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BEGIN:VEVENT
SUMMARY:Kevin O'Bryant (CUNY)
DTSTART:20260713T130000Z
DTEND:20260713T132500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aradhya Goel (Indian Institute of Technology Kanpur)
DTSTART:20260713T133000Z
DTEND:20260713T135500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Pal Pach (Renyi Institute)
DTSTART:20260713T140000Z
DTEND:20260713T142500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Ramon Madrid Padilla (Virginia Tech)
DTSTART:20260713T143000Z
DTEND:20260713T145500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Grynkiewicz (Memphis University)
DTSTART:20260713T160000Z
DTEND:20260713T162500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gabdullin (University of Illinois at Urbana-Champaign)
DTSTART:20260713T150000Z
DTEND:20260713T152500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfred Geroldinger (University of Graz\, Austria)
DTSTART:20260713T153000Z
DTEND:20260713T155500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sinan Gunturk (New York University)
DTSTART:20260713T173000Z
DTEND:20260713T175500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Shkredov (Purdue University)
DTSTART:20260713T180000Z
DTEND:20260713T185000Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Duker Lichtman (Stanford University)
DTSTART:20260713T190000Z
DTEND:20260713T195000Z
DTSTAMP:20260730T022806Z
UID:CANT2026/18
DESCRIPTION:Title: Primitive sets and von Mangoldt chains: Erdős #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://master.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:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Miller (Williams College)
DTSTART:20260713T210000Z
DTEND:20260713T213000Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johann Thiel (New York College of Technology (CUNY)
DTSTART:20260714T130000Z
DTEND:20260714T132500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Konyagin (Russia)
DTSTART:20260714T133000Z
DTEND:20260714T142500Z
DTSTAMP:20260730T022806Z
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).\n\nAbstract\nFor any positive integer $N
$\, the equation $\n x^3+y^3=z^3+t^3\, \\quad\nx\,y\,z\,t\\in \\mathbb{N
}\, \\quad \\{x\,y\\}\\not=\\{z\,t\\} $ has no solution satisfying $\n
N\\le x\,y\,z\,t <\nN+\\Bigl(\\frac{38}{3}N+\\frac{1297}{36}\\Bigr)^{1/2}
+\\frac{19}{6}. $ \nThe strict\ninequality ``$<$" can not be substituted b
y ``$\\le$"\, that is\, there exist infinitely many positive integers $N$
such that the equation has a solution\nwith $\n N\\le x\,y\,z\,t \\le\n
N+\\Bigl(\\frac{38}{3}N+\\frac{1297}{36}\\Bigr)^{1/2}+\\frac{19}{6}. $ \
n There is an absolute constant $c>0$ such that for any positive integer $
N$\nthe equation has a solution satisfying $ N\\le x\,y\,z\,t \\le N+cN^
{2/3}. $ \n For any $\\varepsilon>0$ there exist infinitely many positiv
e integers $N$\nsuch that the equation has no solution satisfying $ N\
\le x\,y\,z\,t \\le N+N^{4/7-\\varepsilon}. $ \n There is an absolute co
nstant $c>0$ such that for any positive integer $N$\nthe equation \n$ x^4
+y^4=z^4+t^4\,\\quad x\,y\,z\,t\\in\\mathbb{N}\, \\quad\n\\{x\,y\\}\\not=\
\{z\,t\\}\, $ \\\\& \nhas no solution satisfying \n$ N\\le x\,y\,z\,t \\
le N+cN^{3/5}. $ \n There is an absolute constant $c>0$ such that for an
y positive integer $N$\nthis equation has a solution satisfying \n$ N\\
le x\,y\,z\,t \\le N+cN^{12/13}. $ \nThe talk is based on a joint paper
of the speaker with\nM.~Z.~Garaev and F.~M.~Garayev.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renling Jin (College of Charleston)
DTSTART:20260714T143000Z
DTEND:20260714T145500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Chapman (Sam Houston State University)
DTSTART:20260714T150000Z
DTEND:20260714T152500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akos Magyar (University of Georgia)
DTSTART:20260714T153000Z
DTEND:20260714T165500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Pomerance (Dartmouth College)
DTSTART:20260714T173000Z
DTEND:20260714T182000Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksym Radziwill (New York University)
DTSTART:20260714T183000Z
DTEND:20260714T185500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krishnaswami Alladi (University of Florida)
DTSTART:20260714T190000Z
DTEND:20260714T195000Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Andrews (Pennsylvania State University)
DTSTART:20260714T200000Z
DTEND:20260714T205000Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krishnaswami Alladi (University of Florida)
DTSTART:20260714T210000Z
DTEND:20260714T213000Z
DTSTAMP:20260730T022806Z
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://master.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:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinhui Fang (Nanjing Normal University\, Nanjing\, China)
DTSTART:20260715T133000Z
DTEND:20260715T135500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan V. Morozov (City College (CUNY))
DTSTART:20260715T140000Z
DTEND:20260715T142500Z
DTSTAMP:20260730T022806Z
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 Pythagorean triple.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey C. Lagarias (University of MIchigan)
DTSTART:20260715T143000Z
DTEND:20260715T145500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (Lehman College and CUNY Graduate Center)
DTSTART:20260715T153000Z
DTEND:20260715T162000Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Senger (Missouri State University)
DTSTART:20260715T173000Z
DTEND:20260715T175500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alisa Sedunova (Purdue University)
DTSTART:20260715T180000Z
DTEND:20260715T182500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Borisov (Binghamton University)
DTSTART:20260715T183000Z
DTEND:20260715T185500Z
DTSTAMP:20260730T022806Z
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://master.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:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Trevor Dion Wooley (Purdue University)
DTSTART:20260715T193000Z
DTEND:20260715T202000Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Filaseta (University of South Carolina)
DTSTART:20260715T203000Z
DTEND:20260715T205500Z
DTSTAMP:20260730T022806Z
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 cyclotomic polynomials and
either a constant or an irreducible non-cyclotomic polynomial. Little prog
ress has been made on this conjecture since then. In this talk\, I discuss
recent joint work with Lilit Martirosyan and London Swan\, where\, in par
ticular\, we show that for primes $p$\, $q$ and $\\ell$ with $p > q > \\el
l$ 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. We also discuss cases of the conjecture in
which the number of prime factors of $n$ and $m$ can be arbitrary.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Senger (Missouri State University)
DTSTART:20260715T210000Z
DTEND:20260715T213000Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arindam Biswas (Polynom Research\, Paris\, France)
DTSTART:20260716T130000Z
DTEND:20260716T132500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Kravitz (Oxford University\, UK)
DTSTART:20260716T133000Z
DTEND:20260716T135500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan McNew (Towson University)
DTSTART:20260716T140000Z
DTEND:20260716T142500Z
DTSTAMP:20260730T022806Z
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://master.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:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pramana Saldin (University of California\, Berkeley)
DTSTART:20260716T150000Z
DTEND:20260716T152500Z
DTSTAMP:20260730T022806Z
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).\n\nAbstract\nFor a group $G$
\, we define the right quotient set and the left quotient set as follows:
$$\n AA^{-1}:=\\{a_1a_2^{-1}:a_1\,a_2\\in A\\} \\qquad A^{-1}A:=\\{a_1^{-1
}a_2:a_1\,a_2\\in A\\}.$$ \nWe examine the relationships between the left
and right quotient sets. If $G$ is an abelian group\, then these sets are
equal\, but subtleties arise in non-abelian settings\, as these sets may n
ot have the same cardinality. Tao remarked that the cardinality difference
$|AA^{-1}| - |A^{-1}A|$ may be arbitrarily large for certain groups. \n\n
We first give explicit constructions of sets $A$ where this difference att
ains every possible integer\, proving that the difference can be any possi
ble value if $G$ has elements of order 2. \n\nWe also find the minimum car
dinality of $A$ so that the difference between the cardinalities of the le
ft and right quotient sets is nonzero\, depending on the existence of orde
r $2$ elements in $G$. \n\nTo prove these results\, we construct a graph c
alled the difference graph $D_A$ that encodes equality in the right quotie
nt set. Similarly\, $D_{A^{-1}}$ encodes equality in the left quotient set
. By observing an isomorphism of edges in $D_A$ and $D_{A^{-1}}$ and count
ing connected components\, we are able to prove the results above. In the
free group on two generators\, we can prove that the difference $|AA^{-1}|
- |A^{-1}A|$ is always even. We explicitly construct subsets of $F_2$ tha
t achieve every even integer. In the infinite dihedral group $D_\\infty \\
cong \\mathbb{Z} \\rtimes \\mathbb{Z}/2$\, we prove that every integer dif
ference is achievable\, using the results of Martin and O'Bryant on the ca
rdinality differences of sum sets and difference sets in $\\mathbb{Z}.$ \n
\nJoint work with June Duvivier\, Xiaoyao Huang\, Ava Kennon\, Say-yeon Kw
on\, Steven J. Miller\, Arman Rysmakhanov\, and Ren Watson\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonah Klein (University of South Carolina)
DTSTART:20260716T153000Z
DTEND:20260716T155500Z
DTSTAMP:20260730T022806Z
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).\n\nAbstract\nA covering system is a finite set
of arithmetic progressions\, with the property that every integer belongs
to at least one of them. Covering systems were introduced by Erdös in 19
50. In the same article where he introduced them\, he asked if there was a
uniform upper bound on the smallest modulus of covering systems with dist
inct moduli. This problem was resolved by Hough in 2015\, showing that the
smallest modulus is always smaller than $10^{16}$. Expanding upon his wor
k\, Balister\, Bollobás\, Morris\, Sahasrabudhe\, and Tiba reduced this b
ound to $616 000$\, with a method that they coined the distortion method.
The aim of this talk is to give a brief overview of the distortion method
and its applications\, with a particular focus on showing that it is impos
sible to construct 10 disjoint distinct covering systems. This is work in
progress with Michael Filaseta and Alexandros Kalogirou.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norbert Hegyvári (Eötvös University and Rényi Institute\, Hung
ary)
DTSTART:20260716T160000Z
DTEND:20260716T162500Z
DTSTAMP:20260730T022806Z
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).\n\nAbstract\nIn the field of additive combinatorics\, sum-differ
ence sets and subset\nsums have been extensively investigated.\nHowever\,
the properties and behavior of the so-called consecutive sums\nof sequence
s represent a significantly less explored area.\nMy talk addresses this ga
p by discussing both old results and recent\ndevelopments concerning conse
cutive sums\, highlighting their connections\nto Sidon sequences and conve
x sequences. Finally\, we will conclude the\ntalk by outlining several ope
n questions and problems.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Montejano (Mexico)
DTSTART:20260716T173000Z
DTEND:20260716T175500Z
DTSTAMP:20260730T022806Z
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).\n\nAbstract\nThe Brunn–Minkowski inequality is a cornerstone of
convex geometry\, with deep connections to several areas of mathematics. I
n recent years\, there has been growing interest in developing discrete ve
rsions of this inequality. Attempts to formulate a discrete version of the
Brunn–Minkowski inequality naturally lead to problems in additive combi
natorics\, particularly those involving lower bounds and structural aspect
s of finite sumsets in ${\\mathbb R}^d$ or ${\\mathbb Z}^d$. In the contin
uous setting\, a refinement due to Bonnesen incorporates the $(d-1)$-dimen
sional volume of projections onto a hyperplane\, yielding sharper bounds t
hat capture geometric structure. A discrete counterpart of this refinement
is currently known only in dimension two\, due to Grynkiewicz and Serra.
In this paper\, we explore extensions of this result to higher dimensions.
In particular\, we introduce a framework for deriving discrete Brunn–Mi
nkowski-type inequalities in arbitrary dimension that incorporate projecti
on data of the underlying sets. This is a joint work with Oriol Serra and
Luis Montejano.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Rajagopal (MIT)
DTSTART:20260716T180000Z
DTEND:20260716T182500Z
DTSTAMP:20260730T022806Z
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).\n\nAbstrac
t\nNathanson introduced the range of cardinalities of $h$-fold sumsets $ \
\mathcal{R}(h\,k):= \\{|hA|:A \\subseteq \\mathbb{Z} \\text{ and }|A| = k\
\}. $ Following a remark of Erdös and Szemerédi 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 $\\le
ft[hk-h+1\,\\binom{h+k-1}{h}\\right]$ except for a specified set of $\\bin
om{h-1}{2}$ numbers. Moreover\, we show that one can take $k_3 = 2$.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cosmin Pohoata (Emory University)
DTSTART:20260716T183000Z
DTEND:20260716T185500Z
DTSTAMP:20260730T022806Z
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).\n\nAbstract\nWe dis
cuss a new combinatorial large-sieve method that uses algebraic splitting
modulo many small primes to turn local congruence restrictions into global
constraints on repeated values. This has various applications\, for examp
le: (i) every Sidon subset of $\\{1^2\, 2^2\, \\ldots\, N^2\\}$ has size a
t most $N \\cdot \\exp(-c \\log N / \\log \\log N)$\, the first super-poly
logarithmic saving for a classical problem of Alon and Erdös\; (ii) a new
upper bound on the largest subset of $[N]^2$ with no repeated distances\,
a problem of Erdös and Guy\; and (iii) a new upper bound on the largest
subset of $[N]^2$ with no isosceles triangle\, a problem recently populari
zed by Charton\, Ellenberg\, Wagner\, and Williamson. Based on recent join
t work with Ernie Croot\, Junzhe Mao\, Adam Sheffer\, and Kyle Yip. We wil
l also discuss how these ideas recently led to a counterexample for the El
ekes--R\\'onyai problem (and to a few other constructions).\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amita Malik (Pennsylvania State University)
DTSTART:20260716T190000Z
DTEND:20260716T192500Z
DTSTAMP:20260730T022806Z
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).\n\nAbstract\nMotivated by Lehmer’s work on weighted p
artitions\, we discuss generalized (super)norms of various classes of part
itions\nand overpartitions. This is joint work with A. Dhar.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandra Kingan (Brooklyn College and the Graduate Center\, CUNY)
DTSTART:20260716T193000Z
DTEND:20260716T195500Z
DTSTAMP:20260730T022806Z
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).\n\nAbst
ract\nI will analyze 3-connected graphs that contain a fixed 3-connected g
raph $H$ as a minor\, but in which no edge can be deleted while preserving
3-connectivity and an $H$-minor. Let $G$ and $H$ be simple 3-connected g
raph such that $G$ has an $H$-minor. An edge $e$ in $G$ is called $H$-d
eletable if $G\\backslash e$ is 3-connected and has an $H$-minor. If $G$ h
as no $H$-deletable edge\, then $G$ can be reduced to $H$ using three spec
ific local operations. This gives a framework for studying extremal grap
hs with no $H$-deletable edges and yields applications to excluded-minor q
uestions. This talk is based on a paper in Discrete Mathematics (Vol 349\,
Issue 6).\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:C. J. Mozzochi (Connecticut)
DTSTART:20260716T200000Z
DTEND:20260716T202500Z
DTSTAMP:20260730T022806Z
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://master.researchseminars.org/talk/CANT2026/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O’Bryant (College of Staten Island and CUNY Graduate Cente
r)
DTSTART:20260716T210000Z
DTEND:20260716T213000Z
DTSTAMP:20260730T022806Z
UID:CANT2026/56
DESCRIPTION:Title: Problem Session\nby Kevin O’Bryant (College of Staten Islan
d and CUNY Graduate Center) as part of Combinatorial and additive number t
heory seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Gr
aduate Center (4th floor).\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaurav Kumar (Indian Institute of Technology Gandhinagar\, India)
DTSTART:20260717T120000Z
DTEND:20260717T122500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/57
DESCRIPTION:Title: Some identities of the sums-of-tails type\nby Gaurav Kumar (I
ndian Institute of Technology Gandhinagar\, India) as part of Combinatoria
l and additive number theory seminar (CANT 2026)\n\nLecture held in Scienc
e Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nA new sums-
of-tails identity involving two parameters b and d is obtained and is used
to derive more results of similar type. One of Ramanujan’s sums-of-tail
s identities from the Lost Notebook is shown to be a special case of our r
esult. In the course of deriving Ramanujan’s identity\, we obtain a new
result of combinatorial significance. Two new representations for an infin
ite series associated to a mock theta function are derived. Also\, we give
an application of an identity of Andrews and Onofri. This talk is based o
n joint work with Prof. Atul Dixit and Aviral Srivastava.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vivekanand Goswami (Indian Institute of Technology Bhilai\, India)
DTSTART:20260717T123000Z
DTEND:20260717T125500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/58
DESCRIPTION:Title: Restricted set addition in finite abelian groups\nby Vivekana
nd Goswami (Indian Institute of Technology Bhilai\, India) 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\nLet
$A$ be a nonempty subset of a finite abelian group $G$ of order $n$. For
an integer $h \\geq 2$\, the restricted $h$-fold sumset $h^\\wedge A$ is t
he set of all sums of $h$ distinct elements of $A$. It is known that if $G
$ is a group of order $n$ and $A$ is a subset of $G$ such that $|A| > \\fr
ac{n}{2}$\, then $h^{\\wedge}A = G$ under some conditions on $h$ and $n$.
While the constant $1/2$ is optimal for groups of even order\, it is not o
ptimal for groups of odd order. For an integer $h \\geq 4$\, let $\\alpha_
h$ be the unique positive root of the polynomial $3^{h - 2} x^{h - 1} + x
- 1$. In this talk\, we discuss that for any $\\alpha > \\alpha_h$\, there
exists a positive integer $M_h(\\alpha)$\, which is determined precisely\
, such that for all $n > M_h(\\alpha)$ with $n$ odd\, if $A$ is a subset o
f a finite abelian group $G$ of order $n$ and if $|A| \\geq \\alpha n$\, t
hen $h^{\\wedge} A = G$. Moreover\, $\\alpha_h > \\alpha_{h + 1}$ for $h \
\geq 4$ and $\\alpha_h$ approaches $\\frac{1}{3}$ as $h$ increases\, and t
he constant $\\frac{1}{3}$ is optimal when the smallest prime dividing $n$
is $3$.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semin Yoo (Institute for Basic Science\, Korea)
DTSTART:20260717T130000Z
DTEND:20260717T132500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/59
DESCRIPTION:Title: Multiplicative irreducibility of shifted multiplicative subgroups
\nby Semin Yoo (Institute for Basic Science\, Korea) as part of Combin
atorial and additive number theory seminar (CANT 2026)\n\nLecture held in
Science Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nA cen
tral theme in additive combinatorics is the interplay between addition and
multiplication. Roughly speaking\, sets with strong multiplicative struct
ure are not expected to exhibit rich additive structure\, and vice versa.
In a recent breakthrough\, Kalmynin resolved a conjecture of Lev--Sonn and
Sárközy on additive decompositions of multiplicative subgroups in prime
fields and quadratic residues. Motivated by this work\, we study multipli
cative analogues of these questions. We show that\, under a certain additi
onal condition\, a shifted multiplicative subgroup cannot be written as a
product set\, and that it also cannot be written as a ratio set unconditio
nally. In this talk\, I will discuss these results and the main ideas of t
he proofs. This talk is based on joint work with Seoyoung Kim (University
of Basel) and Chi Hoi Yip (Georgia Institute of Technology).\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sándor Kiss (Budapest University of Technology and Economics\, an
d HUN-REN Rényi Institute of Mathematics\, Hungary)
DTSTART:20260717T133000Z
DTEND:20260717T135500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/60
DESCRIPTION:Title: Monotone increasing representation functions\nby Sándor Kiss
(Budapest University of Technology and Economics\, and HUN-REN Rényi Ins
titute of Mathematics\, Hungary) as part of Combinatorial and additive num
ber theory seminar (CANT 2026)\n\nLecture held in Science Center in the CU
NY Graduate Center (4th floor).\n\nAbstract\nLet $k\\ge 2$ be an integer a
nd let $A$ be a set of nonnegative integers. The representation function $
R_{A\,k}(n)$ for the set $A$ is the number of representations of a nonnega
tive integer $n$ as the sum of $k$ terms from $A$. A few years ago\, Bell
and Shallit constructed a set $A$ of natural numbers such that $\\mathbb{N
}\\setminus A$ is infinite\, but the corresponding representation function
is strictly increasing. Later\, together with Csaba Sándor and Yang Quan
-Hui\, we improved their result. Furthermore\, we constructed a dense set
such that the corresponding representation function is not strictly increa
sing. In my talk I will also give an overview of the recent progress on th
is topic.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Eichhorn (University of California - Irvine)
DTSTART:20260717T140000Z
DTEND:20260717T142500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/61
DESCRIPTION:Title: The combinatorics of sequences that enjoy a curious self-convolut
ive property\nby Dennis Eichhorn (University of California - Irvine) a
s part of Combinatorial and additive number theory seminar (CANT 2026)\n\n
Lecture held in Science Center in the CUNY Graduate Center (4th floor).\n\
nAbstract\nIn 2002\, Andrews\, Lewis\, and Lovejoy introduced the combinat
orial objects called partitions with designated summands.\nIf we restrict
our attention to $\\mathrm{PDO}(n)$\, the number of partitions with design
ated summands in which all parts are odd\, a very curious property emerges
.\nThe very unexpected identity $\\qquad\n \\sum_{n=0}^\\infty \\mathrm{PD
O}(2n)q^n = \\left ( \\sum_{n=0}^\\infty \\mathrm{PDO}(n)q^n \\right )^2\n
$ holds.\nThat is\, the sequence $\\{\\mathrm{PDO}(2n)\\}_{n=0}^\\infty$ i
s the convolution of the sequence $\\{\\mathrm{PDO}(n) \\}_{n=0}^\\infty$
with itself!\nSequences sharing this curious property are now called ``$2$
-convolutive\,'' and a small handful of such sequences appear in the OEIS.
Many authors have called for a combinatorial proof of the $2$-convolutivi
ty of $\\mathrm{PDO}(n)$. After a nearly two-year-long collaboration with
Chern\, Fu\, and Sellers\, we are happy to announce that we have finally f
ound the requested combinatorial proof.\nIn this talk\, we discuss this ne
w proof\, along with the combinatorial proofs of the $2$-convolutivity of
several other partition functions.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kalmynim (Higher School of Economics\, Russia)
DTSTART:20260717T143000Z
DTEND:20260717T145500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/62
DESCRIPTION:Title: Sárközy’s conjecture on quadratic residues\nby Alexander
Kalmynim (Higher School of Economics\, Russia) 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\nFor an odd prim
e number $p$\, let $\\mathcal R_p\\subset \\mathbb F_p$ be the set of all
non-zero quadratic residues. A. Sárközy conjectured that the set $\\math
cal R_p$ does not admit a non-trivial additive decomposition for large eno
ugh $p$\, i.e. for $p>p_0$ the identity $A+B=\\mathcal R_p$ implies $\\min
(|A|\,|B|)=1$. In this talk we present a complete resolution of Sárközy'
s conjecture. Further\, we show that\, for a subgroup $G\\subset \\mathbb
F_p^*$\, the equality $G\\cup\\{0\\}=A-A$ for some $A$ implies $|G|=2$ or
$6$ and if $G=A+B$ non-trivially\, then $|A|=|B|=\\sqrt{|G|}$.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohan (BK Birla Institute of Engineering and Technology\, Pilani\,
India)
DTSTART:20260717T150000Z
DTEND:20260717T152500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/63
DESCRIPTION:Title: Lehmer-type conjectures and open problems for Nathanson’s totie
nt functions\nby Mohan (BK Birla Institute of Engineering and Technolo
gy\, Pilani\, India) as part of Combinatorial and additive number theory s
eminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate
Center (4th floor).\n\nAbstract\nNathanson’s totient functions $\\Phi(n)
$ and $\\Phi_k(n)$\, where $\\Phi(n)$ counts the number of nonempty sets $
A \\subseteq \\{1\, 2\, \\dots\, n\\}$ for which $\\gcd(A)$ is relatively
prime to $n$\, and $\\Phi_k(n)$ restricts those of size $k$. We formulate
and analyze some analogue of Lehmer's conjecture in the setting of Nathans
on’s totient functions $\\Phi(n)$ and $\\Phi_k(n)$. We further discuss d
ivisibility phenomena for $\\Phi(n)$. We conclude with several conjectures
and open problems concerning density\, arithmetic progressions\, and furt
her structural properties of these functions.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yasuaki Gyoda (Nagoya University\, Japan)
DTSTART:20260717T153000Z
DTEND:20260717T155500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/64
DESCRIPTION:Title: Generalized discrete Lagrange–Markov spectra\nby Yasuaki Gy
oda (Nagoya University\, Japan) as part of Combinatorial and additive numb
er theory seminar (CANT 2026)\n\nLecture held in Science Center in the CUN
Y Graduate Center (4th floor).\n\nAbstract\nThis talk concerns a discrete
extension of the classical Lagrange and Markov\nspectra\, motivated by gen
eralized Markov equations. In the classical case\,\nthe discrete spectral
values below $3$ are organized by Markov numbers and are\ndescribed throug
h continued fractions\, Christoffel words\, and Cohn matrices.\nI will exp
lain how an analogous picture can be developed for generalized\nMarkov num
bers arising from \n $$ x^2+y^2+z^2+k_1yz+k_2zx+k_3xy\n =(3+k_1+k_2+k_3)xy
z.\n$$\nFor each generalized Markov number\, one obtains an explicit spect
ral value\nwhich is realized both as the Lagrange constant of a quadratic
irrational and\nas the Markov constant of an indefinite binary quadratic f
orm with rational\ncoefficients. The emphasis of the talk will be on the m
ain idea of the\nconstruction: generalized Cohn matrices and symbolic sequ
ences coming from\nstraight-line codings play the role classically played
by Christoffel words and \nCohn matrices. The aim is to present a combinat
orial and matrix-theoretic\nframework for viewing classical and generalize
d discrete Diophantine spectra in\na unified way.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippa Holdridge (Alfréd Rényi Institute\, Hungary)
DTSTART:20260717T160000Z
DTEND:20260717T162500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/65
DESCRIPTION:Title: The size of certain symmetric differences of sets of integers
\nby Philippa Holdridge (Alfréd Rényi Institute\, Hungary) 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\nC
onsider a set $A\\subseteq \\mathbb{N}$ which is finite and nonempty. Lett
ing $\\Delta$ denote the symmetric difference of sets and $k\\cdot A=\\{ka
:a\\in A\\}$\, it can be shown that $A\\Delta (2\\cdot A)$ always contains
at least two elements. It also turns out that $A\\Delta (2\\cdot A) \\Del
ta (3\\cdot A)$ has at least three elements. Does $A\\Delta (2\\cdot A)\\D
elta\\cdots \\Delta (n\\cdot A)$ have at least $n$ elements for all $n\\in
\\mathbb{N}$? This question was posed by Pilz in an equivalent form invol
ving the minimal distance of certain linear codes. If true\, then this low
er bound is best possible\, as seen by considering $A=\\{1\\}$. The lower
bound is also attained when $A=\\{1\,2\,\\dots\,n\\}$ and\, in fact\, for
each $n$\, there are arbitrarily large sets $A$ such that $A\\Delta (2\\cd
ot A)\\Delta\\cdots \\Delta (n\\cdot A)$ has exactly $n$ elements.\n\nPilz
proved the conjecture for $n\\le 6$\, and it can also be proven for $n=7$
and $8$. For larger $n$\, Pach and Szabó proved a lower bound of the for
m $n/(\\log n)^{\\lambda}$ for $\\lambda\\approx 0.22$. Until recently\, t
his was the strongest result known\, but in a recent work\, we have proven
the conjecture for all sufficiently large $n$. \nMore precisely\, wheneve
r $n\\ge 3^{81}$. In this talk we will outline the proof and discuss some
related problems. Joint work with P. Pach.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Leonetti (Universit`a degli Studi dell’Insubria and Univer
sit`a Bocconi\, Italy)
DTSTART:20260717T163000Z
DTEND:20260717T165500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/66
DESCRIPTION:Title: Independent families and asymptotic density\nby Paolo Leonett
i (Universit`a degli Studi dell’Insubria and Universit`a Bocconi\, Italy
) 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 $\\mathcal{D}$ be the family of sets $S\\subseteq \\math
bb{N}$ for which the asymptotic density $$\nd(S):=\\lim_{n\\to \\infty}\\f
rac{|S\\cap [1\,n]|}{n}\n$$\nexists. Treating $d$ as a finitely additive p
robability measure on $\\mathcal{D}$\, we study structural properties of f
amilies of sets $\\mathcal{A}\\subseteq \\mathcal{P}(\\mathbb{N})$ which a
re independent (in its classical statistical meaning). We conclude with se
veral open questions. Reference: \nJ. Keith and P. Leonetti\, On maximal f
amilies of independent sets with respect to asymptotic density \, https://
arxiv.org/abs/2603.28922.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neetu (National Institute of Technology Karnataka\, India)
DTSTART:20260717T170000Z
DTEND:20260717T172500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/67
DESCRIPTION:Title: Small doubling in right-ordered groups\nby Neetu (National In
stitute of Technology Karnataka\, India) 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).\n\nAbstract\nFreiman conjectured t
hat if $S$ is a finite subset of a torsion-free group $G$ with $k\\geq 3$
elements and $|S^{2}|\\leq 3k-4\,$ then $S$ is a subset of a small geometr
ic progression of length at most $2k-3$. In 2014\, Freiman et al. settled
this conjecture when $S$ is a finite subset of an ordered group. In this t
alk\, we study this problem in the broader framework of right-ordered grou
ps. Under suitable structural conditions on the subset $S$\, we discuss re
sults that extend aspects of Freiman's conjecture to this setting. We furt
her focus on the right-ordered Baumslag--Solitar group $$\\text{BS}(1\,q)
= \\langle a\, b \\mid ab = b^q a \\rangle\, \\quad q \\in \\mathbb{Z}.$$
We show that for $q \\neq -1$\, if $S$ is a finite subset of $\\text{BS}(1
\,q)$ with the identity element as its minimum and satisfying $|S^2| \\leq
3|S| - 4$\, then the subgroup generated by $S$ is abelian. This is joint
work with Mohan and B. R. Shankar. The results are based on our recent pap
er: https://link.springer.com/article/10.1007/s00025-025-02576-2.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veronica Bitonti (University of Oxford\, UK)
DTSTART:20260717T173000Z
DTEND:20260717T175500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/68
DESCRIPTION:Title: Gap sets of random generalized numerical semigroups\nby Veron
ica Bitonti (University of Oxford\, UK) 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\nFor a fixed positive i
nteger $d$ and a small real $p>0$\, sample a $p$-random subset $A \\subset
eq \\mathbb{Z}_{\\geq 0}^d$\, and let $S:=\\langle A \\rangle$ be the gene
ralized numerical semigroup generated by $A$. We show that\, with high pro
bability (as $p \\to 0$)\, the gap set $\\mathbb{Z}_{\\geq 0}^d \\setminus
S$ is well approximated by the shifted hyperboloid region $$\\{(x_1\, \\l
dots\, x_d) \\in \\mathbb{R}_{\\geq 0}^d: (x_1+\\log p^{-1}) \\cdots (x_d+
\\log p^{-1})\\ll p^{-1}(\\log p^{-1})^{d+1}\\}.$$ This generalizes work o
f Kravitz\, Morales\, and Schildkraut on the $1$-dimensional setting. We a
lso obtain the same result with $S$ replaced by the set of subset sums of
$A$. This is a joint work with Noah Kravitz.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salvatore Tringali (Hebei Normal University\, China)
DTSTART:20260717T180000Z
DTEND:20260717T182500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/69
DESCRIPTION:Title: Power semigroups and two rigidity theorems for groups\nby Sal
vatore Tringali (Hebei Normal University\, China) 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 $\\mathc
al P(H)$ be the semigroup obtained by endowing the family of all non-empty
subsets of a semigroup $H$ with the setwise operation naturally induced b
y $H$ on its power set\, and denote by $\\mathcal P_\\text{fin}(H)$ the su
bsemigroup of $\\mathcal P(H)$ consisting of all non-empty finite subsets
of $H$. We call $\\mathcal P(H)$ and $\\mathcal P_\\text{fin}(H)$ the larg
e power semigroup and the finitary power semigroup of $H$\, respectively.\
n\nWe show that if $H$ is a group and $K$ is an arbitrary semigroup\, then
for\n$\\mathcal P(H)$ to be isomorphic to $\\mathcal P(K)$ it is necessar
y (and sufficient) that $H$ is isomorphic to $K$ (and hence $K$ is itself
a group). The finitary\nanalogue of the same statement appears to be consi
derably more difficult\,\nand we establish it only when $H$ is an additive
subgroup of the\nrationals. The proof of this second result\nrelies\, in
a circuitous way\, on a special case of the Evertse--Schlickewei--Schmidt\
ntheorem. The talk is based on joint work with Shuolin Liu.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katalin Gyarmati (Eötvös Loránd University\, Hungary)
DTSTART:20260717T183000Z
DTEND:20260717T185500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/70
DESCRIPTION:Title: The taxicab problem for polynomials and generalizations of Mason
’s theorem\nby Katalin Gyarmati (Eötvös Loránd University\, Hunga
ry) 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\nThis talk is motivated by Ramanujan's famous taxicab probl
em and is concerned with the solvability of polynomial equations of the fo
rm $p^n+q^n=r^n+s^n$ and\, more generally\, $p_1^{k_1}+\\dots+p_m^{k_m}=0$
over the complex numbers. Using Wronskian determinants and Mason's theore
m\, we obtain sharp upper bounds for the exponents. In particular\, we wil
l show that there are no relatively prime polynomials (with at least one n
on-constant) satisfying the generalised taxicab equation for $n \\ge 16$.
We also consider an extension of Mason's theorem to $f_0+f_1+\\dots+f_k=0$
for several polynomial terms over the complex numbers and finite fields\,
obtaining the corresponding degree bounds. Finally\, the talk points out
interesting future cryptographic applications of these theoretical result
s\, in particular\, the construction of large families of pseudorandom bin
ary sequences with small cross-correlation measures.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Russell Hendel (Towson University)
DTSTART:20260717T190000Z
DTEND:20260717T192500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/71
DESCRIPTION:Title: Improvements in calculating the recursion satisfied by a family o
f determinants\nby Russell Hendel (Towson University) as part of Combi
natorial and additive number theory seminar (CANT 2026)\n\nLecture held in
Science Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nA va
riety of problems can be elegantly solved by identifying the recursion sat
isfied by the determinants of a family of matrices. In 2016\, Jia\, Yang\,
and Li provided a general 6-th order recursion for the family of arbitrar
y pentdiagonal Toeplitz matrices by using Laplace expansions. Recently\, E
vans and Hendel showed that this method is potentially generalizable and a
pplied it to prove an outstanding conjecture on resistance distance in lin
ear 3-trees. However\, Evans and Hendel left as an open problem the conver
gence of their procedure in the general case. Hendel has recently proven c
onvergence for such a Laplace-expansion approach for an arbitrary family o
f square\, banded\, Toeplitz matrices with $k$ super and sub diagonals for
any positive integer $k.$ Hendel also eliminated the computational matrix
methods of Evans and Hendel replacing them with a simpler algebraic manip
ulative system. This note supplements this procedure by showing an improve
d method to solve the resulting system of several simultaneous equations i
n families of determinants. This improved procedure\, applied to explore a
n outstanding conjecture of Bareett\, Evans\, and Francis on the general $
k$-linear tree\, uncovers several interesting patterns which are presented
.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manjil P. Saikia (Ahmedabad University\, Ahmedabad\, India)
DTSTART:20260717T193000Z
DTEND:20260717T195500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/72
DESCRIPTION:Title: Hook length biases in t-regular and t-core partitions\nby Man
jil P. Saikia (Ahmedabad University\, Ahmedabad\, India) as part of Combin
atorial and additive number theory seminar (CANT 2026)\n\nLecture held in
Science Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nRecen
tly\, the theory of hook length biases has emerged as a prominent research
topic. Led by Ballantine\, Burson\, Craig\, Folsom\, and Wen\, hook lengt
h biases are being explored for ordinary partitions\, odd versus distinct
partitions\, self-conjugate versus distinct odd partitions. Recently\, Sin
gh and Barman opened the door to hook length biases in $t$-regular partiti
ons as well. \n\nThe objective of this talk is two fold. First\, we presen
t a previously unobserved connection of hook-lengths in $t$-regular partit
ions with certain distinct parts partitions. Second\, we extend the theory
of hook length biases to $t$-core partitions. For example\, let $a_{t\,k}
(n)$ denote the number of hooks of length $k$ in all $t$-core partitions o
f $n$\, then we find that $a_{3\,1}(n) \\ge a_{3\,2}(n) \\ge a_{3\,4}(n)$
and $a_{4\,1}(n) \\ge a_{4\,3}(n)$ for all $n$. Most of the methods employ
ed in this work are combinatorial. Joint work with Talukdar\; and Baruah\,
Das\, and Mahanta.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neranga Fernando (Knox College)
DTSTART:20260717T200000Z
DTEND:20260717T202500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/73
DESCRIPTION:Title: Contributions to the famiily of reversed Dickson polynomials\
nby Neranga Fernando (Knox College) 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 $p$ be a prime\, $q$ a
power of $p$\, and $\\mathbb{F}_q$ the finite field with $q$ elements. A
polynomial $f\\in \\mathbb{F}_q[\\tt X]$ is called a permutation polynomia
l of $\\mathbb{F}_q$ if the associated mapping $\\tt X\\mapsto f(\\tt X)$
from $\\mathbb{F}_q$ to $\\mathbb{F}_q$ is a permutation of $\\mathbb{F}_q
$. Permutation polynomials have gained widespread attention due to their a
pplications in cryptography\, coding theory\, and combinatorics. The $n$th
reversed Dickson polynomial is given by the explicit expression \n$$ D_n(
a\,\\tt X)=\\sum_{i=0}^{\\lfloor n/2\\rfloor}\\\,\\frac{n}{n-i}\\\,\\binom
{n-i}{i}\\\,a^{n-2i}\\\,(-\\tt X)^i $$ where $a\\in \\mathbb{F}_q$ is a pa
rameter. Reversed Dickson polynomials have played an important role in the
area of permutation polynomials since their introduction in 2009. \n\nA s
elf-reciprocal polynomial is a polynomial whose coefficients form a palind
rome. Self-reciprocal polynomials have important applications in coding th
eory. In this talk\, I will first speak about my contribution to the areas
of permutation polynomials over finite fields and self-reciprocal polynom
ials via reversed Dickson polynomials. I will also speak about a recent RE
U project conducted with my students at College of the Holy Cross on rever
sed Dickson permutation polynomials. Moreover\, I will present a list of r
esearch projects for students.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lindsay Dever (Millersville University)
DTSTART:20260717T203000Z
DTEND:20260717T205500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/74
DESCRIPTION:Title: Atoms in the semigroup of non-negative integer matrices\nby L
indsay Dever (Millersville University) as part of Combinatorial and additi
ve number theory seminar (CANT 2026)\n\nLecture held in Science Center in
the CUNY Graduate Center (4th floor).\n\nAbstract\nIn the semigroup of $2\
\times 2$ matrices with non-negative integer entries and non-zero determin
ant\, we study the factorization of matrices into atoms\, or irreducible m
atrices. In 2022\, Baeth et al. discovered classes of atoms in this semigr
oup\; however\, the factorability of most matrices remains unknown. As the
result of joint work with Eva Goedhart\, Gregory Heilbrunn\, and Tony W.
H. Wong\, I will discuss additional classes of atoms: a class of atoms wit
h determinant $p$\, $2p$\, or $4p$\, where $p$ is prime\, and a class of a
toms where the main diagonal is much ``larger'' than the off-diagonal (or
vice-versa). In addition\, we find that bisymmetric matrices with relative
ly prime entries are a divisor-closed subset and use a factor-search algor
ithm to classify bisymmetric atoms with minimum entry up to 4000.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yasuaki Gyoda (Nagoya University\, Japan)
DTSTART:20260718T110000Z
DTEND:20260718T115500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/75
DESCRIPTION:Title: Generalized discrete Lagrange–Markov spectra\nby Yasuaki Gy
oda (Nagoya University\, Japan) as part of Combinatorial and additive numb
er theory seminar (CANT 2026)\n\nLecture held in Science Center in the CUN
Y Graduate Center (4th floor).\n\nAbstract\nThis talk concerns a discrete
extension of the classical Lagrange and Markov\nspectra\, motivated by gen
eralized Markov equations. In the classical case\,\nthe discrete spectral
values below $3$ are organized by Markov numbers and are\ndescribed throug
h continued fractions\, Christoffel words\, and Cohn matrices.\nI will exp
lain how an analogous picture can be developed for generalized\nMarkov num
bers arising from \n $$ x^2+y^2+z^2+k_1yz+k_2zx+k_3xy\n =(3+k_1+k_2+k_3)xy
z.\n$$\nFor each generalized Markov number\, one obtains an explicit spect
ral value\nwhich is realized both as the Lagrange constant of a quadratic
irrational and\nas the Markov constant of an indefinite binary quadratic f
orm with rational\ncoefficients. The emphasis of the talk will be on the m
ain idea of the\nconstruction: generalized Cohn matrices and symbolic sequ
ences coming from\nstraight-line codings play the role classically played
by Christoffel words and \nCohn matrices. The aim is to present a combinat
orial and matrix-theoretic\nframework for viewing classical and generalize
d discrete Diophantine spectra in\na unified way.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chahat Ahuja (Indraprastha Institute of Information Technology\, I
ndia)
DTSTART:20260718T120000Z
DTEND:20260718T122500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/76
DESCRIPTION:Title: Visibility of lattice points across polynomial curves\nby Cha
hat Ahuja (Indraprastha Institute of Information Technology\, India) as pa
rt of Combinatorial and additive number theory seminar (CANT 2026)\n\nLect
ure held in Science Center in the CUNY Graduate Center (4th floor).\n\nAbs
tract\nThe visibility of lattice points from the origin along a polynomial
family of curves constitutes a significant generalization of visibility a
long straight lines.\nFollowing the classical notion\, where the density o
f visible lattice points equals\n$1/\\zeta(2)$\, and its generalization to
monomial curves of the form $y = ax^b$\,\nwhere the density equals $1/(b+
1)$\, we study a family of polynomial curves defined\nby $$ \n y \\\;=\\\;
q\\bigl(a_n x^n + a_{n-1}x^{n-1} + \\cdots + a_1 x\\bigr)\,\n$$ where $q$
is a positive rational number.\n\nWe introduce a new criterion based on a
\\emph{polynomial greatest common divisor\ncondition} that provides a low
er bound on the number of visible lattice points in\n$\\mathbb{N}^2$. Conv
ersely\, we derive conditions under which a given lattice point\nbecomes t
he next visible point along such a polynomial curve. Using the\nprinciple
of inclusion-exclusion\, we obtain an exact double-sum formula for the\nnu
mber of pairs $(a\, b) \\leq N$ that are visible with respect to this poly
nomial\nfamily. \nFinally\, we extend the framework to related problems an
d pose several open\nquestions concerning gap distributions and quantitati
ve bounds for non-visible\npoints. This work provides a broader theoretica
l foundation for lattice point\nvisibility beyond linear and monomial sett
ings.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Baczkowski (University of Findlay)
DTSTART:20260718T123000Z
DTEND:20260718T125500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/77
DESCRIPTION:Title: Building off the Ideas of Erdós\, Sierpiński\, Riesel\, and Mor
e\nby Daniel Baczkowski (University of Findlay) 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\nIn 1950\,
Erdós proved there are infinitely many odd integers that are not of the f
orm $2^k + p$\, where $p$ is a prime. \nIn 1956\, using similar methods\,
Riesel proved there are infinitely many odd integers $k$ such that $k\\cdo
t 2^n - 1$ is composite for all positive integers $n$. Then\, in 1960\, Si
erpiński proved that there are infinitely many odd integers $\\ell$ such
that $\\ell\\cdot 2^n + 1$ is composite for all positive integers $n$. \nW
e will discuss various other related results such as how some classical se
quences like Fibonacci\, triangular\, and more intersect the set of all po
ssible Riesel and/or Sierpiński numbers.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eshita Mazumdar (Ahmedabad University\, Ahmedabad\, India)
DTSTART:20260718T130000Z
DTEND:20260718T132500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/78
DESCRIPTION:Title: Extending zero-sum theory from abelian to non-abelian groups\
nby Eshita Mazumdar (Ahmedabad University\, Ahmedabad\, India) 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\
nZero-sum theory is a central topic in additive combinatorics that studies
the structure of sequences over finite groups and the conditions guarante
eing the existence of zero-sum subsequences. Fundamental parameters in thi
s area include the Davenport constant and the Erdős–Ginzburg–Ziv cons
tant\, which measure the threshold lengths forcing zero-sum behavior. Thes
e invariants originated in the study of non-unique factorizations in algeb
raic number theory\, but determining their exact values remains a challeng
ing problem even for many finite abelian groups. In this talk\, I will dis
cuss recent progress on zero-sum problems in finite non-abelian groups. In
particular\, I will highlight how combinatorial techniques developed for
abelian groups can be adapted—or fail—to extend to the non-abelian set
ting\, and how new phenomena arise due to the lack of commutativity. I wil
l also present several results that reveal surprising connections between
classical zero-sum invariants of abelian groups and their analogues for no
n-abelian groups\, pointing toward a broader combinatorial framework for z
ero-sum theory.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krystian Gajdzica (Jagiellonian University\, Poland)
DTSTART:20260718T133000Z
DTEND:20260718T135500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/79
DESCRIPTION:Title: On the Bessenrodt-Ono inequality for polynomials\nby Krystian
Gajdzica (Jagiellonian University\, Poland) 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\nIn 2016\, Bessenr
odt and Ono proved that the partition function satisfies the inequality $\
n p(a)p(b)>p(a+b)\n$\nfor all $a\,b\\geqslant2$ with $a+b>9$. Since then\,
analogous properties have been investigated for many partition statistics
. In this talk\, following Gian-Carlo Rota's advice\, we move from the dis
crete problem to the continuous one\, and consider a family of recursively
defined polynomials \n$\nP_n^g(x) := \\frac{x}{n} \\sum_{k=1}^n g(k) P_{n
-k}^g(x)\n$\nwith the initial condition $P_0^g(x):=1$\, where $(g(n))_{n\\
in\\mathbb{N}}$ is an arbitrary sequence of positive real numbers such tha
t $g(1)=1$. We derive an efficient criterion characterizing when the inequ
ality \n$\n P_{a}^g(x)P_{b}^g(x)\\geqslant P_{a+b}^g(x)\n$\n is satisfied
for all $x\\geqslant x_0$ and $a\,b\\geqslant1$\, where $x_0$ is some real
number depending on $g$. Moreover\, we illustrate the usefulness of this
criterion by applying it to various combinatorial sequences.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debyani Manna (Indian Institute of Technology Roorkee\, India)
DTSTART:20260718T140000Z
DTEND:20260718T142500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/80
DESCRIPTION:Title: Extended Inverse results for restricted h-fold sumset in integer<
/a>\nby Debyani Manna (Indian Institute of Technology Roorkee\, India) as
part of Combinatorial and additive number theory seminar (CANT 2026)\n\nLe
cture held in Science Center in the CUNY Graduate Center (4th floor).\n\nA
bstract\nLet $A$ be a finite set of $k$ integers. For $2 \\leq h \\leq k$\
, the restricted h-fold sumset $h^{\\wedge}A$ is the set of all sums of $h
$ distinct elements of the set $A$. In additive combinatorics\, much of th
e focus has traditionally been on finite integer sets whose sumsets are un
usually small (cf. Freiman’s theorem and its extensions). More recently\
, Nathanson posed the inverse problem for the restricted sumset $h^{\\wedg
e}A$ when $|h^{\\wedge}A|$ is small. For $h \\in \\{2\,3\,4\\}$\, this que
stion has already been studied by Mohan and Pandey. In this article\, we s
tudy the inverse problems for $h^{\\wedge}A$ with arbitrary $h \\geq 3$ an
d characterize all possible sets $A$ for certain cardinalities of $h^{\\we
dge}A$. Joint work with Mohan and Ram Krishna Pandey.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi Hoi Yip (Hong Kong University of Science and Technology\, Hong
Kong)
DTSTART:20260718T143000Z
DTEND:20260718T145500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/81
DESCRIPTION:Title: Additive properties of multiplicatively defined sets\nby Chi
Hoi Yip (Hong Kong University of Science and Technology\, Hong Kong) as pa
rt of Combinatorial and additive number theory seminar (CANT 2026)\n\nLect
ure held in Science Center in the CUNY Graduate Center (4th floor).\n\nAbs
tract\nUnderstanding the additive structure of multiplicatively defined se
ts\, including the primes\, perfect squares\, perfect powers\, powerful nu
mbers\, and smooth numbers\, remains a fundamental open challenge. In this
talk\, I will talk about some recent progress on related results. In part
icular\, I will discuss arithmetic progressions\, sumsets\, and Hilbert cu
bes in some well-studied multiplicatively defined sets\, as well as their
interactions. Joint work with Ernie Croot and Junzhe Mao.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akshat Mudgal (University of Warwick\, UK)
DTSTART:20260718T150000Z
DTEND:20260718T152500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/82
DESCRIPTION:Title: A structure theorem for sets with doubling 4 + δ\nby Akshat
Mudgal (University of Warwick\, UK) 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 question of Ben Green as
ks whether every finite set $A$ of integers with doubling constant $K$ mus
t contain a subset $A'$ of comparable size whose doubling is at most $K +
o(1)$ due to some explicit algebraic structure on $A'$. This was previousl
y understood in the regime $K < 4 - o(1)$ by work of Eberhard\, Green\, an
d Manners\, who showed that one can find such a subset $A'$ with density a
t least $1/2 + o(1)$ inside a long arithmetic progression. In this talk\,
I will provide a brief survey of this question as well as mention some new
progress towards this. This is joint work with Yifan Jing.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Cantarini (University of Perugia\, Italy)
DTSTART:20260718T153000Z
DTEND:20260718T155500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/83
DESCRIPTION:Title: Averages of the diagonal Elliott-Halberstam problem twisted by th
e Möbius function with Sobolev and Hölder-Zygmund weights\nby Marco
Cantarini (University of Perugia\, Italy) as part of Combinatorial and add
itive number theory seminar (CANT 2026)\n\nLecture held in Science Center
in the CUNY Graduate Center (4th floor).\n\nAbstract\nRecalling that the s
o-called Elliott-Halberstam conjecture twisted\nby the Möbius function $\
\mu(n)$ claims that $$\\sum_{q\\leq N^{\\theta}}\\max_{y\\leq N}\\max_{(a\
,q)=1}\\left|\\sum_{\\underset{{\\scriptstyle n\\equiv a\\\,\\mod\\\,q}}{n
\\leq y}}\\Lambda(n)\\mu\\left(N-n\\right)-\\frac{1}{\\varphi\\left(q\\rig
ht)}\\sum_{n\\leq y}\\Lambda(n)\\mu\\left(N-n\\right)\\right|\\ll\\frac{N}
{\\log\\left(N\\right)^{A}} \n$$\nfor every $A>0$\, where $0<\\theta<1$ is
fixed\, and also recalling\nthat the validity of this conjecture\, in com
bination with the validity\nof the classical Elliott-Halberstam for suitab
le $\\theta$\, proves\nthe binary Goldbach conjecture\, in this talk we an
alyze weighted average\nvariants of this problem. We will show that\, unde
r Generalized Riemann\nHypothesis\, a weak version of the Gonek-Hejhal con
jecture and working\nwith weights belonging to the Sobolev space $W^{2\,1}
$ or in the Hölder-Zygmund\nspaces $\\mathcal{C}^{\\delta}$ for suitable
range of $\\delta$\, the\nbound of the average is consistent with the boun
d of the ``diagonal\nversions'' of this conjecture (that is\, taking $y=N$
and taking\n$n\\equiv N\\mod q)$. In particular\, in the case of weights
in Sobolev\nspace\, the consistent upper bound holds for the whole $0<\\th
eta<1$\nand\, in the case of weights in the Hölder-Zygmund class $\\mathc
al{C}^{\\delta}$\,\nfor $\\theta$ that depends on the choice of $\\delta$
but still not\nbelow the $1/2-2\\varepsilon$ threshold.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aviral Srivastava (IIT Gandhinagar\, India)
DTSTART:20260718T160000Z
DTEND:20260718T162500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/84
DESCRIPTION:Title: Non-Rascoe partitions and a rank parity function associated to th
e Rogers–Ramanujan partitions\nby Aviral Srivastava (IIT Gandhinagar
\, India) as part of Combinatorial and additive number theory seminar (CAN
T 2026)\n\nLecture held in Science Center in the CUNY Graduate Center (4th
floor).\n\nAbstract\nThe rank-parity function associated with a class of
partitions gives rise to objects with rich analytical and combinatorial pr
operties. In this talk\, we will discuss the rank-parity function associat
ed with Rogers-Ramanujan partitions and show their close correspondence wi
th an interesting class of restricted partitions\, namely\, partitions int
o distinct parts where the number of parts is not a part. We will show som
e interesting congruences related to these functions. This talk is based o
n joint\nwork with Gaurav Kumar and Prof. Atul Dixit.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiseok Yeon (University of California - Davis)
DTSTART:20260718T170000Z
DTEND:20260718T172500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/85
DESCRIPTION:Title: On the density of rational lines on diagonal cubic hypersurfaces<
/a>\nby Kiseok Yeon (University of California - Davis) as part of Combinat
orial and additive number theory seminar (CANT 2026)\n\nLecture held in Sc
ience Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nIn this
paper\, we establish the asymptotic estimates for the rational lines on d
iagonal cubic hypersurfaces defined by $\\sum_{i=1}^sc_ix^3_i=0$ with $c_i
\\in\\mathbb{Z}\\setminus \\{0\\}\,$ provided that $s\\geq 18.$ This impro
ves the previously known bound $s\\geq 21$ required to obtain such asympto
tic estimates. Our approach develops a multidimensional shifting variables
argument\, and exploits the recent progress on the Parsell-Vinogradov sys
tem. This talk is based on the speaker’s recent work and a joint work wi
th Parsell.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Luca (Stellenbosch University\, South Africa)
DTSTART:20260718T173000Z
DTEND:20260718T175500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/86
DESCRIPTION:Title: Multiply gleeful numbers\nby Florian Luca (Stellenbosch Unive
rsity\, South Africa) 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\nFor positive integers $k$ and $n$ let $f
_k(n)$ be the number of ways of representing $n$ as a sum of $k$ powers of
consecutive primes. A number is called $k$-gleeful if \n$f_k(n)>0$ and mu
ltiply gleeful if $f_k(n)>1$ or $f_k(n)f_{k'}(n)>0$ for some positive inte
gers $k< k'.$ Under Schinzel's hypothesis H\, we show that there are infin
itely many positive integers $n$ such that $f_2(n)f_4(n)>0$. Under the sam
e assumption we show that $\\limsup_{n\\to\\infty} f_2(n)=\\infty$. This g
ives a conditional proof of a stronger version of a conjecture of Moore an
d Sorenson from the preprint arXiv:2507.09012v1\, July 2025.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francis Atta Howard (University of Abomey-Calavi\, Benin Republic)
DTSTART:20260718T180000Z
DTEND:20260718T182500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/87
DESCRIPTION:Title: Gertsch quotient living in the “poor man’s adele ring” A: K
urepa-Bell-Wilson congruence\nby Francis Atta Howard (University of Ab
omey-Calavi\, Benin Republic) 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\nThis study examines Kurepa\, Bel
l\, and Wilson congruences for odd prime $p \\geq 3$\, focusing on the le
ft factorial relation $K_p \\equiv \\mathbf{Bell}_{p-1} - 1 \\pmod p$. We
demonstrate that the Kurepa modulo $p$ naturally generates the Gertsch quo
tient $\\mathbb{G}_p \\coloneqq \\frac{K_p - \\mathbf{Bell}_{p-1} + 1}{p}$
\, which\, for larger primes\, resides in the poor man's adele ring $\\mat
hcal{A}$.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bobby Jacobs
DTSTART:20260718T183000Z
DTEND:20260718T185500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/88
DESCRIPTION:Title: Fibonacci multiplication\nby Bobby Jacobs as part of Combinat
orial and additive number theory seminar (CANT 2026)\n\nLecture held in Sc
ience Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nWe will
define an interesting product for generalized Fibonacci sequences\, explo
re the consequences of this definition\, extend this to a ring\, define th
e notion of a prime among these sequences\, and show that this ring cont
ains infinitely many primes. This product can be viewed as sums of shift
s of scalar multiples of the canonical Fibonacci sequence\, and may provi
de new insight into sequences of continuing interest.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Augustine O. Munagi (University of the Witwatersrand\, South Afric
a)
DTSTART:20260718T190000Z
DTEND:20260718T192500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/89
DESCRIPTION:Title: A Bessenrodt-Ono inspired inequality for compositions proved cons
tructively\nby Augustine O. Munagi (University of the Witwatersrand\,
South Africa) 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\nIn 2016 Bessenrodt-Ono published an analytic pro
of of the inequality $p(a+b)\\leq p(a)p(b)$\, where $p(n)$ is the partitio
n function and $a\,b$ are positive integers with $a+b>8$. In this talk we
consider a similar result for $c(n)$\, the number of integer compositions
of $n$\, and show that $c(a+b)>c(a)c(b)$ for all positive integers $a\,b$.
Besides numerical verifications\, we provide a constructive bijective pro
of based on the inherent symmetry of compositions. It is known that such a
proof is still elusive in the partitions case. We also give an applicatio
n of our machinery to efficient generation of compositions.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurence P. Wijaya (University of Kentucky)
DTSTART:20260718T193000Z
DTEND:20260718T195500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/90
DESCRIPTION:Title: Polynomial corners over finite field\nby Laurence P. Wijaya (
University of Kentucky) as part of Combinatorial and additive number theor
y seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Gradua
te Center (4th floor).\n\nAbstract\nRecently there has been some progress
in understanding the density of a subset of $[N]^2$ that avoids polynomial
patterns. Kravitz\, Kuca\, and Leng showed that if $P\\in\\Z[z]$ satisfie
s certain conditions\, then any set $A\\subseteq[N]^2$ does not contain $(
x\,y)\,(x+P(z)\,y)\,(x\,y+P(z))$\, we must have \n \\[\n |A|\\ll_P\\frac{N
^2}{(\\log\\log\\log N)^c}\n \\]\n for some small constant $c$. \n \n In t
his talk\, we show a similar result in $(\\F_p)^2$ where we get a better b
ound on the density of a set $A\\subseteq (\\F_p)^2$ not containing $(x\,y
)\,(x+P(z)\,y)\,(x\,y+P(z))$ with some conditions on $P\\in \\F_p[z]$.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Glenn T. Bruda (University of Florida)
DTSTART:20260718T200000Z
DTEND:20260718T202500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/91
DESCRIPTION:Title: Generalized polygonal number representations\nby Glenn T. Bru
da (University of Florida) 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\nLet $r_n^{{k}}(N)$ be the number of
representations of $N$ as the sum of $n$ generalized $k$-gonal numbers an
d $r_n^{\\square}(N)$ be the number of representations of $N$ as the sum o
f $n$ squares. By modifying the Heath-Brown circle method\, we prove a clo
sed-form asymptotic relation between $r_n^{{k}}(N)$ and $r_n^{\\square}(8(
k-2)N+n(k-4)^2)$ for any $k\\geq3$ and any $n\\geq4$. Consequently\, we es
timate $\\sum_{N\\leq x}r_4^{{k}}(N)^2$ and\, via a result of Bringmann\,
Jang\, Kane\, and Tse\, prove a similar closed-form asymptotic relation be
tween the number $r_{4\,+}^{{k}}(N)$ of representations of $N$ as the sum
of four ordinary $k$-gonal numbers and $r_4^{\\square}(8(k-2)N+n(k-4)^2)$.
We also show that if $4\\mid k$\, any strictly increasing infinite subseq
uence on which $r_{4\,+}^{{k}}$ is bounded converges $2$-adically to $(k-4
)^2/(4-2k)\\in\\mathbb{Z}_2$\, supplementing a result of Meng and Sun\, an
d if $4\\nmid k$\, there is no strictly increasing infinite subsequence on
which $r_{4\,+}^{{k}}$ is bounded.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Collier Gaiser (Community College of Aurora\, Colorado)
DTSTART:20260718T203000Z
DTEND:20260718T205500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/92
DESCRIPTION:Title: On Rado numbers for equations with unit fractions\nby Collier
Gaiser (Community College of Aurora\, Colorado) 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 $R_r(k)$
be the smallest $n$ such that every $r$-coloring of $\\{1\,2\,...\,n\\}$ h
as a monochromatic solution to $x_1+x_2+\\cdots+x_k=y$\, where $x_1\,x_2\,
\\ldots\,x_k$ are not necessarily distinct. Beutelspacher and Brestovansky
proved that $R_2(k)=k^2+k-1$ and\, recently\, Boza\, Mar\\'{i}n\, Revuelt
a\, and Sanz proved that $R_3(k)=k^3+2k^2-2$. Similarly\, let $f_r(k)$ be
the smallest $n$ such that every $r$-coloring of $\\{1\,2\,...\,n\\}$ has
a monochromatic solution to the equation $1/x_1+1/x_2+\\cdots+1/x_k=1/y$\,
where $x_1\,x_2\,\\ldots\,x_k$ are not necessarily distinct. Brown and R\
\"{o}dl proved that $f_2(k)=O(k^6)$. In this talk\, we show that $f_2(k)=O
(k^3)$ and $f_3(k)=O(k^{43})$. The main ingredient in our proof is a finit
e set $A\\subseteq\\mathbb{N}$ such that every $r$-coloring of $A$ has a m
onochromatic solution to the linear equation $x_1+x_2+\\cdots+x_k=y$ and t
he least common multiple of $A$ is sufficiently small. As for the lower bo
und\, we show that $f_r(k)\\geq k^r$ which leads to an interesting open qu
estion: Is $f_2(k)=\\Theta(k^2)$?\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Austin Abraham Cramer (Penn State)
DTSTART:20260716T203000Z
DTEND:20260716T205500Z
DTSTAMP:20260730T022806Z
UID:CANT2026/93
DESCRIPTION:Title: Lattice points under polynomial curves\nby Austin Abraham Cra
mer (Penn State) as part of Combinatorial and additive number theory semin
ar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate Cent
er (4th floor).\n\nAbstract\nThis presentation is concerned with various a
nalogs of the Gauss circle and Dirichlet divisor problems. For a given po
lynomial $f(x_1\,\\ldots\,x_s)$ with integer coefficients\, let $r_f(n) =
\\#\\{(x_1\,\\ldots\,x_s) \\in \\mathbb{N}^s: f(x_1\,\\ldots\,x_s) = n\\}
$. Using van der Corput's method to control error terms\, we obtain asympt
otic formulas for averages of this function of the form $\\sum_{n \\leq N}
r_f(n)$ with various choices of $f$. When $f(x_1\,x_2)$ is a polynomial i
n two variables\, this counts the lattice points in the first quadrant bou
nded by the curve $f(x_1\,x_2) = N$. In this setting\, we demonstrate how
to obtain asymptotics for various curves of low degree as well as how the
method can be extended to apply to some simple hypersurfaces bounding poin
ts in $\\mathbb{N}^s$.\n
LOCATION:https://master.researchseminars.org/talk/CANT2026/93/
END:VEVENT
END:VCALENDAR