BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20260910T190000Z
DTEND:20260910T200000Z
DTSTAMP:20261107T155102Z
UID:NYNTS/1
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /1/">Sidon 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 
 $B_h$-set if every element of the sumset $hA$ has a unique representation 
 as a sum 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 $\\Delta$-
 separated\, 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   $\\{1\,2\,\\ldots\, n\\}$\, t
 hat is\, sets $A \\subseteq \\{1\,2\,\\ldots\, n\\}$ such that\, if $a\,b\
 ,c\,d \\in A$ and $\\{a\,b\\} \\neq \\{c\,d\\}$\, then $|(a+b)-(c+d)| \\ge
 q \\Delta$.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20260917T190000Z
DTEND:20260917T200000Z
DTSTAMP:20261107T155102Z
UID:NYNTS/2
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /2/">B_h-sets and perturbations in normed vector spaces</a>\nby Mel Nathan
 son (CUNY) as part of New York Number Theory Seminar\n\n\nAbstract\nThe su
 bset $A = \\{a_i:i \\in I\\}$ of a normed vector space is a $B_h$-set if e
 very element \nof the sumset $hA$ has a unique representation as a sum of 
 $h$ elements 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
 $. \nLet $\\Delta_{hA} = \\inf\\{|x'-x| : x\,x' \\in hA \\text{ and } x\\n
 eq x'\\}$.  \nIt is proved that if $A$ is  finite or countably infinite se
 t with $\\Delta_{hA}>0$\, \nthen there is a $B_h$-set $A'$ that is an $\\v
 arepsilon$-perturbation of $A$.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20260910T183000Z
DTEND:20260910T190000Z
DTSTAMP:20261107T155102Z
UID:NYNTS/3
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /3/">Discussion of AI and Navier-Stokes solution</a>\nby Mel Nathanson (CU
 NY) as part of New York Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (Lehman College (CUNY))
DTSTART:20260924T190000Z
DTEND:20260924T200000Z
DTSTAMP:20261107T155102Z
UID:NYNTS/4
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /4/">Positivity and negativity for additive h-bases for n</a>\nby Mel Nath
 anson (Lehman College (CUNY)) as part of New York Number Theory Seminar\n\
 n\nAbstract\nA finite set $A$ of integers is an $h$-basis for $n$ if every
  integer in the interval of integers \n$\\{0\,1\,2\,\\ldots\, n\\}$ can be
  represented as the sum of exactly \n $h$  not necessarily distinct elemen
 ts of $A$.  \n In additive number theory\, attention has focused on sets o
 f nonnegative integers\, \n but one can also consider sets that contain ne
 gative integers and investigate  \n the effects of ``negativity'' on the c
 lassical problem of extremal properties of $h$-bases for $n$.    \nThere a
 re new results and  a new class of problems \nfor additive bases that cont
 ain both positive and negative integers.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O'Bryant (College of Staten Island (CUNY))
DTSTART:20261001T190000Z
DTEND:20261001T200000Z
DTSTAMP:20261107T155102Z
UID:NYNTS/5
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /5/">On the thickness of infinite generalized Sidon sets</a>\nby Kevin O'B
 ryant (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
  consider the possible values of $\\liminf_{n} A(n)/\\sqrt{n/\\log n}$. Er
 dos proved that this is finite for Sidon sets\, and Chen for $B_{2h}$-sets
 . We are concerned with actually bounding the limit for $B_{2h}$-sets and 
 $g$-Golomb rulers. We will review what is known for $B_h$-sets (odd $h$) a
 lso.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Kravitz (Oxford University)
DTSTART:20261015T190000Z
DTEND:20261015T200000Z
DTSTAMP:20261107T155102Z
UID:NYNTS/6
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /6/">Inequalities among sums of dilates</a>\nby Noah Kravitz (Oxford Unive
 rsity) as part of New York Number Theory Seminar\n\n\nAbstract\nLet $c \\c
 dot A$ denote the dilate of the set $A$ by the scalar $c$.  For which choi
 ces of complex numbers $\\lambda_1\, \\ldots\, \\lambda_\\ell\, \\mu_1\, \
 \ldots\, \\mu_m$ does the inequality\n$$|\\lambda_1 \\cdot A+\\cdots+\\lam
 bda_\\ell \\cdot A| \\leq |\\mu_1 \\cdot A+\\cdots+\\mu_m \\cdot A|$$\nhol
 d for all 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 w
 here the dilates are integers.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:David  Chudnovsky and Gregory Chudnovsky (NYU)
DTSTART:20261022T190000Z
DTEND:20261022T200000Z
DTSTAMP:20261107T155102Z
UID:NYNTS/7
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /7/">40 years later</a>\nby David  Chudnovsky and Gregory Chudnovsky (NYU)
  as part of New York Number Theory Seminar\n\n\nAbstract\nWe describe new 
 inequalities related to various Diophantine problems.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wooter van Doorn (Netherlands)
DTSTART:20261105T200000Z
DTEND:20261105T210000Z
DTSTAMP:20261107T155102Z
UID:NYNTS/8
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /8/">Short Egyptian fractions</a>\nby Wooter van Doorn (Netherlands) as pa
 rt of New 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 number of unit fractions you need? Over $75$ years ago\, Erd\\H{o}s 
 conjectured that $O(\\log \\log b)$ unit fractions always suffices\, which
  would be optimal if true. This conjecture was recently proven by an inter
 nal model of OpenAI\, and in this talk we aim to explain a simplified vers
 ion of the proof\, which was obtained in joint work with Thomas Bloom.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Riblet (ENS Paris-Saclay\, France)
DTSTART:20261203T200000Z
DTEND:20261203T210000Z
DTSTAMP:20261107T155102Z
UID:NYNTS/9
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /9/">On the largest Sidon subset in a finite subset of R^N</a>\nby Robin R
 iblet (ENS Paris-Saclay\, France) as part of New York Number Theory Semina
 r\n\n\nAbstract\nA set is called a Sidon set if all pairwise sums of its e
 lements are distinct\, up to the order of the summands. A classical questi
 on in additive combinatorics\, related to a conjecture of Erd\\H{o}s\, ask
 s how large 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 a
 t least\n$$\\left(\\frac{1}{3\\sqrt{3}}+o(1)\\right)\\sqrt{n}.$$ \nIn part
 icular\, this improves a previous lower bound of Abbott for finite sets of
  integers.\n
LOCATION:/talk/NYNTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Montejano (Universidad Nacional Aut\\' onoma de M\\' exico)
DTSTART:20261210T200000Z
DTEND:20261210T210000Z
DTSTAMP:20261107T155102Z
UID:NYNTS/10
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /10/">Sidon–Ramsey and B_h Ramsey numbers</a>\nby Amanda Montejano (Univ
 ersidad Nacional Aut\\' onoma de M\\' exico) as part of New York Number Th
 eory Seminar\n\n\nAbstract\nThe Sidon--Ramsey number \\(SR(k)\\) is the sm
 allest positive integer\n\\(n\\) such that every \\(k\\)-coloring of the s
 et of positive integers \\([1\,n]\\) contains two\ndistinct unordered pair
 s with the same sum\, all of whose elements\nhave the same color (repetiti
 on within each pair is allowed).\nEquivalently\, \\(SR(k)\\) is the first 
 value of \\(n\\) for which\n\\([1\,n]\\) cannot be partitioned into \\(k\\
 ) Sidon sets.\nIn this talk\, we explore this parameter and  its\nconnecti
 ons with Ramsey theory and additive combinatorics.\nWe discuss the asympto
 tic behavior of  \\(SR(k)\\)  and two generalizations\,\nwith particular e
 mphasis 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:/talk/NYNTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hu Tan (University of Chinese Academy of Sciences\, China)
DTSTART:20261119T200000Z
DTEND:20261119T210000Z
DTSTAMP:20261107T155102Z
UID:NYNTS/11
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /11/">A proof of Fraenkel’s conjecture</a>\nby Hu Tan (University of Chi
 nese Academy of Sciences\, China) as part of New York Number Theory Semina
 r\n\n\nAbstract\nFraenkel’s conjecture asserts that any partition of the
  integers into $m \\geq 3$ Beatty sequences with pairwise distinct moduli 
 must have densities $2^j/(2^m - 1)$ \nfor $j = 0\, …\, m - 1$. In this t
 alk\, I will present a proof whose main ingredient is a density bound inde
 pendent of the number of parts: every such partition contains a sequence o
 f density at least 1/3. Building on the discrete Fourier framework develop
 ed by Graham and O’Bryant\, we establish this bound by combining analyti
 c estimates with exact finite verification using integer and rational arit
 hmetic. The bound supplies the missing input for Tijdeman’s deletion met
 hod\, allowing us to recover the binary density pattern by induction. I wi
 ll explain how the Fourier argument connects with the combinatorial recons
 truction and discuss the role of the finite computations. This is joint wo
 rk with Professor Ying Zhang.\n
LOCATION:/talk/NYNTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashvin Varada Rajan (Baltimore)
DTSTART:20261112T200000Z
DTEND:20261112T210000Z
DTSTAMP:20261107T155102Z
UID:NYNTS/12
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /12/">Notes on a cubic diophantine equation</a>\nby Ashvin Varada Rajan (B
 altimore) as part of New York Number Theory Seminar\n\n\nAbstract\nWe stud
 y the cubic Diophantine equation\n\\[\nH_k : Y^3 - Y = k(X^3 - X)\,\n\\]\n
 where $k > 1$ is a fixed integer\, describing some methods to explicitly f
 ind all integral solutions when $k$ is given\, and establishing qualitativ
 e properties of the set of integral solutions for certain infinite sets $\
 \{H_k\\}$ of such equations.\n
LOCATION:/talk/NYNTS/12/
END:VEVENT
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