of New York Number Theory Seminar\n\n\nAbstract\nMany mathematical s
 tatements have the following form:  Let $X$ be an infinite set of equation
 s.  If every finite subset of the equations has a common solution\,  then 
 the infinite set of equations  has a common solution.   A result of this t
 ype will be  described for certain infinite sets of polynomial equations i
 n infinitely many variables.  \n\n This is joint work with David Ross.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ross (University of Hawaii)
DTSTART:20240208T200000Z
DTEND:20240208T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/81
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/81/">Finitely many implies infinitely many\, par
 t 3: the nonstandard version</a>\nby David Ross (University of Hawaii) as 
 part of New York Number Theory Seminar\n\n\nAbstract\nIn a pair of recent 
 seminars\, Mel Nathanson has discussed proofs\, using the Tychonoff Theore
 m\, for existence of solutions to infinite sets of equations in infinitely
  many variables. In at least one case the proof was an adaptation of an ar
 gument using nonstandard analysis. In this talk I'll try to explain such n
 onstandard arguments\, hopefully making them intelligible to mathematician
 s who haven't seen nonstandard methods before.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Luca (Wits and Oxford)
DTSTART:20240215T200000Z
DTEND:20240215T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/82
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/82/">Positive integers $k$ such that $3^k+1\\equ
 iv 0\\pmod {3k+1}$</a>\nby Florian Luca (Wits and Oxford) as part of New Y
 ork Number Theory Seminar\n\n\nAbstract\nIn my talk we will look at positi
 ve integers $k$ such that $3^k+1\\equiv 0\\pmod {3k+1}$. We show that ther
 e are infinitely many such. They are all odd and composite and they have a
  counting function that is much smaller than the primes. This is work in p
 rogress.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sayak Sengupta (Binghamton University (SUNY))
DTSTART:20240222T200000Z
DTEND:20240222T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/83
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/83/">Nilpotent and infinitely nilpotent integer 
 sequences</a>\nby Sayak Sengupta (Binghamton University (SUNY)) as part of
  New York Number Theory Seminar\n\n\nAbstract\nWe say that an integer sequ
 ence $\\{r_n\\}_{n\\ge 0}$ has a generating polynomial $u(x)$ over $\\math
 bb{Z}$ if for every positive integer $n$ one has $u^{(n)}(r_0)=r_n$. In ad
 dition\, if such a sequence satisfies the condition that $r_n=0$ for some 
 positive integer $n$ (respectively\, $r_n=0$ for infinitely many positive 
 integers $n$)\, then we say that $\\{r_n\\}_{n\\ge 0}$ is a nilpotent sequ
 ence (respectively\, $\\{r_n\\}_{n\\ge 0}$ is an infinitely nilpotent sequ
 ence). In this talk we will provide (and discuss) some important character
 istics of nilpotent and infinitely nilpotent sequences.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Senia Sheydvasse (Bates College)
DTSTART:20240229T200000Z
DTEND:20240229T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/84
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/84/">Hidden structures in families of Ulam seque
 nces</a>\nby Senia Sheydvasse (Bates College) as part of New York Number T
 heory Seminar\n\n\nAbstract\nStanislaw Ulam defined the original Ulam sequ
 ence as follows: Start with 1\,2\, and then each subsequent term is the ne
 xt smallest integer that is the sum of two distinct prior terms in exactly
  one way. (The next few terms are 1\,2\,3\,4\,6\,8\,...) There is now a ve
 ritable zoo of "Ulam-like" sequences and sets\, most of which share the ma
 in trait of the original: there is clear numerical evidence that there is 
 an underlying structure\, but for the most part we can prove almost nothin
 g. (As a simple example: computation of trillions of terms of the Ulam seq
 uence strongly suggests that it grows linearly. The best known bound is th
 at it can't grow faster than exponentially fast.) One of the few partial r
 esults that we can prove concerns what has been termed the Rigidity Conjec
 ture. The original proofs surrounding this were model-theoretic in nature-
 --what we shall show is that there is a completely constructive proof usin
 g a new variation of Ulam sequences\, and the hints toward a broader solut
 ion that this offers.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Sellers (University of Minnesota - Duluth)
DTSTART:20240307T200000Z
DTEND:20240307T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/85
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/85/">Surprising connections between integer part
 itions statistics: The crank\, minimal excludant\, and partition fixed poi
 nts</a>\nby James Sellers (University of Minnesota - Duluth) as part of Ne
 w York Number Theory Seminar\n\n\nAbstract\nA {\\it partition} of an integ
 er $n$ is a finite sequence of positive integers $p_1\\geq p_2\\geq  \\dot
 s \\geq p_k$ such that $n=p_1+p_2+\\dots + p_k.$  We let $p(n)$ denote the
  number of partitions of $n$.  For example\, $p(4) = 5$ because there are 
 five partitions of the integer $n=4$:  \n\n$$4\, \\ \\ 3+1\, \\ \\ 2+2\, \
 \ \\ 2+1+1\, \\ \\ 1+1+1+1$$\n\nIn 1919\, just one year before his death\,
  Ramanujan discovered and proved some unexpected\, and truly amazing\, div
 isibility properties for the function $p(n).$  Since then\, several mathem
 aticians have studied $p(n)$ from different perspectives\, trying to bette
 r understand these divisibility properties\, especially from a combinatori
 al perspective.  In the process\, numerous ``statistics'' have been define
 d on partitions\, including the rank and crank of a partition.  In this ta
 lk\, I will discuss this history in more detail\, and then I will transiti
 on to some relatively new partition statistics\, including the {\\it missi
 ng excludant} (or {\\it mex}) of a partition.  I will discuss unexpected c
 onnections between this mex statistic and the crank\, and then we will tra
 nsition to some very recent work of Blecher and Knopfmacher on partition f
 ixed points which\, unbeknownst to them\, is very closely connected to the
  crank and mex statistics.  We will close by generalizing this concept of 
 partition fixed points and show how this new family of functions naturally
  connects with generalized versions of the aforementioned partition statis
 tics.  \n\nThis is joint work with Brian Hopkins\, St. Peter's University.
 \n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David and Gregory Chudnovsky (New York University)
DTSTART:20240314T190000Z
DTEND:20240314T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/86
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/86/">The telephone gossip problem: An hommage to
  Richard Bumby</a>\nby David and Gregory Chudnovsky (New York University) 
 as part of New York Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O'Bryant (College of Staten Island (CUNY))
DTSTART:20240411T190000Z
DTEND:20240411T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/87
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/87/">$B_h$-sets</a>\nby Kevin O'Bryant (College 
 of Staten Island (CUNY)) as part of New York Number Theory Seminar\n\n\nAb
 stract\nFix a positive integer $h$. A $B_h$-set is a set of natural number
 s that does not contain $x_i\,y_i$ with $x_1+\\cdots +x_h=y_1+\\cdots +y_h
 $\, except for the trivial solutions where $x_1\,\\dots\,x_h$ is a rearran
 gement of $x_1\,\\dots\,x_h$. The primary challenge is to make the $k$-th 
 largest element of a $B_h$-set as small as possible. This talk will contai
 n the state of the art for this problem\, with special attention to how th
 e problem changes as $h$ grows.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20240328T190000Z
DTEND:20240328T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/88
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/88/">Landau's converse to Holder's inequality\, 
 and other inequalities</a>\nby Mel Nathanson (CUNY) as part of New York Nu
 mber Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leo Schaefer (University of Gottingen)
DTSTART:20240418T190000Z
DTEND:20240418T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/89
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/89/">Telling apart coarsifications of the intege
 rs</a>\nby Leo Schaefer (University of Gottingen) as part of New York Numb
 er Theory Seminar\n\n\nAbstract\nWe introduce an invariant for coarse grou
 ps that is able to differentiate some coarsifications of the integers up t
 o isomorphism. In particular\, we will see that coarsifications coming fro
 m pro-$Q$ topologies (and therefore also the $p$-adic topologies) are not 
 isomorphic.\n    Partial results for metrics stemming from Cayley graphs a
 re also obtained\, but there remain open questions in this regard.\n    \n
     This is joint work with Federico Vigolo.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Borisov (Binghamton University)
DTSTART:20240502T190000Z
DTEND:20240502T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/90
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/90/">Locally integer polynomial functions</a>\nb
 y Alexander Borisov (Binghamton University) as part of New York Number The
 ory Seminar\n\n\nAbstract\nA locally integer polynomial function on a subs
 et $X$ of  $\\mathbb Z$ is a function $f: X\\to \\mathbb Z$ such that its 
 restriction to every finite subset is given by a polynomial in $\\mathbb Z
 [x]$. I hope to convince you that these objects are interesting and deserv
 e further study.  The talk will be based on my recent preprint https://arx
 iv.org/abs/2401.17955 and on  further work in progress on a rather mysteri
 ous analogy between locally integer  polynomial functions on infinite $X$ 
 and complex analytic functions. Several open  questions will be proposed\,
  highlighting how little appears to be known about these  seemingly elemen
 tary objects.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quentin Dubroff (Rutgers University)
DTSTART:20240509T190000Z
DTEND:20240509T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/91
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/91/">The Erdos distinct subset sums problem</a>\
 nby Quentin Dubroff (Rutgers University) as part of New York Number Theory
  Seminar\n\n\nAbstract\nA conjecture of Erd\\H{o}s from the 1930s  states 
 that any set of $n$ positive integers with distinct subset sums contains a
 n element larger than $c2^n$ for some fixed constant c. I'll give (at leas
 t) three proofs of the weaker result that any such set contains an element
  larger than $c2^n/\\sqrt{n}$. Two of these proofs will achieve a bound wi
 th the best-known constant $c = \\sqrt{2/\\pi}$\, which seems to be a sign
 ificant sticking point. I'll highlight similarities and differences betwee
 n the proofs\, which use a wide range of tools such as isoperimetric inequ
 alities\, Minkowski's theorem in the geometry of numbers\, and the Berry-E
 sseen quantitative central limit theorem.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Luca (University of Witwatersrand)
DTSTART:20240516T190000Z
DTEND:20240516T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/92
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/92/">On transcendence of Sturmian and Arnoux-Rau
 zy words</a>\nby Florian Luca (University of Witwatersrand) as part of New
  York Number Theory Seminar\n\n\nAbstract\nWe consider numbers of the form
  $\\alpha={\\displaystyle{\\sum_{n=0}^{\\infty} \\frac{u_n}{\\beta^n}}}$\,
  where $(u_n)$ \nis an infinite word  over a finite alphabet and $\\beta$ 
 is a complex number of absolute\nvalue greater than one. We present a comb
 inatorial criterion on $u$\, called\nechoing\, that implies that $\\alpha$
  is transcendental whenever $\\beta$ is algebraic. We\nshow that every Stu
 rmian word is echoing\, as is the Tribonacci word\, a leading\nexample of 
 an Arnoux-Rauzy word. We give an application of our\ntranscendence results
  to the theory of dynamical systems\, showing that for\na contracted rotat
 ion on the unit circle with algebraic slope\, its limit set is\neither fin
 ite or consists exclusively of transcendental elements other than its\nend
 points $0$ and $1$. This confirms a conjecture of Bugeaud\, Kim\, Laurent\
 ,\nand Nogueira.\n\nJoint work with P. Kebis\, A. Scoones\, J. Ouaknine an
 d J. Worrell.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20240905T190000Z
DTEND:20240905T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/93
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/93/">Shnirel'man density and the Dyson transform
 </a>\nby Mel Nathanson (CUNY) as part of New York Number Theory Seminar\n\
 n\nAbstract\nA ``hot topic'' in the 1930s and 1940s was Khinchin's $\\alph
 a+\\beta$ conjecture for the Shnirel'man density of the sum of two sets of
  integers.  This was solved by Henry B. Mann in 1942.   The following year
  Emil Artin and Peter Scherk published a refinement of his proof.   In 194
 5\, Freeman Dyson introduced the ``Dyson transform'' of an $n$-tuple of se
 ts of positive integers and extended Mann's result to rank $r$ sums of $n$
  sets of integers.  The goal of this talk to simplify Dyson's method and g
 eneralize his result.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Xu (NYU Courant)
DTSTART:20240912T190000Z
DTEND:20240912T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/94
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/94/">Two stories about multiplicative energy</a>
 \nby Max Xu (NYU Courant) as part of New York Number Theory Seminar\n\n\nA
 bstract\nThe multiplicative energy $E_{\\times}(A)$ of a given set $A$ is 
 defined to be the number \n of solutions to the equation \n$a_1a_2 = a_3a_
 4$\,\nwhere all $a_i$ are in $A$. \n We show two recent applications of st
 udying multiplicative energy. \n The first application is to study conject
 ures of Elekes and Ruzsa on the size  \n of product sets of arithmetic pro
 gressions. \n The second story is about a recent popular topic\, random mu
 ltiplicative functions\,  \n and we show how multiplicative energy is invo
 lved. \n The talk is based on joint work with Yunkun Zhou and K. Soundarar
 ajan\, respectively.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O'Bryant (College of Staten Island and CUNY Graduate Center)
DTSTART:20241017T190000Z
DTEND:20241017T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/95
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/95/">Visualizing the sum-product conjecture</a>\
 nby Kevin O'Bryant (College of Staten Island and CUNY Graduate Center) as 
 part of New York Number Theory Seminar\n\n\nAbstract\nThe Erdos sum-produc
 t conjecture states that\, for every $\\epsilon>0$\, there is $k_0$ such t
 hat if $A$ is any finite set of positive integers with $|A|>k_0$\, \nthen 
 $|(A+A)\\cup(AA)| > |A|^{2-\\epsilon}$. In other words\, for sufficiently 
 large sets either the sumset or the product set will be nearly as large as
  conceivable. We survey progress on this conjecture\, and provide a visual
  representation of progress and counterexamples. There will be a few beaut
 iful proofs (not the speaker's)\, several interesting examples\, and score
 s of striking pictures.{\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (Lehman Callege and CUNY Graduate Center)
DTSTART:20240919T190000Z
DTEND:20240919T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/96
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/96/">Sums of lattice points\, ordered groups\, a
 nd the Hahn embedding theorem</a>\nby Mel Nathanson (Lehman Callege and CU
 NY Graduate Center) as part of New York Number Theory Seminar\n\n\nAbstrac
 t\nExtension of Shnirel'man's theorem to sums of sets of nonnegative latti
 ce points and to other additive problems associated with ordered groups.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (Lehman Callege and CUNY Graduate Center)
DTSTART:20240926T190000Z
DTEND:20240926T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/97
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/97/">Addition theorems in partially ordered  gro
 ups</a>\nby Mel Nathanson (Lehman Callege and CUNY Graduate Center) as par
 t of New York Number Theory Seminar\n\n\nAbstract\nShnirel'man's inequalit
 y and Shnirel'man's basis theorem are fundamental \nresults about sums of 
 sets of positive integers in additive number theory.   \nIt is proved that
  these results are inherently order-theoretic \nand extend to partially or
 dered abelian and nonabelian groups.  \nOne abelian application is an addi
 tion theorem \nfor sums of sets of $n$-dimensional lattice points.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ross (University of Hawai'i)
DTSTART:20241031T190000Z
DTEND:20241031T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/98
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/98/">Egyptian fractions on groups</a>\nby David 
 Ross (University of Hawai'i) as part of New York Number Theory Seminar\n\n
 \nAbstract\nIn 1956 Sierpinski published several results about the structu
 re of the set of Egyptian fractions. A few years ago Nathanson extended th
 ese results to more general sets of real numbers\, and independently I sho
 wed that nonstandard methods make it possible to simplify and extend Sierp
 inski's results.  In this talk I'll describe a further generalization\, to
  certain subsets of ordered topological groups.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Senia Sheydvasser (Bates College)
DTSTART:20241114T200000Z
DTEND:20241114T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/99
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/99/">Distribution of Ulam words</a>\nby Senia Sh
 eydvasser (Bates College) as part of New York Number Theory Seminar\n\n\nA
 bstract\nLet 0\,1 denote the generators of the free semigroup on two gener
 ators. We say that a word is 'Ulam' if it is either 0 or 1\, or it can be 
 written as the concatenation of two smaller (distinct) Ulam words in exact
 ly one way. This is a nonabelian analog of Ulam sequences\, defined by Bad
 e et al. in 2020. In this talk\, we will discuss a few new conjectures and
  results about the distribution of Ulam words---we will see that there is 
 a natural corresponding integer sequence\, and so it makes sense to ask qu
 estions about density\, equidistribution modulo $N$\, and so on.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20241024T190000Z
DTEND:20241024T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/100
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/100/">Orderable groups and inverse theorems</a>\
 nby Mel Nathanson (CUNY) as part of New York Number Theory Seminar\n\n\nAb
 stract\nThis talk will review some basic facts about orderable groups and 
 the extension \nof Freiman's $3k+4$ theorem from the integers to orderable
  groups.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan M. Keith (Monash University\, Australia)
DTSTART:20241107T200000Z
DTEND:20241107T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/101
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/101/">Asymptotic density and related set functio
 ns</a>\nby Jonathan M. Keith (Monash University\, Australia) as part of Ne
 w York Number Theory Seminar\n\n\nAbstract\nAsymptotic density is a conven
 ient measure of the size of a set of natural numbers\, which has uses in m
 any mathematical contexts including statistics\, ergodic processes\, compl
 ex analysis and number theory. In this talk\, I'll briefly review the hist
 ory and uses of asymptotic density and related set functions\, then discus
 s how such functions can be used to induce pseudometrics on the power set 
 of the natural numbers $\\mathcal{P}(\\mathbb{N})$\, and why this is mathe
 matically useful. I'll present some new theorems about the completeness of
  such pseudometrics\, and characterisations of closed sets in these topolo
 gies.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Fischer (INSAIT\, Sofia University\, Bulgaria)
DTSTART:20241121T200000Z
DTEND:20241121T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/102
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/102/">Recognizing sumsets is NP-complete</a>\nby
  Nick Fischer (INSAIT\, Sofia University\, Bulgaria) as part of New York N
 umber Theory Seminar\n\n\nAbstract\nSumsets are central objects in additiv
 e combinatorics. In 2007\, Granville asked whether one can efficiently rec
 ognize whether a given set $S$ is a sumset\, i.e. whether there is a set $
 A$ such that $A+A=S$. Granville suggested an algorithm that takes exponent
 ial time in the size of the given set\, but can we do polynomial or even l
 inear time? This basic computational question is indirectly asking a funda
 mental structural question: do the special characteristics of sumsets allo
 w them to be efficiently recognizable? In this paper\, we answer this ques
 tion negatively by proving that the problem is NP-complete. Specifically\,
  our results hold for integer sets and over any finite field.\n\nJoint wor
 k with Amir Abboud\, Ron Safier\, and Nathan Wallheimer.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grazyna Horbaczewska and Sebastian Lindner (University of Lodz\, P
 oland)
DTSTART:20241212T200000Z
DTEND:20241212T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/103
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/103/">On permutations preserving density</a>\nby
  Grazyna Horbaczewska and Sebastian Lindner (University of Lodz\, Poland) 
 as part of New York Number Theory Seminar\n\n\nAbstract\nIn the 71st probl
 em included in the Scottish Book\, Stanis{\\l}aw Ulam asks about the chara
 cteristics of permutations that preserve the density of subsets of natural
  numbers. An overview of partial answers to this problem will be presented
 .\n\n\n M. Blumlinger\, N. Obata\, \\emph{Permutations preserving Ces\\`ar
 o mean\, densities of natural numbers and uniform distribution of sequence
 s}\, Annales de l'institut Fourier 41 (3) (1991)\, 665-678.\n\nJ. Coquet\,
  \\emph{Permutations des entiers et reparition des suites}\, in:Analytic a
 nd Elementary Number Theory\, Marseille\, 1983\, Publ. Math. Orsay 86 (198
 6)\, 25-39. \n	\n M.B. Nathanson\, R. Parikh\, \\emph{Density of sets of n
 atural numbers and the Levy group}\, J. Number Theory 124 (2007)\, 151-158
 .\n	\n	\n N. Obata\, \\emph{A note on certain permutation groups in the in
 finite-dimensional rotation group}\, Nagoya Math. J. 109 (1988)\, 91-107\n
 	\nM. Sleziak\, M. Ziman\, \\emph{Levy group and density measures} Journal
  of Number Theory 128 (2008)\, 3005–3012\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20241219T193000Z
DTEND:20241219T210000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/104
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/104/">Richard Bumby memorial session</a>\nby Mel
  Nathanson (CUNY) as part of New York Number Theory Seminar\n\nAbstract: T
 BA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Rowland (Hofstra University)
DTSTART:20250123T200000Z
DTEND:20250123T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/105
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/105/">The exact values of the entries of a Sinkh
 orn limit</a>\nby Eric Rowland (Hofstra University) as part of New York Nu
 mber Theory Seminar\n\n\nAbstract\nThe Sinkhorn limit of a positive square
  matrix is obtained by scaling the rows so each row sum is 1\, then scalin
 g the columns so each column sum is 1\, then scaling the rows again\, then
  the columns again\, and so on. It has been used for almost 90 years in ap
 plications ranging from predicting telephone traffic to machine learning. 
 But until recently\, nothing was known about the exact values of its entri
 es. In 2020\, Nathanson determined the Sinkhorn limit of a $2 \\times 2$ m
 atrix. Shortly after that\, Ekhad and Zeilberger determined the Sinkhorn l
 imit of a symmetric $3 \\times 3$ matrix. Recently\, Jason Wu and I determ
 ined the Sinkhorn limit of a general $3 \\times 3$ matrix. The result sugg
 ests the form for $n \\times n$ matrices\; in particular\, the entries see
 m to be algebraic numbers with (generic) degree $\\binom{2 n - 2}{n - 1}$.
  This degree has a combinatorial interpretation as the number of minors of
  an $(n - 1) \\times (n - 1)$ matrix.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Kravitz (Princeton University)
DTSTART:20250130T200000Z
DTEND:20250130T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/106
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/106/">Relative sizes of iterated sumsets</a>\nby
  Noah Kravitz (Princeton University) as part of New York Number Theory Sem
 inar\n\n\nAbstract\nNathanson recently posed the following natural questio
 n about the possible relative sizes of iterated sumsets: Given permutation
 s $\\sigma_1\,\\ldots\,\\sigma_H \\in \\mathfrak{S}_n$\, can one find fini
 te subsets $A_1\,\\ldots\, A_n \\subseteq \\mathbb{Z}$ such that for each 
 $1 \\leq h \\leq H$\, the quantities $|hA_1|\,\\ldots\,|hA_n|$ have the sa
 me relative order as $\\sigma_h$?  We will describe several constructions
  that provide affirmative answers to this and related questions.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salvatore Tringali (School of Mathematical Sciences\, Hebei Normal
  University\, China)
DTSTART:20250206T200000Z
DTEND:20250206T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/107
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/107/">A survey of power semigroups</a>\nby Salva
 tore Tringali (School of Mathematical Sciences\, Hebei Normal University\,
  China) as part of New York Number Theory Seminar\n\n\nAbstract\nThe term 
 ``power semigroups''  is loosely used to refer to an assorted class of (co
 mmutative and non-commutative) semigroups that\, among other things\, prov
 ide a natural algebraic framework for the formulation or reformulation of 
 many intriguing questions in additive combinatorics and related fields. \n
 \nI will provide an overview of power semigroups\, with emphasis on additi
 ve-theoretic aspects of their study\, recent developments\, and open probl
 ems.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20250213T200000Z
DTEND:20250213T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/108
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/108/">New problems in additive number theory</a>
 \nby Mel Nathanson (CUNY) as part of New York Number Theory Seminar\n\n\nA
 bstract\nIn the study of sums of finite sets of integers\, most attention 
 has been paid to sets with small sumsets (Freiman's theorem and related wo
 rk) and to sets with large sumsets (Sidon sets and $B_h$ sets).  The focus
  of this talk is on the full range of sizes of h-fold sums of a set of k i
 ntegers.   Many new results and open problems will be presented.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Tait (Villanova University)
DTSTART:20250306T200000Z
DTEND:20250306T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/109
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/109/">Cardinalities of g-difference sets</a>\nby
  Michael Tait (Villanova University) as part of New York Number Theory Sem
 inar\n\n\nAbstract\nWhat is the minimum/maximum size of a set $A$ of integ
 ers that has the property that every integer in $\\{1\,2\,\\cdots\, n\\}$ 
 can be written in at least/at most $g$ ways as a difference of elements of
  $A$? For the first question\, we show that the limit of this minimum size
  divided by $\\sqrt{n}$ exists and is nonzero\, answering a question of Kr
 avitz. For the second question\, we give an asymptotic formula for the max
 imum size. We also consider the same problems but in the setting of a vect
 or space over a finite field. We will end the talk by discussing open prob
 lems and connections to coding theory. \n\nThis is joint work with Eric Sc
 hmutz.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ross (University of Hawai'i)
DTSTART:20250227T200000Z
DTEND:20250227T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/110
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/110/">A nonstandard construction of a B_h set</a
 >\nby David Ross (University of Hawai'i) as part of New York Number Theory
  Seminar\n\n\nAbstract\nIn last week's seminar\, Mel Nathanson showed that
  given an integer $h>1$and a finite set $A$ of positive reals that are lin
 early independent over the rationals\, $A$ can be transformed into a $B_h$
 -Sidon set by multiplying its  elements by a sufficiently large integer q 
 and rounding off.  I'll give an extremely short proof of this using nonsta
 ndard analysis.  (Unfortunately\, in contrast to Mel's argument\, this pro
 of gives no estimate for ``large enough".)\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Moreno (CUNY)
DTSTART:20250227T203000Z
DTEND:20250227T210000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/111
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/111/">Multi-quadratic extensions of the rational
  field</a>\nby Carlos Moreno (CUNY) as part of New York Number Theory Semi
 nar\n\n\nAbstract\nWe will discuss briefly some elementary properties of q
 uadratic extensions of the field of rationals. Some relations to quadratic
  reciprocity law and cyclotomy will also be mentioned.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20250313T190000Z
DTEND:20250313T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/112
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/112/">Problems and results in combinatorial addi
 tive number theory</a>\nby Mel Nathanson (CUNY) as part of New York Number
  Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norbert Hegyvari (E\\"otv\\"os University and R\\'enyi Institute\,
  Budapest)
DTSTART:20250403T190000Z
DTEND:20250403T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/113
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/113/">Inverse results in combinatorial number th
 eory</a>\nby Norbert Hegyvari (E\\"otv\\"os University and R\\'enyi Instit
 ute\, Budapest) as part of New York Number Theory Seminar\n\n\nAbstract\nT
 he inverse problems can be roughly described as follows:   \n  Given an ad
 ditive (or multiplicative) structure\, the task is to determine   \n  the 
 structure of the original set. The celebrated Freiman theorem is an  \n  i
 nverse question par excellence. \n  In this talk we consider inverse probl
 ems of the  subset sums in both the  \n  finite and infinite cases. For an
 y additive set $X$\,   \n\\[ \nFS(X):= \\left\\{ \\sum_{i=1}^\\infty\\vare
 psilon_ix_i: \\ x_i\\in X\, \\ \\varepsilon_i\n\\in \\{0\,1\\}\, \\ \\sum_
 {i=1}^\\infty\\varepsilon_i<\\infty \\right\\}\n\\] \n  denotes the set of
  subset sums.\nThe finite case is due to Erd\\H os and Szemer\\'edi\,  \n 
  who asked the question:  For which integer $t$ does there exist  a set $X
 $   \n  with  $n$ elements for which $|FS(X)|=t$?   S. Burr introduced the
  analogous  \n   problem for the infinite case.  \n\n  In the rest of the 
 talk we  discuss related questions in\nhigher dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James A. Sellers (University of Minnesota Duluth)
DTSTART:20250320T190000Z
DTEND:20250320T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/114
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/114/">Arithmetic properties of $d$--fold partiti
 on diamonds</a>\nby James A. Sellers (University of Minnesota Duluth) as p
 art of New York Number Theory Seminar\n\n\nAbstract\nIn this talk\, we int
 roduce new combinatorial objects called $d$--fold partition diamonds\, whi
 ch generalize both the classical partition function (for unrestricted inte
 ger partitions) and the partition diamonds of Andrews\, Paule\, and Riese.
  We consider two counting functions related to these combinatorial objects
 \, the second of which we call ``Schmidt type'' $d$--fold partition diamon
 ds\, which have counting function $s_d(n)$. After finding the generating f
 unction for $s_d(n)$\, we identify a surprising connection to a well--know
 n family of polynomials. This allows us to develop elementary proofs of in
 finitely many Ramanujan--like congruences satisfied by $s_d(n)$ for variou
 s values of $d$\, including the following family: for all $d\\geq 1$ and a
 ll $n\\geq 0\,$ $s_d(2n+1) \\equiv 0 \\pmod{2^d}.$\n\nThe talk will be sel
 f--contained and accessible to all.\n\nThis is joint work with Dalen Docke
 ry\, Marie Jameson\, and Samuel Wilson (all of the University of Tennessee
 ).\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20250327T190000Z
DTEND:20250327T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/115
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/115/">Compression of sumsets of sets of lattice 
 points</a>\nby Mel Nathanson (CUNY) as part of New York Number Theory Semi
 nar\n\n\nAbstract\nLet $\\mathcal{R}_{\\Z^n}(h\,k)$ be the set of all inte
 gers $t$ \nsuch that there exists a subset $A$ of $\\Z^n$ \n with $|A|=k$ 
 and $|hA|=t$. \nIt is an open problem to compute a number \n $N = N(h\,k)$
  such that there exists \n$A' \\subseteq \\Z^n$ with $|A'|= k$\, $|hA'| = 
 t$\, \n and $\\|a\\|_1 \\leq N$ \nfor all $a \\in A$.  It is shown how to 
 ``compress'' a widely disbursed set \n of lattice points while preserving 
 the $h$-fold sumset size.  \nThis is a step toward the goal.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bloom (University of Manchester\, UK)
DTSTART:20250410T190000Z
DTEND:20250410T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/116
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/116/">Control in additive combinatorics and its 
 applications</a>\nby Thomas Bloom (University of Manchester\, UK) as part 
 of New York Number Theory Seminar\n\n\nAbstract\nBounds for the third mome
 nt of the convolution have played an important role recently in additive c
 ombinatorics\, most notably in the study of the sum-product problem and th
 e growth of convex sets of real numbers. In this talk I will give a unifie
 d overview of how and why such third moment bounds are useful in additive 
 combinatorics\, including recent advances in the sum-product problem\, gro
 wth of convex sets\, and the Balog-Szemeredi-Gowers theorem.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Russell Jay Hendel (Towson University)
DTSTART:20250424T190000Z
DTEND:20250424T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/117
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/117/">A family of Sequences Generalizing the Thu
 e–Morse and Rudin-Shapiro Sequences</a>\nby Russell Jay Hendel (Towson U
 niversity) as part of New York Number Theory Seminar\n\n\nAbstract\nFor $m
  \\ge 1\,$ let $P_m =1^m\,$ the binary string of $m$ ones. Further define 
 the infinite sequence $s_m$ by \n $s_{m\,n} = 1$ iff  the number of (possi
 bly overlapping) occurrences of $P_m$ in the binary representation of $n$ 
 is odd\, $n \\ge 0.$  For $m=1\,2$ respectively $s_m$ is the Thue-Morse an
 d Rudin-Shapiro sequences. This paper shows: (i) $s_m$ is automatic\; (ii)
  the   minimal\, DFA (deterministic finite automata)  accepting $s_m$ has 
 $2m$ states\; (iii) it suffices to use prefixes of length $2^{m-1}$ to dis
 tinguish all sequences in the 2-kernel of $s_m$\; and (iv) the characteris
 tic function of the length $2^{m-1}$ prefix of the 2-kernel sequences of $
 s_m$ can be formulated using the Vile and Jacobstahl sequences. The proofs
  exploit connections between string operations on binary strings and the n
 umbers they represent. Both Mathematica and Walnut are employed for explor
 atory analysis of patterns. In particular\, we generalize the famous resul
 t about the Thue-Morse sequence that the orders of squares in the sequence
  are of the form $(2^i)_{i \\ge 0} \\cup 3 \\times (2^i)_{i \\ge 0.}$\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashvin  Rajan (Baltimore)
DTSTART:20250501T190000Z
DTEND:20250501T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/118
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/118/">On a cubic Diophantine equation</a>\nby As
 hvin  Rajan (Baltimore) as part of New York Number Theory Seminar\n\n\nAbs
 tract\nWe develop a method to find all the integral solutions of the cubic
  Diophantine equation \n ${H_k}:y^3 - y = k(x^3 - x)$\,  for certain posit
 ive integers $k$ that are not perfect cubes\, and illustrate our method by
  completely solving \n this  Diophantine equation for the cases $k =2$\, $
 k=3$\, and $k =6$.   \n Our approach relies on lower bounds for all ration
 al approximations to $\\sqrt[3]{k}$ \n  that were obtained by M. Bennett\,
  D. Easton\, and P. Voutier\, who build  \n on a fundamental approach to f
 inding such estimates devised by A. Baker. \n This is joint work with Teru
 take Abe and Francois Ramaroson.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20250918T190000Z
DTEND:20250918T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/119
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/119/">Hilbert polynomials and growth of sumsets<
 /a>\nby Mel Nathanson (CUNY) as part of New York Number Theory Seminar\n\n
 \nAbstract\nGraded and multi-graded rings and modules and applications to 
 additive number theory.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20251009T190000Z
DTEND:20251009T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/120
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/120/">Dickson's lemma and perfect numbers</a>\nb
 y Mel Nathanson (CUNY) as part of New York Number Theory Seminar\n\n\nAbst
 ract\nAn exposition of Dickson's classic 1913 paper and its relation to Gr
 oebner bases and Hilbert's basis theorem.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Senger (Missouri State University)
DTSTART:20251023T190000Z
DTEND:20251023T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/121
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/121/">Triangular gaps in the most frequent sizes
  of the iterated sumsets of sets of four natural numbers</a>\nby Steven Se
 nger (Missouri State University) as part of New York Number Theory Seminar
 \n\n\nAbstract\nWe discuss the triangular gaps observed experimentally in 
 the most popular sizes of the $h$-fold iterated sumset\, $hA\,$ when $A$ i
 s a randomly chosen four-element subset of the first $q$ natural numbers\,
  for $q$ much larger than $h.$ In particular\, we quantify frequent and in
 frequent sumset sizes\, and rigorously show that  for any $h>2\,$ the firs
 t two gaps between the largest frequent sumset sizes must be 1 and 3.  We 
 also outline a method for showing that this pattern must continue.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20251030T190000Z
DTEND:20251030T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/122
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/122/">Sumset sizes in abelian groups</a>\nby Mel
  Nathanson (CUNY) as part of New York Number Theory Seminar\n\nAbstract: T
 BA\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruce Reznick (University of Illinois - Urbana)
DTSTART:20251113T200000Z
DTEND:20251113T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/123
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/123/">The Stern sequence</a>\nby Bruce Reznick (
 University of Illinois - Urbana) as part of New York Number Theory Seminar
 \n\n\nAbstract\nThe Stern sequence is defined by $s(0) = 0\, s(1) = 1$\, a
 nd for $k > 0\, s(2k) = s(k)$\, and \n$ s(2k+1) = s(k) + s(k+1)$. It was d
 efined in 1858 and has many applications to and from number theory\, digit
 al representations\, graph theory\, geometry\,  analysis\, and probability
 . This talk has cameo appearances by Eisenstein\, Minkowski\, Einstein\, d
 e Rham\, and Dijkstra. Stern himself was Gauss' first PhD student  and led
  a very interesting life. He proved that every positive rational $p/q$ can
  be written uniquely as $s(n)/s(n+1)$ well before Cantor\, where the binar
 y expansion of $n$ is related to the simple continued fraction representat
 ion of $p/q$. Others showed\, in effect\, that every positive rational can
  also be written uniquely as $s(m)/s(2^r-m)$  for odd $m$\, where $m$ and 
 $n$ have an unexpected relation. Also\, $s(n)$ is the number of ways to wr
 ite $n-1 = \\sum a_k 2^k$\, where $a_k$ is in $\\{0\,1\,2\\}$. De Rham use
 d the Stern   sequence to define a convex curve on which points of zero fl
 atness and points of infinite flatness are dense.  This talk will be acces
 sible to first-year graduate students.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zach McGuirk (Bard College High School and Early College)
DTSTART:20251016T190000Z
DTEND:20251016T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/124
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/124/">Free resolutions and relations-between-rel
 ations</a>\nby Zach McGuirk (Bard College High School and Early College) a
 s part of New York Number Theory Seminar\n\n\nAbstract\nThe fundamental qu
 estion driving this theory is: Given a module M  over \n a ring R\,  how c
 an we understand its "structure" through its relations and \n relations-be
 tween-relations? This leads naturally to free resolutions\, which \n encod
 e all the algebraic constraints defining M. If\, instead of a module\, we 
 were \n working with a vector space over a field\, then we would have a ba
 sis to work with. \n However\, for an R-module\, there might not be a basi
 s\, i.e. there might be non-trivial \n relations between different generat
 ors\, and then there might be relations between \n  those relations. Hilbe
 rt's Syzygy Theorem states that this process of \n relations-between-relat
 ions must eventually terminate.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Pomerance (Dartmouth College)
DTSTART:20251204T200000Z
DTEND:20251204T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/125
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/125/">Is number theory a science?</a>\nby Carl P
 omerance (Dartmouth College) as part of New York Number Theory Seminar\n\n
 \nAbstract\nI often wonder why mathematics is considered\none of the scien
 ces\, in fact\, even the queen of science.\nIs it really so?\nThe substanc
 e of science is comprised of theories where we\nthink we understand variou
 s processes and we run experiments\nto either verify our understanding or 
 perhaps revise it.\nThere is an element of exactly this process with numbe
 r theory\,\nand perhaps other branches of mathematics as well.  In this\nt
 alk we'll visit various number theoretic conjectures from\nthis point of v
 iew\, from the Riemann Hypothesis\, to the\ntwin prime conjecture\, and th
 e distribution of perfect numbers.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Borisov (SUNY - Binghamton)
DTSTART:20251106T200000Z
DTEND:20251106T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/126
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/126/">A structure sheaf for Kirch topology on N<
 /a>\nby Alexander Borisov (SUNY - Binghamton) as part of New York Number T
 heory Seminar\n\n\nAbstract\nKirch topology on $\\mathbb N$ goes back to a
  1969 paper of Kirch. It can be defined by a basis of open sets that consi
 sts of all infinite arithmetic progressions $a+d\\mathbb N_0$\, such that 
 $\\gcd(a\,d)=1$ and $d$ is square-free. It is Hausdorff\, connected\, and 
 locally connected.   One can hope that in the classical  imperfect analogy
  between arithmetic and geometry this can serve as an arithmetic analog of
  the usual topology on $\\mathbb C$. However\, the usual   topology on $\\
 mathbb C$ comes with a structure sheaf of complex-analytic functions.  As 
 far as I know\, no analog for Kirch topology has been proposed before me. 
 I believe that  I have stumbled upon just such a thing\, more by accident 
 than by a conscious effort:  locally LIP functions. These are functions fr
 om Kirch-open sets to $\\mathbb Z$ such that for every  point in the domai
 n there is a Kirch-open neighborhood on which the function is  "locally in
 teger polynomial" (LIP): its interpolation polynomial on every finite set 
 has  integer coefficients. I will explain why this seems to be a natural o
 bject\, what I know  about it\,  and what I hope to achieve. Some of the m
 aterial of this talk will be based  on my latest paper: https://people.mat
 h.binghamton.edu/borisov/research.html\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James A. Sellers (University of Minnesota - Duluth)
DTSTART:20251211T200000Z
DTEND:20251211T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/127
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/127/">$m$-convolutive sequences through the lens
  of integer partition functions</a>\nby James A. Sellers (University of Mi
 nnesota - Duluth) as part of New York Number Theory Seminar\n\n\nAbstract\
 nIn 2002\, Andrews\, Lewis\, and Lovejoy introduced the combinatorial obje
 cts called \\emph{partitions with designated summands}\, which are partiti
 ons where exactly one part of each size in the partition is marked. For ex
 ample\, $5'+2+2'+2+1'+1$ is a partition of $13$ with designated summands w
 here we have marked the only part of size five\, the second part of size t
 wo\, and the first part of size one.  \n\nIn the same paper\, Andrews\, Le
 wis\, and Lovejoy also considered partitions with designated summands in w
 hich all parts are odd\, and they denoted the number of such objects of we
 ight $n$ by the function $PDO(n)$.  As has been recognized by several auth
 ors over the last two decades\, the $PDO$ function satisfies a very curiou
 s property which we call $2$-convolutivity:\n$$\n	\\sum_{n\\ge 0} PDO(2n)q
 ^n = \\left ( \\sum_{n\\ge 0} PDO(n)q^n \\right )^2\n$$\nThat is to say\, 
 the subsequence $(PDO(2n))_{n\\ge 0}$ is the convolution of the sequence $
 (PDO(n))_{n\\ge 0}$ with itself.    \n\nOur work (which is joint with Shan
 e Chern (Vienna)\, Shishuo Fu (Chongqing)\, and Dennis Eichhorn (UC Irvine
 )) evolved out of our attempts to \\emph{combinatorially} understand the $
 2$-convolutivity of $PDO(n)$. Thus far\, such a combinatorial proof remain
 s elusive. However\, our endeavors led us to consider a more general conce
 pt of convolutivity which will be discussed in the talk\, with the hope th
 at we might identify other restricted integer partition functions that are
  themselves convolutive.\n\nIndeed\, an exhaustive search of the Online En
 cyclopedia of Integer Sequences during the summer 2025 identified a handfu
 l of $2$- and $3$-convolutive sequences. We were able to prove the respect
 ive convolutive property of each such sequence via generating function man
 ipulations\, and we also provided combinatorial proofs for the $2$-convolu
 tive property for three of the sequences identified.  \n\nIn this talk\, I
  will share details of many of the results that we obtained\, and I will c
 lose with several questions for future study.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Fel (Technion\, Israel)
DTSTART:20251218T200000Z
DTEND:20251218T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/128
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/128/">Frobenius problem in numerical semigroups 
 $S({\\bf d}^m)$</a>\nby Leonid Fel (Technion\, Israel) as part of New York
  Number Theory Seminar\n\n\nAbstract\nContent :\n\\begin{itemize}\n\\item 
 Definition and notations\n\\item Frobenius problem -- basic facts\n\\item 
 Special numerical semigroups $S({\\bf d}^m)$\n\\item Symmetric numerical s
 emigroups $S({\\bf d}^m)$\n\\item Semigroups $S({\\bf d}^3)$ and minimal r
 elations\n\\item Semigroup rings $k\\left[S({\\bf d}^m)\\right]$\n\\item G
 orenstein rings and complete intersection\n\\item Identities for degrees o
 f syzygies in $S({\\bf d}^m)$\n\\item Applying identities\n\\item Weak asy
 mptotics of Frobenius numbers $F\\left({\\bf d}^3\n\\right)$\n\\item Conje
 ctures and questions\n\\end{itemize}\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Rajogopal (MIT)
DTSTART:20260212T200000Z
DTEND:20260212T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/129
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/129/">Possible sizes of sumsets</a>\nby Isaac Ra
 jogopal (MIT) as part of New York Number Theory Seminar\n\n\nAbstract\nNat
 hanson introduced the range of cardinalities of $h$-fold sumsets  \n $ \\m
 athcal{R}(h\,k):= \\{|hA|:A \\subseteq \\mathbb{Z} \\text{ and }|A| = k\\}
 . $ \n Following a remark of  Erdos and Szemeredi that determined the form
  of $\\mathcal{R}(h\,k)$ when $h=2$\, Nathanson asked what the form of $\\
 mathcal{R}(h\,k)$ is for arbitrary $h\, k \\in \\mathbb{N}$.  For $h \\in 
 \\mathbb{N}$\, we prove there is some constant $k_h \\in \\mathbb{N}$ such
  that if $k > k_h$\, then $\\mathcal{R}(h\,k)$  is the entire interval $\\
 left[hk-h+1\,\\binom{h+k-1}{h}\\right]$ except for a specified set of $\\b
 inom{h-1}{2}$ numbers.   Moreover\, we show that one can take $k_3 = 2$.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20260219T200000Z
DTEND:20260219T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/130
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/130/">Diversity\, equity\, and inclusion for pro
 blems in additive number theory</a>\nby Mel Nathanson (CUNY) as part of Ne
 w York Number Theory Seminar\n\n\nAbstract\nThis talk will survey the dive
 rsity of problems in additive number theory\, observe that equity requires
  the consideration of less currently popular problems\, and argue for thei
 r inclusion in the additive canon.  Of particular interest will be problem
 s about the sizes of sumsets of finite sets of integers and problems about
  the intersection of sumsets.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruce Reznick (University of Illinois at Urbana-Champaign)
DTSTART:20260226T200000Z
DTEND:20260226T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/131
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/131/">Equal sums of two cubes of quadratic forms
 </a>\nby Bruce Reznick (University of Illinois at Urbana-Champaign) as par
 t of New York Number Theory Seminar\n\n\nAbstract\nWe give a complete desc
 ription of all solutions to the equation $f_1^3 + f_2^3 = f_3^3 + f_4^3$\n
 for quadratic forms $f_j \\in \\mathbb C[x\,y]$ and show how\, roughly two
  thirds of the time\, it can be  \nextended to three equal sums of pairs o
 f cubes. We also count\nthe number of ways a sextic $p \\in \\mathbb C[x\,
 y]$ can be written as a sum of two cubes. The\nextreme example is $p(x\,y)
  = xy(x^4-y^4)$\, which has six such representations. There are name-drops
 \nof Euler and Ramanujan.\n\nThis talk is based on the paper of the same n
 ame\, which appeared in the\n{\\it International Journal of Number Theory}
  {\\bf 17} (2021)\, pp.761-786\, MR4254775.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shalom Eliahou (Universit\\'e du Littoral C\\^ote d'Opale\, Calais
 \, France)
DTSTART:20260326T190000Z
DTEND:20260326T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/132
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/132/">On Wilf's conjecture for numerical semigro
 ups</a>\nby Shalom Eliahou (Universit\\'e du Littoral C\\^ote d'Opale\, Ca
 lais\, France) as part of New York Number Theory Seminar\n\n\nAbstract\nA 
 numerical semigroup $S$ is a cofinite submonoid of $\\mathbb{N}$. This mea
 ns that $S$ is stable under addition\, contains $0$\, and has finite compl
 ement in $\\mathbb{N}$. Some important numbers attached to $S$ are its gen
 us $g = \\text{card}(\\mathbb{N} \\setminus S)$\, its conductor $c=\\max(\
 \mathbb{Z} \\setminus S)+1$ and its minimal number $n$ of generators. Half
  a century ago\, Herbert Wilf came up with a very clever conjectural upper
  bound on the genus $g$ in terms of $c$ and $n$\, namely \n$$g \\le c(1-1/
 n).$$\nIn this talk\, we will provide a brief overview of the current stat
 us of Wilf's conjecture and discuss connections with additive combinatoric
 s\, graph theory and commutative algebra.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Larsen (MIT)
DTSTART:20260305T200000Z
DTEND:20260305T213000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/133
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/133/">Additive bases and minimal subbases</a>\nb
 y Daniel Larsen (MIT) as part of New York Number Theory Seminar\n\n\nAbstr
 act\nWe construct an additive basis $A$ of order 2 whose representation fu
 nction satisfies \n$r_A(n) > \\varepsilon \\log n$ for all sufficiently la
 rge $n$\, yet which contains no minimal asymptotic subbasis.  This confirm
 s a conjecture of Erdos and Nathanson from 1979.  More generally\, we disc
 uss a strategy for constructing asymptotic bases which do not have any min
 imal asymptotic subbases and satisfy other desired properties.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20260312T190000Z
DTEND:20260312T203000Z
DTSTAMP:20260404T111449Z
UID:New_York_Number_Theory_Seminar/134
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/New_Y
 ork_Number_Theory_Seminar/134/">Sumset intersection problems</a>\nby Mel N
 athanson (CUNY) as part of New York Number Theory Seminar\n\n\nAbstract\nL
 et $\n = \\{1\,2\,3\,\\ldots\\}$ be the set of positive integers. Let $A$ 
 be a subset of  an additive abelian semigroup $S$ and let $hA$ be the $h$-
 fold sumset of $A$.   The following question is considered:\nLet $(A_q)_{q
 =1}^{\\infty}$ be a strictly decreasing sequence of sets in\n$S$ and let  
 $A = \\bigcap_{q=1}^{\\infty} A_q$.  \nDescribe the set  $\\mathcal{H}(A_q
 )$  of positive integers such that\n\\[\nhA = \\bigcap_{q=1}^{\\infty} hA_
 q.\n\\]\nA  sample result:  If $A_q$ is a set of positive integers for all
  $q$\, then $\\mathcal{H}(A_q)=\n$.\n\nHere are some nice open problems.  
 \n\n1. For a given set $X$\, does there exist a  strictly decreasing seque
 nce\n$(A_q)_{q=1}^{\\infty} $ of sets of integers such that $\\mathcal{H}(
 A_q)= X$.  \n\n2. For   given sets $A$ and  $X$\, does there exist a  stri
 ctly decreasing sequence\n$(A_q)_{q=1}^{\\infty} $ of sets of integers suc
 h that $A = \\bigcap_{q=1}^{\\infty} A_q$\nand $\\mathcal{H}(A_q)= X$.  \n
 \n3. Does there exist a set $Y$ of positive integers such that $\\mathcal{
 H}(A_q) \\neq Y$\nfor every strictly decreasing sequence $(A_q)_{q=1}^{\\i
 nfty}$ of sets of integers?\n\n4. For a given set $A$\, let $\\mathcal{H}^
 *(A)$ be the set of all sets $X$  such that $\\mathcal{H}(A_q) = X$ for so
 me  strictly decreasing sequence $(A_q)_{q=1}^{\\infty}$ with $A = \\bigca
 p_{q=1}^{\\infty} A_q$.\n\n5. Compute $\\mathcal{H}^*(A)$ for $A = \\{0\\}
 $.\n
LOCATION:https://stable.researchseminars.org/talk/New_York_Number_Theory_S
 eminar/134/
END:VEVENT
END:VCALENDAR