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BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20260910T190000Z
DTEND:20260910T200000Z
DTSTAMP:20261107T161503Z
UID:NYNTS/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/1/">Si
 don sets with Delta-separated sumsets</a>\nby Mel Nathanson (CUNY) as part
  of New York Number Theory Seminar\n\n\nAbstract\nThe set $A$ is a $B_h$-s
 et if every element of the sumset $hA$ has a unique representation as a su
 m of $h$ elements of $A$.  A $B_2$-set is also called a Sidon set.  A $B_{
 h\,\\Delta}$-set is a $B_h$-set $A$ whose sumset $hA$ is $\\Delta$-separat
 ed\, that is\, \n$x'-x \\geq \\Delta$ for all $x\,x' \\in hA$ with $x < x'
 $.\nUpper and lower bounds are obtained for the cardinality of the largest
  $B_{2\,\\Delta}$-sets contained in   $\\{1\,2\,\\ldots\, n\\}$\, that is\
 , sets $A \\subseteq \\{1\,2\,\\ldots\, n\\}$ such that\, if $a\,b\,c\,d \
 \in A$ and $\\{a\,b\\} \\neq \\{c\,d\\}$\, then $|(a+b)-(c+d)| \\geq \\Del
 ta$.\n
LOCATION:https://researchseminars.org/talk/NYNTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20260917T190000Z
DTEND:20260917T200000Z
DTSTAMP:20261107T161503Z
UID:NYNTS/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/2/">B_
 h-sets and perturbations in normed vector spaces</a>\nby Mel Nathanson (CU
 NY) as part of New York Number Theory Seminar\n\n\nAbstract\nThe subset $A
  = \\{a_i:i \\in I\\}$ of a normed vector space is a $B_h$-set if every el
 ement \nof the sumset $hA$ has a unique representation as a sum of $h$ ele
 ments of $A$.  \nAn $\\varepsilon$-perturbation of $A$ is a set $A' = \\{a
 '_i:i\\in I\\}$ such that $|a'-a|<\\varepsilon$ \nfor all $i \\in I$. \nLe
 t $\\Delta_{hA} = \\inf\\{|x'-x| : x\,x' \\in hA \\text{ and } x\\neq x'\\
 }$.  \nIt is proved that if $A$ is  finite or countably infinite set with 
 $\\Delta_{hA}>0$\, \nthen there is a $B_h$-set $A'$ that is an $\\varepsil
 on$-perturbation of $A$.\n
LOCATION:https://researchseminars.org/talk/NYNTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20260910T183000Z
DTEND:20260910T190000Z
DTSTAMP:20261107T161503Z
UID:NYNTS/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/3/">Di
 scussion of AI and Navier-Stokes solution</a>\nby Mel Nathanson (CUNY) as 
 part of New York Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYNTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (Lehman College (CUNY))
DTSTART:20260924T190000Z
DTEND:20260924T200000Z
DTSTAMP:20261107T161503Z
UID:NYNTS/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/4/">Po
 sitivity and negativity for additive h-bases for n</a>\nby Mel Nathanson (
 Lehman College (CUNY)) as part of New York Number Theory Seminar\n\n\nAbst
 ract\nA finite set $A$ of integers is an $h$-basis for $n$ if every intege
 r in the interval of integers \n$\\{0\,1\,2\,\\ldots\, n\\}$ can be repres
 ented as the sum of exactly \n $h$  not necessarily distinct elements of $
 A$.  \n In additive number theory\, attention has focused on sets of nonne
 gative integers\, \n but one can also consider sets that contain negative 
 integers and investigate  \n the effects of ``negativity'' on the classica
 l problem of extremal properties of $h$-bases for $n$.    \nThere are new 
 results and  a new class of problems \nfor additive bases that contain bot
 h positive and negative integers.\n
LOCATION:https://researchseminars.org/talk/NYNTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O'Bryant (College of Staten Island (CUNY))
DTSTART:20261001T190000Z
DTEND:20261001T200000Z
DTSTAMP:20261107T161503Z
UID:NYNTS/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/5/">On
  the thickness of infinite generalized Sidon sets</a>\nby Kevin O'Bryant (
 College of Staten Island (CUNY)) as part of New York Number Theory Seminar
 \n\n\nAbstract\nLet $A$ be an infinite ``generalized" Sidon set. We consid
 er the possible values of $\\liminf_{n} A(n)/\\sqrt{n/\\log n}$. Erdos pro
 ved that this is finite for Sidon sets\, and Chen for $B_{2h}$-sets. We ar
 e concerned with actually bounding the limit for $B_{2h}$-sets and $g$-Gol
 omb rulers. We will review what is known for $B_h$-sets (odd $h$) also.\n
LOCATION:https://researchseminars.org/talk/NYNTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Kravitz (Oxford University)
DTSTART:20261015T190000Z
DTEND:20261015T200000Z
DTSTAMP:20261107T161503Z
UID:NYNTS/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/6/">In
 equalities among sums of dilates</a>\nby Noah Kravitz (Oxford University) 
 as part of New York Number Theory Seminar\n\n\nAbstract\nLet $c \\cdot A$ 
 denote the dilate of the set $A$ by the scalar $c$.  For which choices of 
 complex numbers $\\lambda_1\, \\ldots\, \\lambda_\\ell\, \\mu_1\, \\ldots\
 , \\mu_m$ does the inequality\n$$|\\lambda_1 \\cdot A+\\cdots+\\lambda_\\e
 ll \\cdot A| \\leq |\\mu_1 \\cdot A+\\cdots+\\mu_m \\cdot A|$$\nhold for a
 ll finite sets $A \\subseteq \\mathbb{C}$?  This question captures a vast 
 generalization of the more-sums-than-differences sets phenomenon.  We will
  discuss recent progress\, with a particular focus on the setting where th
 e dilates are integers.\n
LOCATION:https://researchseminars.org/talk/NYNTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David  Chudnovsky and Gregory Chudnovsky (NYU)
DTSTART:20261022T190000Z
DTEND:20261022T200000Z
DTSTAMP:20261107T161503Z
UID:NYNTS/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/7/">40
  years later</a>\nby David  Chudnovsky and Gregory Chudnovsky (NYU) as par
 t of New York Number Theory Seminar\n\n\nAbstract\nWe describe new inequal
 ities related to various Diophantine problems.\n
LOCATION:https://researchseminars.org/talk/NYNTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wooter van Doorn (Netherlands)
DTSTART:20261105T200000Z
DTEND:20261105T210000Z
DTSTAMP:20261107T161503Z
UID:NYNTS/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/8/">Sh
 ort Egyptian fractions</a>\nby Wooter van Doorn (Netherlands) as part of N
 ew York Number Theory Seminar\n\n\nAbstract\nGiven a fraction $a/b \\in (0
 \, 1)$\, write it as a sum of distinct unit fractions. What is the least n
 umber of unit fractions you need? Over $75$ years ago\, Erd\\H{o}s conject
 ured that $O(\\log \\log b)$ unit fractions always suffices\, which would 
 be optimal if true. This conjecture was recently proven by an internal mod
 el of OpenAI\, and in this talk we aim to explain a simplified version of 
 the proof\, which was obtained in joint work with Thomas Bloom.\n
LOCATION:https://researchseminars.org/talk/NYNTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Riblet (ENS Paris-Saclay\, France)
DTSTART:20261203T200000Z
DTEND:20261203T210000Z
DTSTAMP:20261107T161503Z
UID:NYNTS/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/9/">On
  the largest Sidon subset in a finite subset of R^N</a>\nby Robin Riblet (
 ENS Paris-Saclay\, France) as part of New York Number Theory Seminar\n\n\n
 Abstract\nA set is called a Sidon set if all pairwise sums of its elements
  are distinct\, up to the order of the summands. A classical question in a
 dditive combinatorics\, related to a conjecture of Erd\\H{o}s\, asks how l
 arge a Sidon subset one can always find in an arbitrary finite set.\n\nIn 
 this talk\, I will present a new lower bound showing that every set of $n$
  points in $\\mathbb{R}^N$ contains a Sidon subset of cardinality at least
 \n$$\\left(\\frac{1}{3\\sqrt{3}}+o(1)\\right)\\sqrt{n}.$$ \nIn particular\
 , this improves a previous lower bound of Abbott for finite sets of intege
 rs.\n
LOCATION:https://researchseminars.org/talk/NYNTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Montejano (Universidad Nacional Aut\\' onoma de M\\' exico)
DTSTART:20261210T200000Z
DTEND:20261210T210000Z
DTSTAMP:20261107T161503Z
UID:NYNTS/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/10/">S
 idon–Ramsey and B_h Ramsey numbers</a>\nby Amanda Montejano (Universidad
  Nacional Aut\\' onoma de M\\' exico) as part of New York Number Theory Se
 minar\n\n\nAbstract\nThe Sidon--Ramsey number \\(SR(k)\\) is the smallest 
 positive integer\n\\(n\\) such that every \\(k\\)-coloring of the set of p
 ositive integers \\([1\,n]\\) contains two\ndistinct unordered pairs with 
 the same sum\, all of whose elements\nhave the same color (repetition with
 in each pair is allowed).\nEquivalently\, \\(SR(k)\\) is the first value o
 f \\(n\\) for which\n\\([1\,n]\\) cannot be partitioned into \\(k\\) Sidon
  sets.\nIn this talk\, we explore this parameter and  its\nconnections wit
 h Ramsey theory and additive combinatorics.\nWe discuss the asymptotic beh
 avior of  \\(SR(k)\\)  and two generalizations\,\nwith particular emphasis
  on \\(B_h\\)--Ramsey numbers\, which extend\nthe problem from sums of two
  elements to sums of \\(h\\) elements.\n\nThis is a joint work with Manuel
  A. Espinosa-García\, Edgardo Roldán-Pensado and J. David Suárez.\n
LOCATION:https://researchseminars.org/talk/NYNTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hu Tan (University of Chinese Academy of Sciences\, China)
DTSTART:20261119T200000Z
DTEND:20261119T210000Z
DTSTAMP:20261107T161503Z
UID:NYNTS/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/11/">A
  proof of Fraenkel’s conjecture</a>\nby Hu Tan (University of Chinese Ac
 ademy of Sciences\, China) as part of New York Number Theory Seminar\n\n\n
 Abstract\nFraenkel’s conjecture asserts that any partition of the intege
 rs into $m \\geq 3$ Beatty sequences with pairwise distinct moduli must ha
 ve densities $2^j/(2^m - 1)$ \nfor $j = 0\, …\, m - 1$. In this talk\, I
  will present a proof whose main ingredient is a density bound independent
  of the number of parts: every such partition contains a sequence of densi
 ty at least 1/3. Building on the discrete Fourier framework developed by G
 raham and O’Bryant\, we establish this bound by combining analytic estim
 ates with exact finite verification using integer and rational arithmetic.
  The bound supplies the missing input for Tijdeman’s deletion method\, a
 llowing us to recover the binary density pattern by induction. I will expl
 ain how the Fourier argument connects with the combinatorial reconstructio
 n and discuss the role of the finite computations. This is joint work with
  Professor Ying Zhang.\n
LOCATION:https://researchseminars.org/talk/NYNTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashvin Varada Rajan (Baltimore)
DTSTART:20261112T200000Z
DTEND:20261112T210000Z
DTSTAMP:20261107T161503Z
UID:NYNTS/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/12/">N
 otes on a cubic diophantine equation</a>\nby Ashvin Varada Rajan (Baltimor
 e) as part of New York Number Theory Seminar\n\n\nAbstract\nWe study the c
 ubic Diophantine equation\n\\[\nH_k : Y^3 - Y = k(X^3 - X)\,\n\\]\nwhere $
 k > 1$ is a fixed integer\, describing some methods to explicitly find all
  integral solutions when $k$ is given\, and establishing qualitative prope
 rties of the set of integral solutions for certain infinite sets $\\{H_k\\
 }$ of such equations.\n
LOCATION:https://researchseminars.org/talk/NYNTS/12/
END:VEVENT
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