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BEGIN:VEVENT
SUMMARY:Kevin O'Bryant (CUNY)
DTSTART:20260713T130000Z
DTEND:20260713T132500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/1
DESCRIPTION:Title: The Sidon error term\nby Kevin O'Bryant (CUNY) as part of Comb
inatorial and additive number theory seminar (CANT 2026)\n\nLecture held i
n Science Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nA S
idon set is a set ${\\mathcal A}$ of integers that has no nontrivial solut
ions to $a+b=c+d$. It has been known since 1941 (Erd\\H{o}s and Tur\\'an)
that if ${\\mathcal A}$ is a finite Sidon set\, then $\\text{diam}({\\math
cal A}) \\ge k^2 - 2k^{3/2} + O(k)$\, and since 1939 (Singer) that the $k^
2$ term cannot be improved. Only in the last 5 years has the error term $-
2k^{3/2}$ been sharpened (Balogh\, F\\"uredi\, and Roy\, then O'Bryant\, t
hen Carter\, Hunter\, O'Bryant). In this talk\, I will relay the latest im
provements and applications\, and the use of AI (AlphaEvolve) in their dis
covery. Joint work with D.~Carter\, B.~Georgiev\, Z.~Hunter\, J.~G.~Serra
no\, T.~Tao\, and A.~Zs.~Wagner.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aradhya Goel (Indian Institute of Technology Kanpur)
DTSTART:20260713T133000Z
DTEND:20260713T135500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/2
DESCRIPTION:Title: Sophie Germain primes and the totient of Fibonacci numbers\nby
Aradhya Goel (Indian Institute of Technology Kanpur) as part of Combinato
rial and additive number theory seminar (CANT 2026)\n\nLecture held in Sci
ence Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nWe study
the set $S(q)$ of residue classes $r$ modulo the Pisano period $\\pi(q)$
for which $q \\mid \\varphi(F_m)$ for every $m \\equiv r \\pmod{\\pi(q)}$.
We prove that if $q$ is a Sophie Germain prime and $z(2q+1) \\mid \\pi(q)
$\, where $z$ denotes the rank of apparition\, then $S(q)$ is a nonempty a
rithmetic progression\; for $q > 5$\, its cardinality is odd and $q \\equi
v 8 \\pmod{15}$. Conversely\, if a prime $p \\equiv 1 \\pmod{q}$ has $z(p)
\\mid \\pi(q)$\, then necessarily $p = 2q+1$\, so $q$ is Sophie Germain.
\nWe conjecture that $S(q) \\neq \\emptyset$ forces the existence of such
a prime $p$\; this is verified for all $q \\leq 50{\,}000$. Assuming the d
ivisibility $z(2q+1) \\mid \\pi(q)$ holds for infinitely many Sophie Germa
in primes (verified for approximately $23.9\\%$ of the $669$ Sophie Germai
n primes $q \\leq 50{\,}000$)\, the Sophie Germain conjecture implies the
existence of infinitely many primes $q \\equiv 8 \\pmod{15}$ with $(2q+1)
\\mid F_{\\pi(q)}$ -- a purely Fibonacci-theoretic condition. \nThese resu
lts generalize to arbitrary Lucas sequences $U_n(P\,Q)$ with non-square di
scriminant.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Pal Pach (Renyi Institute)
DTSTART:20260713T140000Z
DTEND:20260713T142500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/3
DESCRIPTION:Title: On the density of Kravitz sets\nby Peter Pal Pach (Renyi Insti
tute) as part of Combinatorial and additive number theory seminar (CANT 20
26)\n\nLecture held in Science Center in the CUNY Graduate Center (4th flo
or).\n\nAbstract\nWe show that for a subset $A$ of the cyclic group of pri
me order $p>3$\, if the sumset $A+A-2A=\\{a_1+a_2-2a_3:\\ a_1\,a_2\,a_3 \
\in A\\}$ is not the whole group\, then $|A|\\le \\frac27\\\,p$. \nBesid
es combinatorial arguments\, we utilize a general technique involving lin
ear programming\, which may find further applications in additive combin
atorics in the future. \n Joint work with Vsevolod Lev\, Mate Matolcsi\, D
aniel Varga.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Ramon Madrid Padilla (Virginia Tech)
DTSTART:20260713T143000Z
DTEND:20260713T145500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/4
DESCRIPTION:Title: Convolution inequalities and applications\nby Jose Ramon Madri
d Padilla (Virginia Tech) as part of Combinatorial and additive number the
ory seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Grad
uate Center (4th floor).\n\nAbstract\nIn this talk\, we will discuss a col
lection of optimal convolution inequalities for real-valued functions on t
he hypercube\, motivated by combinatorial applications. In particular\, as
a consequence we obtain sharp bounds for sumsets and additive energies of
subsets of the hypercube.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Grynkiewicz (Memphis University)
DTSTART:20260713T160000Z
DTEND:20260713T162500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/7
DESCRIPTION:Title: On factorizations of zero-sum sequences over abelian torsion grou
ps\nby David Grynkiewicz (Memphis University) as part of Combinatorial
and additive number theory seminar (CANT 2026)\n\nLecture held in Science
Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nLet $G$ be a
n additive abelian torsion group and let $G_0\\subseteq G$ be a subset. A
zero-sum sequence over $G_0$ is an unordered string of terms from $G_0$ (r
epetition of terms allowed) such that the sum of terms is $0$. In the last
few decades\, the connection between factorizations of zero-sum sequences
and factorization of elements in rings of integers has been made more pre
cise and extended into much more general algebraic settings. The extent to
which factorization are wild or well-behaved is often measured by the fin
iteness and size of various arithmetic factorization invariants. Some of t
he most common include the catenary degree $\\mathsf c(G_0)$\, the set of
successive distances $\\Delta(G_0)$\, and the elastacities $\\rho_k(G_0)$.
We begin by introducing what these invariants are in purely combinatorial
terms and explain how they measure constraint of factorization in algebra
ic settings. \n\nIn the past\, there has been much focus on finite groups\
, and more recently\, on subsets of finitely generated groups. However\, v
ery little was known in the case of non-finitely generated abelian groups.
In part\, this is because common invariants used to study factorization\,
such as the Davenport Constant\, are no longer guaranteed to be finite. I
n order to better understand factorization in the setting of infinite abel
ian torsion groups\, we introduce a new technique measuring the size of a
sequence not by the number of its terms but rather by its cross number\, $
\\sum_{i=1}^{\\ell} \\frac{1}{\\text{\\rm ord} (g_i)}$\, where the $g_i\\i
n G_0\\subseteq G$ are the terms in the sequence. The use of cross numbers
allows us to define three constants\, $\\mathsf K(G_0)$\, $\\mathsf k(G_0
)$ and $\\mathsf K_{\\mathsf{inf}}(G_0)$\, defined as the supremum of all
cross numbers of minimal (by inclusion) zero-sum sequences\, the supremum
of all cross numbers of zero-sum free sequences (sequences having no zero-
sum subsequence)\, and the infimum of all cross numbers of nontrivial zero
-sum sequences. The first two of these constants have appeared in the lite
rature before\, but the third is newly introduced here. \n\nIn the first p
art of this two part talk\, it was shown that factorization of zero-sum se
quences can be very ill-behaved when $\\mathsf K_{\\mathsf{inf}}(G_0)=0$.
In this second part\, we consider what happens when $\\mathsf K_{\\mathsf{
inf}}(G_0)>0$\, specifically in the setting of infinite abelian torsion gr
oups with finite total rank. In this setting\, the first two cross number
constants $\\mathsf K(G_0)$ and $\\mathsf k(G_0)$ are always finite. Assum
ing $\\delta:=\\mathsf K_{\\mathsf{inf}}(G_0)>0$\, we then obtain a genera
l upper bound for the catenary degree $$\\mathsf c(G_0)\\leq \\max\\{2\\de
lta^{-1}\\mathsf k(G_0)+1\, \\quad 2\\delta^{-1}\\mathsf K(G_0)\\}.$$ In p
articular\, this implies that both the set of successive distances $\\Delt
a(G_0)$ and catenary degree are always finite under these circumstances\,
with explicit concrete upper bounds. Moreover\, our upper bound on the cat
enary degree is tight\, meaning there are infinite families of subsets $G_
0\\subseteq G$ for which equality holds above. In addition\, for the speci
al case of quasi-cyclic groups\, we are able to partially characterize wha
t subsets $G_0$ with $\\mathsf K_{\\mathsf{inf}}(G_0)>0$ look like and use
this to give a lower bound for the elasticities $\\rho_k(G_0)$. Combined
with the upper bound on the catenary degree\, this yields a structural des
cription of the possible refactorization lengths of a product of $k$ irred
ucibles. This is joint work with Alfred Geroldinger and Guoqing Wang.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gabdullin (University of Illinois at Urbana-Champaign)
DTSTART:20260713T150000Z
DTEND:20260713T152500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/13
DESCRIPTION:Title: Moments of the shifted prime divisor function\nby Mikhail Gab
dullin (University of Illinois at Urbana-Champaign) as part of Combinatori
al and additive number theory seminar (CANT 2026)\n\nLecture held in Scien
ce Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nLet $\\ome
ga^*(n) = \\{d|n: d=p-1\, \\mbox{$p$ is a prime}\\}$ denote the ``shifted
prime divisor'' function. It is easy to see that $\\sum_{n\\leq x}\\omega^
*(n)=x\\log\\log x+O(x)$\, similar to the average value of $\\omega(n)$\,
the number of prime divisors of $n$. We confirm a recent conjecture of Fan
and Pomerance by proving that\, for each integer $k\\geq2$\, $\n\\qquad \
\sum_{n\\leq x}\\omega^*(n)^k \\asymp x(\\log x)^{2^k-k-1}\,\n$ \nwhere th
e implied constant may depend only on $k$. The proof relies on a combinato
rial identity for the least common multiple\, viewed as a multiplicative a
nalogue of the inclusion-exclusion principle\, together with the theory of
multiplicative functions.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfred Geroldinger (University of Graz\, Austria)
DTSTART:20260713T153000Z
DTEND:20260713T155500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/14
DESCRIPTION:Title: On factorizations of zero-sum sequences over abelian torsion grou
ps I\nby Alfred Geroldinger (University of Graz\, Austria) as part of
Combinatorial and additive number theory seminar (CANT 2026)\n\nLecture he
ld in Science Center in the CUNY Graduate Center (4th floor).\n\nAbstract\
nLet $G$ be an additive abelian group and let $G_0\\subseteq G$ be a subse
t. A zero-sum sequence over $G_0$ is an unordered string of terms from $G_
0$ (repetition of terms allowed) such that the sum of terms is $0$. The st
udy of zero-sum sequences dates back over 60 years\, and while they have o
ften been studied for purely combinatorial interest\, the original motivat
ion was due to connections with factorization in rings of integers in alge
braic number fields. In the last few decades\, the connection between fact
orizations of zero-sum sequences and factorization of elements in rings of
integers was made more precise and extended into much more general algebr
aic settings. This then allows the algebraic structure of factorization to
be studied via combinatorial properties of zero-sum sequences. We briefly
review this connection\, making all notions concrete\, and then turn our
focus to the combinatorial part. In the past\, there has been much focus o
n finite groups\, and more recently\, on subsets of finitely generated gro
ups. However\, very little was known in the case of non-finitely generated
abelian groups. In part\, this is because common invariants used to study
factorization\, such as the Davenport Constant\, are no longer guaranteed
to be finite. In order to better understand factorization in the setting
of infinite abelian torsion groups\, we introduce a new technique measurin
g the size of a sequence not by the number of its terms but rather by its
cross number\, $\\sum_{i=1}^{\\ell} \\frac{1}{\\text{\\rm ord} (g_i)}$\, w
here the $g_i\\in G_0 \\subseteq G$ are the terms in the sequence. Cross n
umbers have previously been used almost solely for finite groups. In order
to adapt their use into the infinite torsion group setting\, we need to i
ntroduce a new invariant\, $\\mathsf K_{\\mathsf{inf}}(G_0)$\, defined as
the infimum of all cross numbers of nontrivial zero-sum sequences with ter
ms from $G_0$. This then sets up dichotomy between when $\\mathsf K_{\\mat
hsf{inf}}(G_0)=0$ and when $\\mathsf K_{\\mathsf{inf}}(G_0)>0$. In this fi
rst part of two talks\, we focus on when $\\mathsf K_{\\mathsf{inf}}(G_0)=
0$\, and show that factorization of zero-sum sequences can be very ill-beh
aved under this assumption. In the follow-up talk\, we then instead consid
er when $\\mathsf K_{\\mathsf{inf}}(G_0)>0$ and see that this instead guar
antees that factorization must be well-behaved\, as measured by the finite
ness of several commonly factorization metrics. This is joint work with Da
vid J. Grynkiewicz and Guoqing Wang.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sinan Gunturk (New York University)
DTSTART:20260713T173000Z
DTEND:20260713T175500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/16
DESCRIPTION:Title: Exponential sums and a conjecture involving quantization of bandl
imited functions\nby Sinan Gunturk (New York University) as part of Co
mbinatorial and additive number theory seminar (CANT 2026)\n\nLecture held
in Science Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nS
igma-delta modulation is a classical method for oversampled coarse quantiz
ation which enables approximation of bandlimited functions (e.g. audio sig
nals) at high sampling rates despite using only two fixed levels to round
each sample. In the basic form of this method (the "first order" case)\, t
he approximation rate is $\\lambda^{-1}$ in the uniform norm where $\\lamb
da$ denotes the oversampling ratio\, but the pointwise error has been show
n to decay at least at the rate $\\lambda^{-4/3+\\epsilon}$ under generic
conditions. Meanwhile\, a long-standing folklore conjecture based on numer
ical simulations predicts square-root cancellation "on average"\, i.e. app
roximation rate of order $\\lambda^{-3/2+\\epsilon}$. We disprove the conj
ecture for the Besicovitch norm\, utilizing certain exponential sums of ba
ndlimited phase. Joint work with Maksym Radziwill.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Shkredov (Purdue University)
DTSTART:20260713T180000Z
DTEND:20260713T185000Z
DTSTAMP:20260709T184247Z
UID:CANT2026/17
DESCRIPTION:Title: On Korobov's optimal coefficients\nby Ilya Shkredov (Purdue U
niversity) as part of Combinatorial and additive number theory seminar (CA
NT 2026)\n\nLecture held in Science Center in the CUNY Graduate Center (4t
h floor).\n\nAbstract\nLet $p$ be a prime number\, $d$ be a positive integ
er\, and $M\\ge 1$ be a real parameter. A tuple $(a_1\,\\dots\, a_d) \\in
\\mathbf{F}^d_p$ is called a tuple of (Korobov) {\\it optimal coefficients
} if\, for any nonzero $x\\in \\mathbf{F}_p$\, the inequality$$\n x|a_1 x|
\\dots |a_d x| \\ge \\frac{p^d}{M} \n$$ holds. \n These famous coefficie
nts arise naturally in numerical integration problems. Namely\, if a tupl
e $(a_1\, \\dots\, a_d)$ satisfying the inequality is found\, then any fun
ction $f:[0\,1]^d \\to \\mathbf{R}$ can be integrated using the formula $$
\n\\left| \\int_{[0\,1]^d} f(x)\\\,dx - \\frac{1}{p} \\sum_{x=1}^{p} f\\le
ft(\\frac{a_1 x}{p}\, \\dots\, \\frac{a_d x}{p} \\right) \\right| \\ll \\f
rac{M\\cdot \\mathrm{V}(f)}{p} \\\,\,\n$$\n where $\\mathrm{V}(f)$ is the
Hardy--Krause variation of the function $f$. \nKorobov proved that the cas
e $M=O((\\log p)^{d-1})$ is always realizable\, whereas the special case $
d=1$\, $M=O(1)$ is equivalent to the well-known Zaremba conjecture.\nFor $
d>1$ and arbitrary $M$\, only a few results are known. In our talk\, we wi
ll provide an overview of the problems in this area and describe recent ad
vances and connections to other topics in number theory.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Duker Lichtman (Stanford University)
DTSTART:20260713T190000Z
DTEND:20260713T195000Z
DTSTAMP:20260709T184247Z
UID:CANT2026/18
DESCRIPTION:Title: Primitive sets and von Mangoldt chains: Erdös #1196 and beyond\nby Jared Duker Lichtman (Stanford University) as part of Combinatorial
and additive number theory seminar (CANT 2026)\n\nLecture held in Science
Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nA set of int
egers is primitive if no number in the set divides another. We introduce a
new method for bounding Erdős sums of primitive sets\, suggested from ou
tput of GPT-5.4 Pro\, based on Markov chains with von Mangoldt weights. Th
e method leads to a host of applications\, yet seems to have been overlook
ed by the prior literature since Erdős' seminal 1935 paper. As applicatio
ns\, we prove two 1966 conjectures of Erdős-Sárközy-Szemerédi\, on pri
mitive sets of large numbers (#1196) and on divisibility chains (#1217). T
he method also provides a short proof of the Erdős Primitive Set Conjectu
re (#164)\, as well as the related claim that 2 is an ``Erdős-strong'' pr
ime. Moreover\, the method resolves a revised form of the Banks-Martin con
jecture\, which has long been viewed as a unifying ``master theorem'' for
the area. Joint work with B. Alexeev\, K. Barreto\, Y. Li\, L. Price\, J.
I. Shah\, Q. Tang\, and T. Tao.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Miller’s REU: Probability And Number THeory (Williams Col
lege)
DTSTART:20260713T200000Z
DTEND:20260713T205000Z
DTSTAMP:20260709T184247Z
UID:CANT2026/19
DESCRIPTION:Title: Recent advances in generalized MSTD problems and Zeckendorf games
\nby Steven Miller’s REU: Probability And Number THeory (Williams Co
llege) as part of Combinatorial and additive number theory seminar (CANT 2
026)\n\nLecture held in Science Center in the CUNY Graduate Center (4th fl
oor).\n\nAbstract\nWe report on two areas studied this summer in Miller's
REU: Generalized\nMSTD Problems and Zeckendorf Games. \n\n1. A finite inte
ger subset $A \\subseteq\n\\mathbb{Z}$ is classified as a More Sums Than D
ifferences (MSTD\, or\nsum-dominant) set when it produces strictly more pa
irwise sums than\ndifferences\, satisfying $|A+A| > |A-A|$. Motivated by t
he structural\ndensity of these integer sets\, we generalize this phenomen
on to subsets\n$A$ of a finite group $G$ by comparing the cardinality of t
he product set\n$AA$ against the quotient set $AA^{-1}$. To evaluate globa
l group\nbehavior\, we analyze the weighted difference across all possible
subsets\,\ndefined as $$W(G) = \\sum_{A \\subseteq G} (|AA| - |AA^{-1}|).
$$ Using a\ncombination of combinatorial techniques\, graph theory\, and r
epresentation\ntheory\, we prove that $W(G)$ is strictly negative for all
finite abelian\ngroups—establishing them as inherently quotient-dominant
—and we successfully extend these structural findings to characterize se
lect\nnon-abelian groups. \n\n2. Zeckendorf proved every integer can be wr
itten uniquely as a sum of\nnon-adjacent Fibonacci numbers $\\{F_n\\}$. Us
ing the Fibonacci recurrence\,\nMiller created the Zeckendorf game. Starti
ng with $n$ copies of $F_1$\, a\nplayer either replaces a copy of $F_i$ an
d $F_{i-1}$ with $F_{i+1}$\, or\nsplits two copies of $F_i$ into $F_{i+1}$
and $F_{i-1}$ (with $F_2$\nsplitting to $F_3$ and $F_1$). All games termi
nate in the Zeckendorf\ndecomposition of $n$\; whomever moves last wins. A
non-constructive proof\nexists that Player Two has a winning strategy for
all $n > 2$. We discuss\ncurrent work on a variety of generalizations\, i
ncluding binary\ndecompositions\, first to reach the largest summand wins\
, and higher\ndimensional analogues.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Miller (Williams College)
DTSTART:20260713T210000Z
DTEND:20260713T213000Z
DTSTAMP:20260709T184247Z
UID:CANT2026/20
DESCRIPTION:Title: Problem Session\nby Steve Miller (Williams College) as part o
f Combinatorial and additive number theory seminar (CANT 2026)\n\nLecture
held in Science Center in the CUNY Graduate Center (4th floor).\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johann Thiel (New York College of Technology (CUNY)
DTSTART:20260714T130000Z
DTEND:20260714T132500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/21
DESCRIPTION:Title: Generating functions for maximally expanded α-trees\nby Joha
nn Thiel (New York College of Technology (CUNY) as part of Combinatorial a
nd additive number theory seminar (CANT 2026)\n\nLecture held in Science C
enter in the CUNY Graduate Center (4th floor).\n\nAbstract\nWe construct g
enerating functions whose coefficients enumerate certain directed planar t
rees known as maximally expanded $\\alpha$-trees. We show that the number
of such trees can be expressed as an integer linear combination of Catalan
numbers. This is joint work with David M. Bradley.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Konyagin (Russia)
DTSTART:20260714T133000Z
DTEND:20260714T142500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/22
DESCRIPTION:Title: On Sidon sets with squares\, cubes and quartics in short interval
s\nby Sergei Konyagin (Russia) as part of Combinatorial and additive n
umber theory seminar (CANT 2026)\n\nLecture held in Science Center in the
CUNY Graduate Center (4th floor).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renling Jin (College of Charleston)
DTSTART:20260714T143000Z
DTEND:20260714T145500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/23
DESCRIPTION:Title: Three-in-one in Ramsey theory\nby Renling Jin (College of Cha
rleston) as part of Combinatorial and additive number theory seminar (CANT
2026)\n\nLecture held in Science Center in the CUNY Graduate Center (4th
floor).\n\nAbstract\nThere are three fundamental theorems in Ramsey theory
: Ramsey's theorem\, van der Waerden's theorem\, and Hindman's theorem. Mi
lliken-Taylor proved a result that simultaneously generalizes Ramsey's the
orem and Hindman's theorem. Later\, Bergelson--Hindman and Samet--Tsaban \
n established two distinct theorems\, each providing a simultaneous gener
alization \n of Ramsey's theorem and van der Waerden's theorem in two dif
ferent ways. Using a newly \n developed method of iterated extensions\, we
prove--pending verification--a theorem that \n simultaneously generalizes
all three classical results--Ramsey's theorem\, Hindman's theorem\, and v
an der Waerden's theorem. Moreover\, our theorem subsumes both the Bergels
on--Hindman and the Samet--Tsaban generalizations. Joint work with Mauro D
i Nasso.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Chapman (Sam Houston State University)
DTSTART:20260714T150000Z
DTEND:20260714T152500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/24
DESCRIPTION:Title: A surprising characterization of unique factorization domains
\nby Scott Chapman (Sam Houston State University) as part of Combinatorial
and additive number theory seminar (CANT 2026)\n\nLecture held in Science
Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nA surprising
characterization of unique factorization domains \\\\\nAbstract: & We add
ress some recent work on the generalization of the UFD propery which has p
ointed back to an open problem first mentioned in a paper by myself\, Dan
Anderson\, Muhammad Zafrullah\, and Franz Halter-Koch (Criteria for unique
factorization in integral domains\, J. Pure Appl. Algebra 127(1998)\, 205
--218)\, which we abbreviate as ACHKZ. Fix a positive integer $n>1$. Call
an atomic integral domain $D$ quasi-$n$-factorial if\, for any irreducible
elements \n$x_1\, \\ldots \, x_n\, y_1\, \\ldots \, y_n$\, the equality\n
$x_1\\cdots x_n=y_1\\cdots y_n$ implies that $x_i=u_iy_{\\sigma(i)}$ for s
ome unit $u_i$ and permutation $\\sigma$ of $\\{1\,\\ldots \,n\\}$. Furthe
r\, $D$ is length-factorial if it is quasi-$n$-factorial for all $n>1$. Ji
m Coykendall and William W. Smith showed in 2011 the surprising result tha
t an atomic monoid is a UFD if and only if it is length-factorial. This al
lows one to alter the classic definition of a UFD. in a surprising manner.
The authors in ACHKZ offer examples of monoids which are quasi-$n$-factor
ial for specific $n$\, but are not factorial. They offer no such example o
f an integral domain. Hence\, the Coykendall-Smith result makes the follow
ing problem explored in ACHKZ all the more relevant. Open Problem: Does th
ere exist an atomic integral domain $D$ which is quasi-$n$-factorial for s
ome $n>1$\, but not factorial?\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akos Magyar (University of Georgia)
DTSTART:20260714T153000Z
DTEND:20260714T165500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/25
DESCRIPTION:Title: Almost primes solutions to forms of odd degrees in many variables
\nby Akos Magyar (University of Georgia) as part of Combinatorial and
additive number theory seminar (CANT 2026)\n\nLecture held in Science Cent
er in the CUNY Graduate Center (4th floor).\n\nAbstract\nLet $\\mathcal{F}
=\\{f_1\,\\ldots\,f_R\\}$ be a family of forms of odd degrees at most $d$
in $s$ variables. We study the solutions to the diophantine system: $f_1(\
\mathbf{x})=\\ldots=f_R(\\mathbf{x})=0$ of the form $x_i=y_ip_i$ with $|y_
i|\\leq Y_\\mathcal{F}$ and $p_i$ being a prime for all $i\\in [s]$ inside
the box $[-N\,N]^s$\, for large $N$. We show that if the number of variab
les $s$ is sufficiently large with respect to the parameters $R$ and $d$\,
then there are at least $C_\\mathcal{F} N^{s-D}/(\\log\\\,N)^s$ such solu
tions for some constants $C_\\mathcal{F}>0$ and $D\\in\\mathbb{N}$\, with
$D$ depending only on the initial parameters $R$ and $d$.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Pomerance (Dartmouth College)
DTSTART:20260714T173000Z
DTEND:20260714T182000Z
DTSTAMP:20260709T184247Z
UID:CANT2026/26
DESCRIPTION:Title: Two topics in combinatorial number theory\nby Carl Pomerance
(Dartmouth College) as part of Combinatorial and additive number theory se
minar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate C
enter (4th floor).\n\nAbstract\nThe first topic: In a paper with Erd\\H os
from 40 years ago\,\nwe considered the set of residues $a \\bmod n$ where
\n$a^{n-1} \\equiv 1 \\pmod n$.\nIf $n$ is composite\, these are the bases
for which $n$ is a pseudoprime.\nRecently\, Lenstra asked me about the se
t of residues $a \\bmod n$\nwhere $a^n \\equiv 1 \\pmod n$\, which is rela
ted to a problem he is\nworking on about conditions that ensure a ring is
commutative.\nSome of the methods from the old paper were useful in the ne
w\nproblem\, but not all. I will discuss the more general problem of subgr
oups of the multiplicative group mod $n$. The second topic: I will discuss
\nsome old and new problems on coprime matchings: These are perfect\nmatch
ings between two equally numerous sets of integers\, where each matched pa
ir is relatively prime. Some examples: Given two intervals\nof $n$ consecu
tive integers is there a coprime matching between them?\nIf both intervals
are $\\{1\,2\,\\dots\,n\\}$\, how many such matchings are\nthere? For a p
ositive integer $n$\, is there a coprime matching between\nthe set $D(n)$
of divisors of $n$ and an interval of $D(n)$ consecutive\nintegers? This l
ast problem reflects joint work with Nathan McNew.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksym Radziwill (New York University)
DTSTART:20260714T183000Z
DTEND:20260714T185500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/27
DESCRIPTION:Title: Exponential sums over primes\nby Maksym Radziwill (New York U
niversity) as part of Combinatorial and additive number theory seminar (CA
NT 2026)\n\nLecture held in Science Center in the CUNY Graduate Center (4t
h floor).\n\nAbstract\nA classical result of Vinogradov shows that\, for a
ny $\\alpha$ with $$\n\\Big | \\alpha - \\frac{a}{q} \\Big | \\leq \\frac{
1}{q^2} \\ \, \\ q \\leq x^{1/2}\,\n$$ \nand for any $\\varepsilon > 0$\,
we have\, $$\n\\Big | \\sum_{p \\leq x} e^{2\\pi i \\alpha p} \\Big | \\le
q C(\\varepsilon) x^{\\varepsilon} \\cdot \\Big ( \\frac{x}{\\sqrt{q}} + x
^{4/5} \\Big ).\n$$ \nwith $C(\\varepsilon) > 0$ a constant depending only
on $\\varepsilon$.\nThis has resisted improvements for the past 80 years\
, beyond\nrefinements to the $x^{\\varepsilon}$ term. The $x / \\sqrt{q}$
term cannot be improved without eliminating the existence of a Siegel zero
. I'll discuss joint work with James Maynard and Mayank Pandey\, in which
we reduce the exponent $4/5$ appearing in $x^{4/5}$ to $19/24$\, which sho
uld have various applications to additive problems related to primes.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krishnaswami Alladi (University of Florida)
DTSTART:20260714T190000Z
DTEND:20260714T195000Z
DTSTAMP:20260709T184247Z
UID:CANT2026/28
DESCRIPTION:Title: Duality between prime factors and prime numbers in arithmetic pro
gressions\nby Krishnaswami Alladi (University of Florida) as part of C
ombinatorial and additive number theory seminar (CANT 2026)\n\nLecture hel
d in Science Center in the CUNY Graduate Center (4th floor).\n\nAbstract\n
In 1977\, I noticed a duality between the largest and smallest\n prime fac
tors of the integers involving the Mobius function\, and used this to est
ablish the following result as a consequence of the Prime Number Theorem\
n for Arithmetic Progressions: \n If $k$ and $\\ell$ are positive\n intege
rs\, with $1\\le \\ell\\le k$ and $(\\ell\, k)=1$\, then $$ \n \\sum_{n\\
ge 2\, \\\, p(n)\\equiv\\ell(mod\\\,k)}\\frac{\\mu(n)}{n}=\\frac{-1}{\\phi
(k)}\, $$ where $\\mu(n)$ is the Mobius function\, $p(n)$ is the\n smalles
t prime factor of $n$\, and $\\phi(k)$ is the Euler function. In the last
decade\, several authors have obtained analogues of (1) in the setting of
algebraic number fields by using the Chebotarev Density Theorem. Also in
1977\, I proved higher order duality identities involving the $k$-th larg
est and smallest prime factors\, facilitated by the Mobius function and $\
\omega(n)$\, the number of distinct prime factors of $n$. In this talk we
will exploit the second order duality between the second largest prime fac
tor and the smallest prime factor\, to show that if $\\ell$ and $k$ are as
above\, then $$ \n \\sum_{n\\ge 2\,\\\, p(n)\\equiv\\ell(mod\\\,k)}\\frac
{\\mu(n)\\omega(n)}{n}=0. \n $$ The proof of (2) is more complicated owing
to the weight $\\omega(n)$\, and also because it relies on the distribut
ion of the second largest prime factor which is more subtle compared to th
e distribution of the largest prime factor. All results are established q
uantitatively. This is joint work with my PhD student Jason Johnson. Rece
ntly\, another PhD student of mine\, Sroyon Sengupta\, has extended the A
lladi-Johnson results to algebraic number fields using the Chebotarev Dens
ity Theorem. \nTowards the end of the talk\, we will briefly mention furth
er joint work with Sengupta on consequences of such dualities involving th
e $k-th$ largest and smallest prime factors\, when $k\\ge 3$.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Andrews (Pennsylvania State University)
DTSTART:20260714T200000Z
DTEND:20260714T205000Z
DTSTAMP:20260709T184247Z
UID:CANT2026/29
DESCRIPTION:Title: The mystery of two-color partitions with distinct parts\nby G
eorge Andrews (Pennsylvania State University) as part of Combinatorial and
additive number theory seminar (CANT 2026)\n\nLecture held in Science Cen
ter in the CUNY Graduate Center (4th floor).\n\nAbstract\nWe shall present
some old and some new results about two-color partitions with distinct pa
rts. In the midst of our exploration\, a power series arises that seems
to be "semi-lacunary." What is going on anyway? The answers to this an
d other mysteries will be provided. Joint work with M. El Bachraoui.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krishnaswami Alladi (University of Florida)
DTSTART:20260714T210000Z
DTEND:20260714T213000Z
DTSTAMP:20260709T184247Z
UID:CANT2026/30
DESCRIPTION:Title: Problem session\nby Krishnaswami Alladi (University of Florid
a) as part of Combinatorial and additive number theory seminar (CANT 2026)
\n\nLecture held in Science Center in the CUNY Graduate Center (4th floor)
.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sukumar Das Adhikar (Ramakrishna Mission Vivekananda Educational a
nd Research Institute\, India)
DTSTART:20260715T130000Z
DTEND:20260715T132500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/31
DESCRIPTION:Title: A pearl of number theory: Some old and new applications\nby S
ukumar Das Adhikar (Ramakrishna Mission Vivekananda Educational and Resear
ch Institute\, India) as part of Combinatorial and additive number theory
seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate
Center (4th floor).\n\nAbstract\nAfter stating the classical van der Waer
den's theorem\, and a brief discussion of its relation with some early Ram
sey-type theorems\,\nwe go through some old and new applications of the th
eorem. We shall also see some open questions in Ramsey Theory.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinhui Fang (Nanjing Normal University\, Nanjing\, China)
DTSTART:20260715T133000Z
DTEND:20260715T135500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/32
DESCRIPTION:Title: Minimal asymptotic bases related to G-adic sequences\nby Jinh
ui Fang (Nanjing Normal University\, Nanjing\, China) as part of Combinato
rial and additive number theory seminar (CANT 2026)\n\nLecture held in Sci
ence Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nLet $A$
be a set of nonnegative integers and $h\\ge 2$. The set $A$ is defined as
an asymptotic basis of order $h$ if all sufficiently large integers $n$ ca
n be expressed as the sum of $h$ elements taken from $A$. Such $A$ is furt
her defined as \\emph{minimal} if no proper subset of $A$ is an asymptotic
basis of order $h$. In 1974\, Nathanson explicitly constructed a minimal
asymptotic basis of order $2$ by using binary representations. In 2022\, N
athanson constructed a new class of minimal asymptotic bases of order $h$
based on the $\\mathcal{G}$-adic sequence\, where a $\\mathcal{G}$-adic se
quence $\\mathcal{G}=\\{g_i\\}_{i=0}^{\\infty}$ is a strictly increasing s
equence of positive integers such that $g_0=1$ and $g_{i-1}$ divides $g_i$
for all $i\\ge 1$. Recently\, we improve the above result.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan V. Morozov (City College (CUNY))
DTSTART:20260715T140000Z
DTEND:20260715T142500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/33
DESCRIPTION:Title: On quotients of a more general theorem of Wilson\nby Ivan V.
Morozov (City College (CUNY)) as part of Combinatorial and additive number
theory seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY
Graduate Center (4th floor).\n\nAbstract\nThe basis of this work is a coro
llary and generalization of Wilson’s theorem\, $(-1)^{k}k!(n-k-1)!\\equi
v -1\\pmod{n}$ iff $n$ is non-composite\, for $0\\leq k\\leq n-1$. This co
rollary generates many more quotients than those already generated by Wils
on’s theorem\, and we derive how they relate to each other and build on
the established properties of the original quotients. The main results are
expressions for sums of these quotients\, modular congruences that extend
the results of Lehmer\, and generating functions. In addition\, a solutio
n will be provided for an open problem raised in CANT 2025 by Brian Hopkin
s regarding a combinatorial proof for the partition identity $p(a\,3)+p(b\
,3)=p(c\,3)$\, where $a$\, $b$\, and $c$ comprise a Pythgagorean triple.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey C. Lagarias (University of MIchigan)
DTSTART:20260715T143000Z
DTEND:20260715T145500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/34
DESCRIPTION:Title: The Collatz problem: Progress and perspectives\nby Jeffrey C.
Lagarias (University of MIchigan) as part of Combinatorial and additive n
umber theory seminar (CANT 2026)\n\nLecture held in Science Center in the
CUNY Graduate Center (4th floor).\n\nAbstract\nThe Collatz problem concern
s the iteration of the map $C(n) = n/2$ if $n$ is even\; $C(n) = 3n + 1$ i
f $n$ is odd\, on the positive integers. It asks whether the integer 1 is
reached for all starting\nvalues $n$. This talk surveys some history and r
ecent progress towards the Collatz Problem. It\noffers some perspectives o
n its difficulty.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (Lehman College and CUNY Graduate Center)
DTSTART:20260715T153000Z
DTEND:20260715T162000Z
DTSTAMP:20260709T184247Z
UID:CANT2026/35
DESCRIPTION:Title: Three problems in additive number theory\nby Mel Nathanson (L
ehman College and CUNY Graduate Center) as part of Combinatorial and addit
ive number theory seminar (CANT 2026)\n\nLecture held in Science Center in
the CUNY Graduate Center (4th floor).\n\nAbstract\nThis will be an introd
uction to three (possibly new) problems in additive number theory. The fir
st concerns the range and frequencies of the sizes of sumsets of finite se
ts of integers. The second considers the sets $H$ of integers such that th
ere exists an increasing sequence $(A_i)_{i=1}^{\\infty} A_i$ of sets of i
ntegers such that $h \\in H$ if and only if $h\\bigcap_{i=1}^{\\infty} A_i
= \\bigcap_{i=1}^{\\infty} hA_i$. The third asks about the possible sizes
of $h$-bases for $n$ for finite sets of integers that contain at least on
e negative integer.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Senger (Missouri State University)
DTSTART:20260715T173000Z
DTEND:20260715T175500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/36
DESCRIPTION:Title: Nathanson’s triangular gap question\nby Steven Senger (Miss
ouri State University) as part of Combinatorial and additive number theory
seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduat
e Center (4th floor).\n\nAbstract\nMel Nathanson recorded the size distrib
ution of iterated sumsets of four natural numbers chosen from a large inte
rval of integers. He observed that the most frequent sizes were not evenly
distributed\, but had gaps between them\, and that these gaps were consec
utive triangular numbers. We explain this phenomenon in full detail.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alisa Sedunova (Purdue University)
DTSTART:20260715T180000Z
DTEND:20260715T182500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/37
DESCRIPTION:Title: Euler-Kronecker constants of maximal real cyclotomic subfields an
d Kummer’s conjecture\nby Alisa Sedunova (Purdue University) as part
of Combinatorial and additive number theory seminar (CANT 2026)\n\nLectur
e held in Science Center in the CUNY Graduate Center (4th floor).\n\nAbstr
act\nThe Euler–Kronecker constant of a number field $K$ is the ratio of
the constant and the residue of the Laurent series of the Dedekind zeta fu
nction at $s = 1$. We study the distribution of the Euler–Kronecker cons
tant $\\gamma_q^+$ of the maximal real subfield $\\mathbb{Q}(\\zeta_q)^+$
as $q$ ranges over the primes. Further\, we consider the distribution of $
\\gamma_q^+ - \\gamma_q$\, with $\\gamma_q$ the Euler–Kronecker constant
of $\\mathbb{Q}(\\zeta_q)$ and show how it is connected with Kummer’s c
onjecture\, which predicts the asymptotic growth of the relative class num
ber of $\\mathbb{Q}(\\zeta_q)$. We improve\, for example\, the known resul
ts on the bounds on average for the Kummer ratio and we prove analogous sh
arp bounds for $\\gamma_q^+ - \\gamma_q$. The methods employed are partly
inspired by those used by Granville (1990) and Croot and Granville (2002)
to investigate Kummer’s conjecture\, that predicts the asymptotic growth
of the relative class number of prime cyclotomic fields. We substantially
improve the known bounds of Kummer’s ratio under three scenarios: no Si
egel zero\, presence of Siegel zero and assuming the Riemann Hypothesis fo
r the Dirichlet $L$-series attached to odd characters only. \nThe talk is
based on joint papers with A. Languasco\, P. Moree\, N. Kandhil and S. Saa
d Eddin.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Borisov (Binghamton University)
DTSTART:20260715T183000Z
DTEND:20260715T185500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/38
DESCRIPTION:Title: A structure sheaf for Kirch topology on N\nby Alexander Boris
ov (Binghamton University) as part of Combinatorial and additive number th
eory seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Gra
duate Center (4th floor).\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 consists of all infinite arithmetic progressions $a+d\\mathbb N_0$\,
such that $\\gcd(a\,d)=1$ and $d$ is square-free. It is Hausdorff\, connec
ted\, and locally connected. One can hope that in the classical imperfect
analogy between arithmetic and geometry this can serve as an arithmetic an
alog of the usual topology on $\\mathbb C$. However\, the usual topology o
n $\\mathbb C$ 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 accide
nt than by a conscious effort: locally LIP functions. These are functions
from Kirch-open sets to $\\mathbb Z$ such that for every point in the doma
in 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 ob
ject\, what I know about it\, and what I hope to achieve.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wladimir Pribitkin (College of Staten Island and CUNY Graduate Cen
ter)
DTSTART:20260715T190000Z
DTEND:20260715T192500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/39
DESCRIPTION:Title: Simple upper bound for the power partition function\nby Wladi
mir Pribitkin (College of Staten Island and CUNY Graduate Center) as part
of Combinatorial and additive number theory seminar (CANT 2026)\n\nLecture
held in Science Center in the CUNY Graduate Center (4th floor).\n\nAbstra
ct\nReimagining Siegel's method\, we shall produce a rather easy proof of
a surprisingly good upper bound on the number of partitions of a positive
integer into perfect $r$th powers\, where $r \\ge 1$. If time permits\, we
shall present a generalization pertaining to partitions into perfect powe
rs of terms in an arithmetic progression.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Trevor Dion Wooley (Purdue University)
DTSTART:20260715T193000Z
DTEND:20260715T202000Z
DTSTAMP:20260709T184247Z
UID:CANT2026/40
DESCRIPTION:Title: Strong paucity in systems of diagonal equations\nby Trevor Di
on Wooley (Purdue University) as part of Combinatorial and additive number
theory seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY
Graduate Center (4th floor).\n\nAbstract\nLet $k$ be a natural number with
$k\\ge 2$\, and let $\\varepsilon>0$. We consider the number\n$V_k^*(P)$
of integral solutions of the system of simultaneous Diophantine equations
$$x_1^{2j-1}+\\ldots +x_{k+1}^{2j-1}=y_1^{2j-1}+\\ldots +y_{k+1}^{2j-1}\\q
uad (1\\le j\\le k).$$ with $1\\le x_i\,y_i\\le P$ $(1\\le i\\le k+1)$. Wr
iting $L_k^*(P)$ for the number of diagonal solutions with \n$\\{x_1\,\\ld
ots \,x_{k+1}\\}=\\{y_1\,\\ldots \,y_{k+1}\\}$\, so that $L_k^*(P)\\sim (k
+1)!P^{k+1}$\, we prove that $$V_k^*(P)-L_k^*(P)\\ll P^{\\sqrt{8k+9}-1+\\v
arepsilon}.$$ This establishes a strong paucity result improving on earlie
r work of Brüdern and Robert. Time permitting\, we describe analogous res
ults for related problems.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Filaseta (University of South Carolina)
DTSTART:20260715T203000Z
DTEND:20260715T205500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/41
DESCRIPTION:Title: On the factorization of a sum of cyclotomic polynomials\nby M
ichael Filaseta (University of South Carolina) as part of Combinatorial an
d additive number theory seminar (CANT 2026)\n\nLecture held in Science Ce
nter in the CUNY Graduate Center (4th floor).\n\nAbstract\nIn 2000\, Charl
es Nicol conjectured that for $n$ and $m$ integers with $n > m >1$\, the s
um $\\Phi_{n}(x)+\\Phi_{m}(x)$ is a product of distinct cyclotomic polynom
ials and either a constant or an irreducible non-cyclotomic polynomial. Li
ttle progress has been made on this conjecture since then. In this talk\,
we discuss recent joint work with Lilit Martirosyan and London Swan\, wher
e\, in particular\, we show that for primes $p$\, $q$ and $\\ell$ with $p
> q > \\ell$ and a non-negative integer $r$\, the sum $\\Phi_{\\ell^{r} p}
(x)+\\Phi_{\\ell^{r} q}(x)$ has this property and determine precisely the
cyclotomic polynomials dividing the sum.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Senger (Missouri State University)
DTSTART:20260715T210000Z
DTEND:20260715T213000Z
DTSTAMP:20260709T184247Z
UID:CANT2026/42
DESCRIPTION:Title: Problem Session\nby Steve Senger (Missouri State University)
as part of Combinatorial and additive number theory seminar (CANT 2026)\n\
nLecture held in Science Center in the CUNY Graduate Center (4th floor).\n
Abstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arindam Biswas (Polynom Research\, Paris\, France)
DTSTART:20260716T130000Z
DTEND:20260716T132500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/43
DESCRIPTION:Title: Asymptotic approximate groups in virtually nilpotent groups\n
by Arindam Biswas (Polynom Research\, Paris\, France) as part of Combinato
rial and additive number theory seminar (CANT 2026)\n\nLecture held in Sci
ence Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nLet \\(G
\\) be a group and let \\(A\\subseteq G\\) be a non-empty subset. For\n\\(
r\,l\\in\\mathbb N\\)\, \\(A\\) is said to be an asymptotic\n\\((r\,l)\\)-
approximate group if there exists \\(h_0\\in\\mathbb N\\) such that\,\nfor
every \\(h\\ge h_0\\)\, there is a set \\(X_h\\subseteq G\\) with\n\\(|X_
h|\\le l\\) and\n$A^{rh}\\subseteq X_hA^h.$\nWe study this property for su
bsets of virtually nilpotent groups and show that\nevery finite non-empty
symmetric subset of a virtually nilpotent group is an\nasymptotic approxim
ate group. More generally\, the same conclusion holds for finite\nsets who
se powers contain a symmetric word ball of radius comparable to \\(h\\). I
n the setting of infinite sets\, we show a restricted nonabelian analogue
of the abelian semilinear-set theorem.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Kravitz (Oxford University\, UK)
DTSTART:20260716T133000Z
DTEND:20260716T135500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/44
DESCRIPTION:Title: Sets with few subset sums\nby Noah Kravitz (Oxford University
\, UK) as part of Combinatorial and additive number theory seminar (CANT 2
026)\n\nLecture held in Science Center in the CUNY Graduate Center (4th fl
oor).\n\nAbstract\nA classical result of Nathanson shows that every $n$-el
ement set of positive reals has at least $\\binom{n+1}{2}+1$ distinct subs
et sums\, with equality exactly for homogeneous arithmetic progressions. W
e establish stability versions of this inverse theorem in two regimes. Fir
st\, for any parameter $0 \\leq M \\leq n-4$\, we precisely characterize t
he $n$-element sets of positive reals with at most $\\binom{n+1}{2}+1+M$ s
ubset sums. Second\, for any constant $C$\, we provide a characterization\
, sharp up to constants\, of the $n$-element sets of positive reals with a
t most $Cn^2$ distinct subset sums. Joint work with Ruben Carpenter and Co
lin Defant.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan McNew (Towson University)
DTSTART:20260716T140000Z
DTEND:20260716T142500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/45
DESCRIPTION:Title: Matchable numbers\nby Nathan McNew (Towson University) as par
t of Combinatorial and additive number theory seminar (CANT 2026)\n\nLectu
re held in Science Center in the CUNY Graduate Center (4th floor).\n\nAbst
ract\nWe say a natural number is matchable if there is a bijection from th
e set of $\\tau(n)$ divisors of $n$ to the set $[1\,2\,\\ldots\,\\tau(n)]$
\, where corresponding numbers are relatively prime. We show that the set
of matchable numbers has an asymptotic density\, which we compute\, and we
show that every squarefree number is matchable. We also present some rela
ted unsolved problems. This is joint work with Carl Pomerance.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gergely Kiss (Rényi Institute of Mathematics and Corvinus Univers
ity\, Hungary)
DTSTART:20260716T143000Z
DTEND:20260716T145500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/46
DESCRIPTION:Title: Lower bounds for mask polynomials with many cyclotomic divisors\nby Gergely Kiss (Rényi Institute of Mathematics and Corvinus Universi
ty\, Hungary) as part of Combinatorial and additive number theory seminar
(CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate Center
(4th floor).\n\nAbstract\nWe study finite subsets and multisets of cyclic
groups \\(\\mathbb{Z}_M\\)\nwhose mask polynomials have prescribed cycloto
mic divisors. More precisely\,\nif \\(A\\subseteq \\mathbb{Z}_M\\)\, we co
nsider its mask polynomial $$\n A(X)=\\sum_{a\\in A} X^a\n \\qquad \\text{
in } \\mathbb{Z}[X]/(X^M-1)\,\n$$ and ask how divisibility by selected cyc
lotomic polynomials constrains\nthe size and structure of \\(A\\). \nThis
question is motivated by its connections with translational tilings\,\nthe
Coven--Meyerowitz conjecture\, and one-dimensional Fuglede-type problems.
\nWe prove new lower bounds for the cardinality of such sets and develop s
everal\nstructural tools\, including \\\\\n & a truncation method and a mu
ltiscale extension of\nthe de Bruijn--Rédei--Schoenberg theorem. These re
sults show that the\nexpected fibre-type extremal configurations do not al
ways give the correct\nminimum once the prescribed cyclotomic divisors bec
ome sufficiently complicated. \nAt the same time\, in the two-dimensional
case and in several further special\nsituations\, the lower bounds agree w
ith the natural fibre constructions. This is joint work with I. Łaba\, C.
Marshall\, and G. Somlai.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pramana Saldin (University of California\, Berkeley)
DTSTART:20260716T150000Z
DTEND:20260716T152500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/47
DESCRIPTION:Title: Left and right quotient sets in non-abelian groups\nby Praman
a Saldin (University of California\, Berkeley) as part of Combinatorial an
d additive number theory seminar (CANT 2026)\n\nLecture held in Science Ce
nter in the CUNY Graduate Center (4th floor).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonah Klein (University of South Carolina)
DTSTART:20260716T153000Z
DTEND:20260716T155500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/48
DESCRIPTION:Title: The distortion method and its applications\nby Jonah Klein (U
niversity of South Carolina) as part of Combinatorial and additive number
theory seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY G
raduate Center (4th floor).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norbert Hegyvári (Eötvös University and Rényi Institute\, Hung
ary)
DTSTART:20260716T160000Z
DTEND:20260716T162500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/49
DESCRIPTION:Title: Consecutive sums\, Sidon sets\, convex sequences: Old and new pro
blems\nby Norbert Hegyvári (Eötvös University and Rényi Institute\
, Hungary) as part of Combinatorial and additive number theory seminar (CA
NT 2026)\n\nLecture held in Science Center in the CUNY Graduate Center (4t
h floor).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Montejano (Mexico)
DTSTART:20260716T173000Z
DTEND:20260716T175500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/50
DESCRIPTION:Title: Discrete Brunn–Minkowski inequalities\nby Amanda Montejano
(Mexico) as part of Combinatorial and additive number theory seminar (CANT
2026)\n\nLecture held in Science Center in the CUNY Graduate Center (4th
floor).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Rajagopal (MIT)
DTSTART:20260716T180000Z
DTEND:20260716T182500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/51
DESCRIPTION:Title: Possible sizes of sumsets\nby Isaac Rajagopal (MIT) as part o
f Combinatorial and additive number theory seminar (CANT 2026)\n\nLecture
held in Science Center in the CUNY Graduate Center (4th floor).\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cosmin Pohoata (Emory University)
DTSTART:20260716T190000Z
DTEND:20260716T192500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/52
DESCRIPTION:Title: Sidon sets in the squares\, repeated distances\, and the Elekes-R
onyai problem\nby Cosmin Pohoata (Emory University) as part of Combina
torial and additive number theory seminar (CANT 2026)\n\nLecture held in S
cience Center in the CUNY Graduate Center (4th floor).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amita Malik (Pennsylvania State University)
DTSTART:20260716T195000Z
DTEND:20260716T195500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/53
DESCRIPTION:Title: Lehmer-type partition statistics\nby Amita Malik (Pennsylvani
a State University) as part of Combinatorial and additive number theory se
minar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate C
enter (4th floor).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandra Kingan (Brooklyn College and the Graduate Center\, CUNY)
DTSTART:20260716T200000Z
DTEND:20260716T202500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/54
DESCRIPTION:Title: Deletable edges in 3-connected graphs and their applications\
nby Sandra Kingan (Brooklyn College and the Graduate Center\, CUNY) as par
t of Combinatorial and additive number theory seminar (CANT 2026)\n\nLectu
re held in Science Center in the CUNY Graduate Center (4th floor).\nAbstra
ct: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:C. J. Mozzochi (Connecticut)
DTSTART:20260716T203000Z
DTEND:20260716T205500Z
DTSTAMP:20260709T184247Z
UID:CANT2026/55
DESCRIPTION:Title: A new approach to the circle method attack on the m-prime conject
ure\nby C. J. Mozzochi (Connecticut) as part of Combinatorial and addi
tive number theory seminar (CANT 2026)\n\nLecture held in Science Center i
n the CUNY Graduate Center (4th floor).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O’Bryant
DTSTART:20260716T210000Z
DTEND:20260716T213000Z
DTSTAMP:20260709T184247Z
UID:CANT2026/56
DESCRIPTION:Title: Problem Session\nby Kevin O’Bryant as part of Combinatorial
and additive number theory seminar (CANT 2026)\n\nLecture held in Science
Center in the CUNY Graduate Center (4th floor).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CANT2026/56/
END:VEVENT
END:VCALENDAR