BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Mohan (BK Birla Institute of Engineering and Technology\, India)
DTSTART:20250520T110000Z
DTEND:20250520T112500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/1/"
 >Special additive complements of a set of natural numbers</a>\nby Mohan (B
 K Birla Institute of Engineering and Technology\, India) as part of Combin
 atorial and additive number theory (CANT 2025)\n\nLecture held in CUNY Gra
 duate Center - Science Center (4th floor).\n\nAbstract\nLet $A$ be a set o
 f natural numbers.	A set $B$ of natural numbers is said to be an additive 
 complement of the set $A$ if all sufficiently large natural numbers can be
  represented as $x+y$ for some $x\\in A$ and $y\\in B$.  We shall describe
  various types of additive complements of the set $A$ such as those additi
 ve complements of $A$  that do or do not intersect  $A$\, additive complem
 ents which are the union of disjoint infinite arithmetic progressions\, an
 d additive complements having various densities etc. We estabilish that if
    $A=\\{a_i: i\\in \\mathbb{N}\\}$ is a set of natural numbers such that 
  $a_{i} < a_{i+1} $ for $i \\in \\mathbb{N}$ and $\\liminf_{n\\rightarrow 
 \\infty } (a_{n+1}/a_{n})>1$\, then there exists a set $B\\subset \\mathbb
 {N}$  such that $B\\cap A = \\varnothing$ and $B$ is a sparse additive com
 plement of the set $A$.  Besides this\,  for a given positive real number 
 $\\alpha \\leq 1$ and a finite set $A$\, we investigate a set $B$ such tha
 t $B$ can be written as a union of disjoint infinite arithmetic progressio
 ns with the natural density of $A+B$ equal to $\\alpha$.\n
LOCATION:https://researchseminars.org/talk/CANT2025/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harald Helfgott (CNRS/Institut de Math\\' ematiques de Jussieu)
DTSTART:20250520T113000Z
DTEND:20250520T115500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/2/"
 >Explicit estimates for sums of arithmetic functions\, or the optimal use 
 of finite information on Dirichlet series</a>\nby Harald Helfgott (CNRS/In
 stitut de Math\\' ematiques de Jussieu) as part of Combinatorial and addit
 ive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Sc
 ience Center (4th floor).\n\nAbstract\nLet $F(s) = \\sum_n a_n n^{-s}$ be 
 a Dirichlet series. Say we have an analytic continuation of $F(s)$\, and i
 nformation on the poles of $F(s)$ with $|\\Im s|\\leq T$ for some large co
 nstant $T$. \n What is the best way to use this information to give explic
 it estimates on sums $\\sum_{n\\leq x} a_n$? \n\n  The problem of giving e
 xplicit bounds on the Mertens function $M(x) = \\sum_{n\\leq x} \\mu(n)$ i
 llustrates how open this basic question was.\n  One might think that bound
 ing $M(x)$ is essentially equivalent to estimating $\\psi(x) = \\sum_{n\\l
 eq x} \\Lambda(n)$ or the number of primes $\\leq x$.\n  However\, we have
  long had fairly satisfactory explicit bounds on $\\psi(x)-x$\, whereas bo
 unding $M(x)$ well was a notoriously recalcitrant problem.\n\nWe give an o
 ptimal way to use information on the poles of $F(s)$ with $|\\Im s|\\leq T
 $. In particular\, we give bounds on the Mertens function much stronger th
 an those in the literature\, while also substantially improving on estimat
 es on $\\psi(x)$.\n\n We use functions of "Beurling-Selberg" type -- namel
 y\, an optimal approximant due to Carneiro-Littmann and an optional majora
 nt/minorant due to Graham-Vaaler. Our procedure has points of contact \n w
 ith Wiener-Ikehara and also with work of Ramana and Ramaré\, but does not
  rely on results in the explicit analytic-number-theory literature. \n\n(j
 oint work with Andrés Chirre)\n
LOCATION:https://researchseminars.org/talk/CANT2025/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norbert Hegyvari (E\\"otv\\"os University  and R\\'enyi Institute)
DTSTART:20250521T130000Z
DTEND:20250521T132500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/3/"
 >Variants of Raimi's theorem</a>\nby Norbert Hegyvari (E\\"otv\\"os Univer
 sity  and R\\'enyi Institute) as part of Combinatorial and additive number
  theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Cent
 er (4th floor).\n\nAbstract\nThere exists $E\\subseteq \\mathbb{N}$ such t
 hat\, whenever $r\\in \\mathbb{N}$ and $\\mathbb{N}=\\bigcup_{i=1}^rD_i$ t
 here exist\n$i\\in\\{1\,2\,\\ldots\,r\\}$ and $k\\in \\mathbb{N}$ such tha
 t $(D_i+k)\\cap E$ is\ninfinite and $(D_i+k)\\setminus E$ is infinite.\n\n
 A new proof of the theorem is due to N. Hindman\, then to Bergelson and We
 iss\, and the generalization to the author.\nIn the present talk\, we give
  an outline of the new proofs and the generalization and some variations a
 re discussed in different structures (e.g. in $\\Z_n^k$\, in $SL_2(\\mathb
 b F_p)$.)\n\nThese variations are joint work with J\\'anos Pach and Thang 
 Pham.\n
LOCATION:https://researchseminars.org/talk/CANT2025/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alisa Sedunova (Purdue University)
DTSTART:20250521T133000Z
DTEND:20250521T135500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/4/"
 >The multiplication table constant and sums of two squares</a>\nby Alisa S
 edunova (Purdue University) as part of Combinatorial and additive number t
 heory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center
  (4th floor).\n\nAbstract\nLet $r_1(n)$ be the number of representations o
 f $n$ as the sum of a square and a square of a prime. We discuss the errat
 ic behavior of $r_1$\, which is similar to the one of the divisor function
 . \nWe will show that the number of integers up to $x$ that have at least 
 one such representation \nis asymptotic to $(\\pi/2) x \\log x$ minus a se
 condary term of size $x/(\\log x)^{1+d+o(1)}$\, \nwhere $d$ is the multipl
 ication table constant. Detailed heuristics suggest very precise asymptoti
 c \nfor the secondary term as well. In particular\, our proofs imply that 
 the main contribution to the mean \nvalue of $r_1(n)$ comes from integers 
 with “unusual” number of prime factors\, i.e. those with\n $\\omega(n)
  \\sim 2 \\log \\log x$ (for which $r_1(n) \\sim (\\log x)^{\\log 4-1}$)\,
  where $\\omega(n)$ \n is the number of district prime factors of $n$.   \
 \\\\nIn the talk we will review the results of several works that include 
 a recent joint preprint with Andrew Granville and Cihan Sabuncu and my pap
 er from 2022 as well as some work in progress.\n
LOCATION:https://researchseminars.org/talk/CANT2025/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinhui Fang (Nanjing Normal University\, China)
DTSTART:20250522T130000Z
DTEND:20250522T132500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/5/"
 >On  bounded unique representation bases</a>\nby Jinhui Fang (Nanjing Norm
 al University\, China) as part of Combinatorial and additive number theory
  (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th
  floor).\n\nAbstract\nFor a nonempty set $A$ of integers and an integer $n
 $\,  let $r_{A}(n)$ be the number of representations of $n=a+a'$ with $a\
 \le a'$ and $a\, a'\\in A$\, and let $d_{A}(n)$ be the number of represent
 ations of $n=a-a'$ with $a\, a'\\in A$. In 1941\, Erd\\H{o}s and Tur\\'{a}
 n posed the profound conjecture: If $A$ is a set of positive integers such
  that $r_A(n)\\ge 1$ for all sufficiently large $n$\, then $r_A(n)$ is unb
 ounded. In 2004\, Ne\\v{s}et\\v{r}il and Serra introduced the notion of bo
 unded sets and confirmed the Erd\\H{o}s-Tur\\'{a}n conjecture for all boun
 ded bases. In 2003\, Nathanson considered the existence of the set $A$ wit
 h logarithmic growth such that $r_A(n)=1$ for all integers $n$. Recently\,
  we prove that\, for any positive function $l(x)$ with $l(x)\\rightarrow 0
 $ as $x\\rightarrow \\infty$\,  there is a bounded set $A$ of integers su
 ch that $r_A(n)=1$ for all integers $n$ and $d_A(n)=1$ for all positive in
 tegers $n$\, and $A(-x\,x)\\ge l(x)\\log x$ for all sufficiently large $x$
 \, where $A(-x\,x)$ is the number of elements $a\\in A$ with $-x\\le a\\le
  x$.  \nThis is joint work with Prof. Yong-Gao Chen.\n
LOCATION:https://researchseminars.org/talk/CANT2025/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gergo Kiss (Budapest Corvinus University and R\\' enyi Institute)
DTSTART:20250522T130000Z
DTEND:20250522T132500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/6/"
 >Weak tiling and the Coven-Meyerowitz conjecture</a>\nby Gergo Kiss (Budap
 est Corvinus University and R\\' enyi Institute) as part of Combinatorial 
 and additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Ce
 nter - Science Center (4th floor).\n\nAbstract\nThe concept of weak tiling
  was originally introduced in $\\mathbb{R}^n$ by Lev and Matolcsi\, and ha
 s proven to be an essential tool in addressing Fuglede's conjecture for co
 nvex domains. In this talk\, we extend the notion of weak tiling to the se
 tting of cyclic groups and further generalize it using a natural averaging
  process. As a result\, the tiles are no longer sets\, \nbut rather become
  step functions--a framework we refer to as functional tiling.\n\nOne adva
 ntage of this approach is that the cyclotomic divisors of the functions in
 volved in a functional tiling remain the same as those of the characterist
 ic functions of the original sets. Another is that functional tilings can 
 be studied using the well-established tools and objective functions of lin
 ear programming\, which is computationally efficient due to its polynomial
 -time solvability.\n\nI will introduce the key quantities involved and pre
 sent basic connections between functional and classical tilings. Finally\,
  I will provide a counterexample to the Coven-Meyerowitz conjecture within
  the context of functional tilings. It is important to note\, however\, th
 at none of the counterexamples we constructed in this setting correspond t
 o tiling pairs of sets. Thus\, the Coven-Meyerowitz conjecture for tiling 
 sets remains open.\nThis is joint work with Itay Londner\, M\\' at\\' e Ma
 tolcsi\, and G\\' abor Somlai.\n
LOCATION:https://researchseminars.org/talk/CANT2025/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salvatore Tringali (Hebei Normal University\, China)
DTSTART:20250523T130000Z
DTEND:20250523T132500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/7/"
 >Power monoids and the Bienvenu-Geroldinger problem for torsion groups</a>
 \nby Salvatore Tringali (Hebei Normal University\, China) as part of Combi
 natorial and additive number theory (CANT 2025)\n\nLecture held in CUNY Gr
 aduate Center - Science Center (4th floor).\n\nAbstract\nLet $M$ be a (mul
 tiplicatively written) monoid with identity element $1_M$.  \nEndowed with
  the operation of setwise multiplication induced by $M$\, the collection \
 nof finite subsets of $M$ containing $1_M$ forms a monoid in its own right
 \, denoted \nby $\\mathcal{P}_{\\mathrm{fin}\,1}(M)$ and called the reduce
 d finitary power monoid of $M$.\n \nIt is natural to ask whether\, for all
  $H$ and $K$ in a given class of monoids\, \n$\\mathcal{P}_{\\mathrm{fin}\
 ,1}(H)$ is isomorphic to $\\mathcal{P}_{\\mathrm{fin}\,1}(K)$ \nif and onl
 y if $H$ is isomorphic to $K$. Originating from a conjecture of Bienvenu a
 nd \nGeroldinger recently settled by Yan and myself\, the problem --- toge
 ther with its numerous \nvariants and ramifications --- has non-trivial co
 nnections to additive number theory and related fields.\nIn this talk\, I 
 will present a positive solution for the class of torsion groups.\n
LOCATION:https://researchseminars.org/talk/CANT2025/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehdi Makhul (London School of Economics)
DTSTART:20250523T133000Z
DTEND:20250523T135500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/8/"
 >Web geometry and the orchard problem</a>\nby Mehdi Makhul (London School 
 of Economics) as part of Combinatorial and additive number theory (CANT 20
 25)\n\nLecture held in CUNY Graduate Center - Science Center (4th floor).\
 n\nAbstract\nLet $P$ be a set of $n$ points in the plane\, not all lying o
 n a single line. \nThe orchard planting problem asks for the maximum numbe
 r of lines passing through exactly three points of $P$. Green and Tao show
 ed that the maximum possible number of such lines \nfor an $n$-element set
  is~$\\lfloor \\frac{n(n-3)}{6} \\rfloor+1$. Lin and Swanepoel also invest
 igated a generalization of the orchard problem in higher dimensions. \nSpe
 cifically\, if $P$ is a set of $n$ points \nin $d$-dimensional space\, the
 y established an upper bound for the maximum number of hyperplanes passing
  through exactly $d+1$ points of $P$. Our goal is to describe the structur
 al properties of configurations that achieve near-optimality in the asympt
 otic regime. \nLet $C \\subset \\mathbb{R}^d$ be an algebraic curve of deg
 ree~$r$\, and suppose that $P \\subset C$ is a set of $n$ points.  If $P$ 
 determines at least~$cn^d$ hyperplanes\, each passing through exactly $d+1
 $ points of $P$\, then the following must hold: The degree of $C$ must be 
 $d+1$\; and the curve $C$ is the complete intersection of ${d\\choose 2}-1
 $ quadric hypersurfaces. Our approach relies on the theory of web geometry
  and the Elekes-Szab\\'o Theorem-a cornerstone of incidence geometry-both 
 of which provide the structural basis for our analysis. \nJoint work with 
 Konrad Swanepoel.\n
LOCATION:https://researchseminars.org/talk/CANT2025/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shashi Chourasiya (University of New South Wales\, Australia)
DTSTART:20250520T120000Z
DTEND:20250520T122500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/9/"
 >Power-free palindromes and reversed primes</a>\nby Shashi Chourasiya (Uni
 versity of New South Wales\, Australia) as part of Combinatorial and addit
 ive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Sc
 ience Center (4th floor).\n\nAbstract\nSeveral long-standing conjectures i
 n number theory are related to the digital properties of integers. Histori
 cally\, such problems have been confined to the realm of elementary number
  theory\, but recently huge breakthroughs have been made by applying deep 
 analytical techniques. In this talk\, we discuss some very recent results 
 on this topic\, focusing on palindromes and reversed primes. We first esta
 blish that for all bases $b \\geq 26000$\, there exist infinitely many pri
 me numbers $p$ for which $\\{ \\overleftarrow{p} \\}$ is square-free. Furt
 hermore\, we demonstrate the existence of infinitely many palindromes (wit
 h $n= \\overleftarrow{n}$) that are cube-free.  \nThis is based on joint w
 ork with Daniel R. Johnston.\n
LOCATION:https://researchseminars.org/talk/CANT2025/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vjekoslav Kovac (University of Zagreb)
DTSTART:20250520T123000Z
DTEND:20250520T125500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/10/
 ">Several irrationality problems for Ahmes series</a>\nby Vjekoslav Kovac 
 (University of Zagreb) as part of Combinatorial and additive number theory
  (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th
  floor).\n\nAbstract\nProving (ir)rationality of infinite series of distin
 ct unit fractions has been an active topic of research for decades\, with 
 numerous occasional breakthroughs. We will investigate what can be obtaine
 d using elementary techniques (such as iterative constructions and the pro
 babilistic method) and address several problems posed by Paul Erdos throug
 hout the 1980s. In particular\, we will study one type of irrationality se
 quences introduced by Erdos and Graham\, (almost entirely) resolve a quest
 ion by Erdos on simultaneous rationality of two or more "consecutive" seri
 es\, and give a negative answer to an "infinite-dimensional" conjecture by
  Stolarsky. This is joint work with Terence Tao (UCLA).\n\nOnline only. Li
 nk: https://www.theoryofnumbers.com/cant/\n
LOCATION:https://researchseminars.org/talk/CANT2025/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Konieczny (University of Oxford)
DTSTART:20250520T130000Z
DTEND:20250520T132500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/11/
 ">Multiplicative generalised polynomial sequences</a>\nby Jakub Konieczny 
 (University of Oxford) as part of Combinatorial and additive number theory
  (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th
  floor).\n\nAbstract\nGeneralised polynomials are sequences constructed fr
 om polynomial sequences using the integer part function\, addition\, and m
 ultiplication. Determining whether a given sequence is a generalised polyn
 omial is often a non-trivial task. In joint work with J. Byszewski and B. 
 Adamczewski\, we have discovered both surprising examples of such sequence
 s and developed criteria to disprove that a given sequence is a generalise
 d polynomial. More broadly\, given a family of sequences\, one can pose a 
 classification problem: Which sequences in the family are generalized poly
 nomials? In this talk\, I will present a complete resolution of this probl
 em for the family of multiplicative sequences\, as well as partial results
  for (non-completely) multiplicative sequences.\n
LOCATION:https://researchseminars.org/talk/CANT2025/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro A. Garcia-Sanchez (Universidad de Granada)
DTSTART:20250520T133000Z
DTEND:20250520T135500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/12/
 ">Some problems related to the ideal class monoid of a numerical semigroup
 </a>\nby Pedro A. Garcia-Sanchez (Universidad de Granada) as part of Combi
 natorial and additive number theory (CANT 2025)\n\nLecture held in CUNY Gr
 aduate Center - Science Center (4th floor).\n\nAbstract\nLet $S$ be a nume
 rical semigroup (a submonoid of the set of non-negative integers under add
 ition such that $\\max(\\mathbb{Z}\\setminus S)$ exists). A non-empty set 
 of integers $I$ is said to be an ideal of $S$ if $I+S\\subseteq I$ and $I$
  has a minimum. If $I$ and $J$ are ideals of $S$\, we write $I\\sim J$ if 
 there exists an integer $z$ such that $I=z+J$. The ideal class monoid of $
 S$ is defined as the set of ideals of $S$ modulo this relation\, where add
 ition of two classes $[I]$ and $[J]$ is defined as $[I]+[J]=[I+J]$\, with 
 $I+J=\\{i+j\\mid i\\in I\, j\\in J\\}$. \n\nAn ideal $I$ is said to be nor
 malized if $\\min(I)=0$. The set of normalized ideals of $S$\, denoted by 
 $\\mathfrak{I}_0(S)$\, is a monoid isomorphic to the ideal class monoid of
  $S$ [1]. \n\nIt is known that if $S$ and $T$ are numericals semigroups fo
 r which $\\mathfrak{I}_0(S)$ is isomorphic to $\\mathfrak{I}_0(T)$\, then 
 $S$ and $T$ must be the same numerical semigroup [2].\n\nOn $\\mathfrak{I}
 _0(S)$ we can define a partial order $\\preceq$ as $I\\preceq J$ if there 
 exists $K\\in \\mathfrak{I}_0(S)$ such that $I+K=J$. We know that if $S$ a
 nd $T$ are numerical semigroups with multiplicity three such that the pose
 t $(\\mathfrak{I}_0(S)\,\\preceq)$ is isomorphic to the poset $(\\mathfrak
 {I}_0(T)\,\\preceq)$\, then $S$ and $T$ are the same numerical semigroup [
 3]. However\, if we remove the multiplicity three condition\, this poset i
 somorphsm problem is still open. \n\nIn [4]\, we study the case when the p
 oset $(\\mathfrak{I}_0(S)\,\\preceq)$ is a lattice. We show that this is t
 he case if and only if the multiplicity of $S$ is at most four. \n\nRefere
 nces:\n\n1.  L. Casabella\, M. D'Anna\, P. A. García-Sánchez\, Apéry se
 ts and the ideal class monoid of a numerical semigroup\, Mediterr. J. Math
 . 21\, 7 (2024). \n\n2. P. A. García-Sánchez\, The isomorphism problem f
 or ideal class monoids of numerical semigroups\, Semigroup Forum 108 (2024
 )\, 365--376. \n\n3. S. Bonzio\, P. A. García-Sánchez\, The poset of nor
 malized ideals of numerical semigroups with multiplicity three\, to appear
  in Comm. Algebra. \n\n4. S. Bonzio\, P. A. García-Sánchez\, When the po
 set of the ideal class monoid of a numerical \nsemigroup is a lattice\, ar
 Xiv:2412.07281.\n
LOCATION:https://researchseminars.org/talk/CANT2025/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Val Gladkova (University of Cambridge)
DTSTART:20250520T140000Z
DTEND:20250520T142500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/13/
 ">A lower bound for the strong arithmetic regularity lemma</a>\nby Val Gla
 dkova (University of Cambridge) as part of Combinatorial and additive numb
 er theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Ce
 nter (4th floor).\n\nAbstract\nThe strong  regularity lemma is a combinato
 rial tool originally introduced by Alon\, Fischer\, Krivelevich\, and Szeg
 edy in order to prove an induced removal lemma for graphs. Conlon and Fox 
 showed that for some graphs\, the strong regularity lemma must produce par
 titions of wowzer-type size. This talk will sketch a proof that a comparab
 le lower bound must hold for the arithmetic analogue of this lemma\, in th
 e setting of vector spaces over finite fields.\n
LOCATION:https://researchseminars.org/talk/CANT2025/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debyani Manna (Indian Institute of Technology Roorkee)
DTSTART:20250520T143000Z
DTEND:20250520T145500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/14/
 ">Some results on the extended inverse problem of $A+2 \\cdot A$</a>\nby D
 ebyani Manna (Indian Institute of Technology Roorkee) as part of Combinato
 rial and additive number theory (CANT 2025)\n\nLecture held in CUNY Gradua
 te Center - Science Center (4th floor).\n\nAbstract\nLet $A$ be a finite s
 et of integers and $A+ 2 \\cdot A= \\{a+2a': a\,a' \\in A\\}$.  An extende
 d inverse problem associated with the sumset  $A+2 \\cdot A$ is to  determ
 ine the underlying set $A$ when the size of the sumset $A+2 \\cdot A$ devi
 ates from the minimum possible size.\nWe find all possible arithmetic stru
 ctures of $A$ for certain cardinalities of $A + 2 \\cdot A$ and use them t
 o address extended inverse problems in the Baumslag-Solitar group $BS(1\,2
 )$. \nThis is joint work with Ram Krishna Pandey.\n
LOCATION:https://researchseminars.org/talk/CANT2025/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Huczynska (University of St. Andrews\,)
DTSTART:20250520T150000Z
DTEND:20250520T152500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/15/
 ">Additive triples in groups of odd prime order</a>\nby Sophie Huczynska (
 University of St. Andrews\,) as part of Combinatorial and additive number 
 theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Cente
 r (4th floor).\n\nAbstract\nFor a subset $A$ of an additive group $G$\,  a
  Schur triple in $A$ is a triple of the form $(a\,b\,a+b) \\in A^3$.  Deno
 te by $r(A)$ the number of Schur triples of $A$\; the behaviour of $r(A)$ 
 as $A$ ranges over subsets of a group $G$ has been studied by various auth
 ors. When $r(A)=0$\, $A$ is sum-free. The question of minimum and maximum 
 $r(A)$ for $A$ of fixed size in $\\mathbb{Z}_p$ was resolved by Huczynska\
 , Mullen and Yucas (2009) and independently by Samotij and Sudakov (2016).
   Several generalisations of the Schur triple problem have received attent
 ion.  In this talk\, I will present recent work (with Jonathan Jedwab and 
 Laura Johnson) on the generalisation to triples $(a\,b\,a+b) \\in A \\time
 s B \\times B$\, where $A\,B \\subseteq \\mathbb{Z}_p$.  Denote by $r(A\,B
 \,B)$ the number of triples of this form\; we obtain a precise description
  of its full spectrum of values and show constructively that each value in
  this spectrum can be realised when $B$ is an interval of consecutive elem
 ents in $\\mathbb{Z}_p$.\n
LOCATION:https://researchseminars.org/talk/CANT2025/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshiharu Kohayakawa (University of São Paulo\, Brazil)
DTSTART:20250520T160000Z
DTEND:20250520T162500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/16/
 ">Arithmetic progressions in subsetsums of sparse random sets of integers<
 /a>\nby Yoshiharu Kohayakawa (University of São Paulo\, Brazil) as part o
 f Combinatorial and additive number theory (CANT 2025)\n\nLecture held in 
 CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nGiven a se
 t $S\\subset\\mathbb{N}$\, its sumset $S+S$ is the set of all\nsums $s+s'$
  with both $s$ and $s'$ elements of $S$.  Given\n$p \\colon \\mathbb{N}\\t
 o [0\,1]$\, let $A_n=[n]_p$ be the $p$-random\nsubset of $[n]=\\{1\,\\dots
 \,n\\}$: the random set obtained by including\neach element of $[n]$ in $A
 _n$ independently with probability $p(n)$.\nLet $\\varepsilon>0$ be fixed\
 , and suppose\n$p(n)\\geq n^{-1/2+\\varepsilon}$ for all large enough $n$.
   We prove\nthat\, then\, with high probability\, long arithmetic progress
 ions exist\nin the sumset of any positive density subset of $A_n$\, that i
 s\, with\nprobability approaching $1$ as $n\\to\\infty$\, for any subset $
 S$\nof $A_n$ with a fixed proportion of the elements of $A_n$\, the sumset
 \n$S+S$ contains arithmetic progressions with\n$2^{\\Omega(\\sqrt{\\log n}
 )}$ elements.  \nJoint work with Marcelo Campos and Gabriel Dahia.\n
LOCATION:https://researchseminars.org/talk/CANT2025/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandor Kiss (Budapest University of Technology and Economics)
DTSTART:20250520T153000Z
DTEND:20250520T155500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/17/
 ">Generalized Stanley sequences</a>\nby Sandor Kiss (Budapest University o
 f Technology and Economics) as part of Combinatorial and additive number t
 heory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center
  (4th floor).\n\nAbstract\nFor an  integer $k \\ge 3$\, let $A_{0} = \\{a_
 {1}\, \\dots{} \,a_{t}\\}$ be a set of nonnegative integers which does not
  contain an arithmetic progression of length $k$. The set $S(A)$ is define
 d by the following greedy algorithm. If $s \\ge t$ and $a_{1}\, \\dots{} \
 ,a_{s}$ have already been defined\, then\n$a_{s+1}$ is the smallest intege
 r $a > a_{s}$ such that $\\{a_{1}\, \\dots{} \,a_{s}\\} \\cup \\{a\\}$ als
 o does not contain a $k$-term arithmetic progression. The sequence $S(A)$ 
 is called a \n\\emph{Stanley sequence} of order $k$ generated by $A_{0}$. 
 Starting out from a set of the form $A_{0} = \\{0\, t\\}$\, Richard P. Sta
 nley and Odlyzko tried to generate arithmetic progression-free sets by usi
 ng the greedy algorithm. In 1999\, Erd\\H{o}s\, Lev\, Rauzy\, S\\'andor an
 d S\\'ark\\"ozy extended the notion of Stanley sequence to other initial s
 ets $A_{0}$. In my talk I investigate some further generalizations of Stan
 ley sequences and I give some density type results about them.  \nThis is 
 a joint work with Csaba S\\'andor and Quan-Hui Yang.\n
LOCATION:https://researchseminars.org/talk/CANT2025/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Chapman (University of Warwick)
DTSTART:20250520T173000Z
DTEND:20250520T175500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/19/
 ">Counting commuting integer matrices</a>\nby Jonathan Chapman (University
  of Warwick) as part of Combinatorial and additive number theory (CANT 202
 5)\n\nLecture held in CUNY Graduate Center - Science Center (4th floor).\n
 \nAbstract\nConsider the set of pairs of $d\\times d$ matrices $(A\,B)$ wh
 ose entries are all integers with absolute value at most $N$. We call $(A\
 ,B)$ a \\emph{commuting pair} if $AB=BA$. Browning\, Sawin\, and Wang rece
 ntly showed that the number of commuting pairs is at most $O_d(N^{d^2 + 2 
 - \\frac{2}{d +1}})$. They further conjectured that the lower bound $\\Ome
 ga_d(N^{d^2 + 1})$\, which comes from letting $A$ or $B$ be a multiple of 
 the identity matrix\, should be sharp. In this talk\, I will discuss progr
 ess on the cases $d=2$ and $d=3$\, where we show that this conjecture hold
 s. I will also demonstrate how our approach relates counting commuting pai
 rs of matrices to the study of restricted divisor correlations in number t
 heory.\\\\\nJoint work with Akshat Mudgal (University of Warwick)\n
LOCATION:https://researchseminars.org/talk/CANT2025/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josiah Sugarman (Hebrew University of Jerusalem)
DTSTART:20250520T180000Z
DTEND:20250520T182500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/20/
 ">Explicit spectral gap for the quaquaversal operator</a>\nby Josiah Sugar
 man (Hebrew University of Jerusalem) as part of Combinatorial and additive
  number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Scien
 ce Center (4th floor).\n\nAbstract\nThe spectral gap of an operator is the
  gap between the largest eigenvalue and the rest of the spectrum. In the m
 id 90s\, John Conway and Charles Radin introduced a three dimensional subs
 titution tiling\, the Quaquaversal Tiling\, with the property that the ori
 entations of its tiles equidistribute faster than what is possible for two
  dimensional substitution tilings. Conway and Radin showed that the orient
 ations of the tiles were dense in $SO(3)$ and implicity introduced an oper
 ator (later explicitly studied by Draco\, Sadun\, and Van Wieren) whose sp
 ectral gap controls the equidistribution rate.\nDraco\, Sadun\, and Van Wi
 eren studied the eigenvalues of this operator numerically and conjectured 
 that it has a spectral gap bounded below by approximately $0.0061697$. \nW
 e exploit a fact\, due to Serre\, that the group of orientations for this 
 tiling is $2$-arithmetic and follow a strategy similar to Lubotzky\, Phill
 ips\, and Sarnak's in order to obtain a lower bound of about $0.0061711$\,
   resolving the conjecture.\n
LOCATION:https://researchseminars.org/talk/CANT2025/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Leonetti (Universit\\` a degli Studi dell'Insubria)
DTSTART:20250520T183000Z
DTEND:20250520T185500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/21/
 ">On the completeness induced by densities on natural numbers</a>\nby Paol
 o Leonetti (Universit\\` a degli Studi dell'Insubria) as part of Combinato
 rial and additive number theory (CANT 2025)\n\nLecture held in CUNY Gradua
 te Center - Science Center (4th floor).\n\nAbstract\nLet $\\nu: \\mathcal{
 P}(\\mathbb{N}) \\to \\mathbb{R}$ be an \\textquotedblleft upper density\\
 textquotedblright\\\, on the natural numbers $\\mathbb{N}$ (for instance\,
  $\\nu$ can be the upper asymptotic density or the upper Banach density). 
 Then a natural pseudometric $d_\\nu$ is induced on $\\mathcal{P}(\\mathbb{
 N})$\, namely\, \n$$\n\\forall A\,B\\subseteq \\mathbb{N}\, \\quad \nd_\\n
 u(A\,B):=\\nu(A\\bigtriangleup B)\n$$\nWe provide necessary and sufficient
  conditions for the completeness of $d_\\nu$. \nThen  we identify in which
  cases the latter ones are verified.\n
LOCATION:https://researchseminars.org/talk/CANT2025/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akash Singha Roy (University of Georgia)
DTSTART:20250520T190000Z
DTEND:20250520T192500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/22/
 ">Joint distribution in residue classes of families of multiplicative func
 tions</a>\nby Akash Singha Roy (University of Georgia) as part of Combinat
 orial and additive number theory (CANT 2025)\n\nLecture held in CUNY Gradu
 ate Center - Science Center (4th floor).\n\nAbstract\nThe distribution of 
 values of arithmetic functions in residue classes has been a problem of gr
 eat interest in elementary\, analytic\, and combinatorial number theory. I
 n work studying this problem for large classes of multiplicative functions
 \, Narkiewicz obtained general criteria deciding when a family of such fun
 ctions is jointly uniformly distributed among the coprime residue classes 
 to a fixed modulus. Using these criteria\, he along with \\' Sliwa\, Rayne
 r\, Dobrowolski\, Fomenko\, and others\, gave explicit results on the dist
 ribution of interesting multiplicative functions and their families in cop
 rime residue classes.\n\nIn this talk\, we shall give best possible extens
 ions of Narkiewicz's criteria (and hence also of the other aforementioned 
 results) to moduli that are allowed to vary in a wide range. This is motiv
 ated by the celebrated Siegel-Walfisz theorem on the distribution of prime
 s in arithmetic progressions\, and our results happen to be some of the be
 st possible qualitative analogues of the Siegel-Walfisz theorem for the cl
 asses of multiplicative functions considered by Narkiewicz and others. Our
  arguments blend ideas from multiple subfields of number theory\, as well 
 as from linear algebra over rings\, commutative algebra\, and arithmetic a
 nd algebraic geometry. This talk is partly based on joint work with Paul P
 ollack.\n
LOCATION:https://researchseminars.org/talk/CANT2025/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Keith (Michigan Technical University)
DTSTART:20250520T193000Z
DTEND:20250520T195500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/23/
 ">$s \\pmod{t}$-cores</a>\nby William Keith (Michigan Technical University
 ) as part of Combinatorial and additive number theory (CANT 2025)\n\nLectu
 re held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\
 nWe consider simultaneous $(s\,s+t\,s+2t\,\\dots\,s+pt)$-cores in the larg
 e-$p$ limit\, or (when $s<t$)\, partitions in which no hook may be of leng
 th $s \\pmod{t}$.  As a boundary case of the general study made by Cho\, H
 uh and Sohn\, we find special symmetries and relations\, such as generatin
 g functions\, congruences when $s$ is not coprime to $t$\, and enumeration
 s when $s$ is coprime to $t$.  Of particular interest is the comparison to
  the behavior of simultaneous $(s\,t)$-cores and self-conjugate $(s\,t)$-c
 ores.  \nJoint work with Rishi Nath  and James Sellers.\n
LOCATION:https://researchseminars.org/talk/CANT2025/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladyslav Oles (University of Idaho)
DTSTART:20250520T200000Z
DTEND:20250520T202500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/24/
 ">Vanishing symmetric functions</a>\nby Vladyslav Oles (University of Idah
 o) as part of Combinatorial and additive number theory (CANT 2025)\n\nLect
 ure held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract
 \nWe continue an old solution by Noga Alon of conjectures of Arie Bialosto
 cki. \nThe first problem deals with vanishing symmetric functions on conse
 cutive blocks \nin an arbitrary ${\\mathbb Z}_n$-coloring of the positive 
 integers. The second problem (unpublished) deals with vanishing symmetric 
 functions on grid points inside of a polygon. The problems originated from
  the classical Theorem of Van der Waerden. \nThis is joint work with Arie 
 Bialostocki.\n
LOCATION:https://researchseminars.org/talk/CANT2025/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Baczkowski (University of Findlay)
DTSTART:20250520T203000Z
DTEND:20250520T205500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/25/
 ">Diophantine equations involving arithmetic functions and factorials</a>\
 nby Daniel Baczkowski (University of Findlay) as part of Combinatorial and
  additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Cente
 r - Science Center (4th floor).\n\nAbstract\nF. Luca proved for any fixed 
 rational number $\\alpha>0$ that the Diophantine equations $\\alpha\\\,m!=
 f(n!)$\, where $f$ is either the Euler function\, the divisor sum function
 \, or the function counting the number of divisors\, have finitely many in
 teger solutions in~$m$ and~$n$. In joint work with Novakovi\\'{c} we gener
 alize the mentioned result and show that Diophantine equations of the form
  $\\alpha\\\,m_1!\\cdots m_r!=f(n!)$ have finitely many integer solutions\
 , too. In addition\, we do so by including the case $f$ is the sum of $k$\
 \textsuperscript{th} powers of divisors function. Moreover\, the same hold
 s by replacing some of the factorials with certain examples of Bhargava fa
 ctorials.\n
LOCATION:https://researchseminars.org/talk/CANT2025/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aritram Dhar (University of Florida)
DTSTART:20250520T210000Z
DTEND:20250520T212500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/26/
 ">A bijective proof of an identity of Berkovich and Uncu</a>\nby Aritram D
 har (University of Florida) as part of Combinatorial and additive number t
 heory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center
  (4th floor).\n\nAbstract\nThe BG-rank BG($\\pi$) of an integer partition 
 $\\pi$ is defined as $$\\text{BG}(\\pi) := i-j$$ where $i$ is the number o
 f odd-indexed odd parts and $j$ is the number of even-indexed odd parts of
  $\\pi$. In a recent work\, Fu and Tang ask for a direct combinatorial pro
 of of the following identity of Berkovich and Uncu $$B_{2N+\\nu}(k\,q)=q^{
 2k^2-k}\\left[\\begin{matrix}2N+\\nu\\\n+k\\end{matrix}\\right]_{q^2}$$ fo
 r any integer $k$ and non-negative integer $N$ where $\\nu\\in \\{0\,1\\}$
 \, $B_N(k\,q)$ is the generating function for partitions into distinct par
 ts less than or equal to $N$ with BG-rank equal to $k$ and $\\left[\\begin
 {matrix}a+b\\\\b\\end{matrix}\\right]_q$ is a Gaussian binomial coefficien
 t. In this talk\, I will give a bijective proof of Berkovich and Uncu's id
 entity along the lines of Vandervelde and Fu and Tang's idea. \nThis is jo
 int work with Avi Mukhopadhyay.\n
LOCATION:https://researchseminars.org/talk/CANT2025/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James A. Sellers (University of Minnesota Duluth)
DTSTART:20250521T140000Z
DTEND:20250521T142500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/27/
 ">Extending congruences for overpartitions with $\\ell$-regular non-overli
 ned parts</a>\nby James A. Sellers (University of Minnesota Duluth) as par
 t of Combinatorial and additive number theory (CANT 2025)\n\nLecture held 
 in CUNY Graduate Center - Science Center (4th floor).\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CANT2025/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Somlai (E\\" otv\\" os Lor\\' and University and  R\\' enyi 
 Institute)
DTSTART:20250521T143000Z
DTEND:20250521T145500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/28/
 ">Pushing the gap between tiles and spectral sets even further</a>\nby Gab
 or Somlai (E\\" otv\\" os Lor\\' and University and  R\\' enyi Institute) 
 as part of Combinatorial and additive number theory (CANT 2025)\n\nLecture
  held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nF
 uglede conjectured that a bounded measurable set in a locally compact topo
 logical space endowed with Haar measure is spectral if and only if it is a
  tile and Fuglede also confirmed the conjecture for sets whose tiling comp
 lement is a lattice and for spectral sets one of whose spectrums is a latt
 ice.\n\nThe conjecture was disproved by Tao in the case of finite abelian 
 groups where the counting measure plays the role of the Haar measure. \nTa
 o constructed a spectral set in $\\mathbb{Z}_3^5$ of size 6\, that is not 
 a tile. This construction was lifted to the $5$ dimensional Euclidean spac
 e\, where the original conjecture was mostly studied. \n\nLev and Matolcsi
  verified Fuglede's conjecture for convex sets in $\\mathbb{R}^n$ for ever
 y positive integer $n$. The key of proving the harder direction of the con
 jecture is to introduce the weak tiling property and prove that all spectr
 al sets are weak tilings.\n\nOne of the goals of our work was to answer a 
 question of Kolountzakis\, Lev and Matolcsi\, whether there is a weak tile
   that is neither a tile nor spectral. There is such a set which apparentl
 y makes it harder to prove the spectral-tile direction of the conjecture i
 n the remaining open cases. \n\nThe other result towards structurally dist
 inguishing spectral sets and tiles was a disproof of a conjecture of Green
 feld and Lev. They conjectured that the product of two sets is spectral if
  and only if both of them are spectral. A similar property holds for tiles
 \, but the product of a non-spectral set with a spectral set can be spectr
 al. \nFinally\, we obtain an easy characterization of tiles using the spec
 tral property.\n
LOCATION:https://researchseminars.org/talk/CANT2025/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Spiegel (Zuse Institute Berlin)
DTSTART:20250521T150000Z
DTEND:20250521T152500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/29/
 ">An unsure talk on an un-Schur problem</a>\nby Christoph Spiegel (Zuse In
 stitute Berlin) as part of Combinatorial and additive number theory (CANT 
 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th floor)
 .\n\nAbstract\nGraham\, R\\" odl\, and Ruci\\' nski originally posed the p
 roblem of determining the minimum number of monochromatic Schur triples th
 at must appear in any 2-coloring of the first $n$ integers. This question 
 was subsequently resolved independently by Datskovsky\, Schoen\, and Rober
 tson and Zeilberger. Here we suggest studying a natural anti-Ramsey varian
 t of this question and establish the first non-trivial bounds by proving t
 hat the maximum fraction of Schur triples that can be rainbow in a given 3
 -coloring of the first n integers is at least 0.4 and at most 0.66656. We 
 conjecture the lower bound to be tight. This question is also motivated by
  a famous analogous problem in graph theory due to Erd\\H os and S\\' os r
 egarding the maximum number of rainbow triangles in any 3-coloring of $K_n
 $\, which was settled by Balogh\, et al. \nThis is joint work with Olaf Pa
 rczyk.\n
LOCATION:https://researchseminars.org/talk/CANT2025/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Trevor D. Wooley (Purdue University)
DTSTART:20250521T153000Z
DTEND:20250521T155500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/30/
 ">Equidistribution and $L^p$-sets for $p<2$</a>\nby Trevor D. Wooley (Purd
 ue University) as part of Combinatorial and additive number theory (CANT 2
 025)\n\nLecture held in CUNY Graduate Center - Science Center (4th floor).
 \n\nAbstract\nWe investigate subsets $\\mathcal A$ of the natural numbers 
 having the property that\, for some positive number $p<2$\, one has\n\\[\n
 \\int_0^1 \\Bigl| \\sum_{n\\in \\mathcal A\\cap [1\,N]}e(n\\alpha)\\Bigr|^
 p\\\,{\\rm d}\\alpha \\ll |\\mathcal A\\cap [1\,N]|^pN^{\\varepsilon-1}.\n
 \\]\nExamples of such sets include (but are not restricted to) the squaref
 ree\, or more generally\, the $r$-free numbers. For polynomials \n$\\psi(x
 \;\\boldsymbol\\alpha)=\\alpha _kx^k+\\ldots +\\alpha_1x$\, having coeffic
 ients $\\alpha_i$ satisfying suitable irrationality conditions\, we show t
 hat the sequence $(\\psi(n\;\\boldsymbol\\alpha))_{n\\in \\mathcal A}$ is 
 equidistributed modulo $1$.\n
LOCATION:https://researchseminars.org/talk/CANT2025/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Tafula (Universit\\'e de Montr\\'eal)
DTSTART:20250521T160000Z
DTEND:20250521T162500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/31/
 ">Waring--Goldbach subbases with prescribed representation functions</a>\n
 by Christian Tafula (Universit\\'e de Montr\\'eal) as part of Combinatoria
 l and additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate 
 Center - Science Center (4th floor).\n\nAbstract\nWe investigate represent
 ation functions $r_{A\,h}(n)$ of subsets $A$ of \\( k \\)-th powers \\( \\
 mathbb{N}^k \\) and \\( k \\)-th powers of primes \\( \\mathbb{P}^k \\). B
 uilding on work of Vu\, Wooley\, and others\, we prove that for \\( h \\ge
 q h_k = O(8^k k^2) \\) and regularly varying \\( F(n) \\) satisfying \\( \
 \lim_{n\\to\\infty} F(n)/\\log n = \\infty \\)\, there exists \\( A \\subs
 eteq \\mathbb{N}^k \\) such that\n \\[ r_{A\,h}(n) \\sim \\mathfrak{S}_{k\
 ,h}(n) F(n)\, \\]\n where $\\mathfrak{S}_{k\,h}(n)$ is the singular series
  associated to Waring's problem. In the case of prime powers\, we obtain a
 nalogous results for \\( F(n) = n^{\\kappa} \\). For \\( F(n) = \\log n \\
 )\, we prove that for every \\( h \\geq 2k^2(2\\log k + \\log\\log k + O(1
 )) \\)\, there exists \\( A \\subseteq \\mathbb{P}^k \\) such that \\( r_{
 A\,h}(n) \\asymp \\log n \\)\, showing the existence of thin subbases of p
 rime powers.\n
LOCATION:https://researchseminars.org/talk/CANT2025/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hopper Clark (Bates College)
DTSTART:20250521T173000Z
DTEND:20250521T175500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/32/
 ">Patterns among Ulam words</a>\nby Hopper Clark (Bates College) as part o
 f Combinatorial and additive number theory (CANT 2025)\n\nLecture held in 
 CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nIn 1964\, 
 Stanislaw Ulam wrote about the Ulam sequence: beginning with 1 and 2\, the
  next term is the smallest unique sum of two different earlier terms. In 2
 020\, the parallel notion of the set of Ulam words\, \n$\\mathcal{U}$\, wa
 s introduced by Bade\, Cui\, Labelle\, and Li\, which looks at concatenati
 ons of words in $F_2$\, the free group on two generators. In this talk\, w
 e will discuss patterns of words in $\\mathcal{U}$\, touching on both prov
 en results and conjectured ones. We will see how these patterns come to li
 fe visually\, and see how they produce images such as the discrete Sierp\\
 ' inski triangle.\n
LOCATION:https://researchseminars.org/talk/CANT2025/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asher Roberts (St. Joseph's University New York)
DTSTART:20250521T180000Z
DTEND:20250521T182500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/33/
 ">Large deviations of Selberg's central limit theorem on RH</a>\nby Asher 
 Roberts (St. Joseph's University New York) as part of Combinatorial and ad
 ditive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center -
  Science Center (4th floor).\n\nAbstract\nAssuming the Riemann hypothesis\
 , we show that for $k>0$ and $V\\sim k\\log\\log T$\,\n     \\[\n     \\fr
 ac{1}{T}\\operatorname{meas}\\bigg\\{t\\in[T\,2T]: \\log |\\zeta(1/2+{\\rm
  i} t)|>V\\bigg\\}\\leq C_k \\frac{e^{-V^2/\\log\\log T}}{\\sqrt{\\log\\lo
 g T}}.\n     \\]\n     This shows that Selberg's central limit theorem per
 sists in the large deviation regime. As a corollary\, we recover the resul
 t of Soundararajan and of Harper on the moments of $\\zeta$. This directly
  implies the sharp moment bounds of Soundararajan and Harper\, i.e.\,\n   
   \\[\n     \\frac{1}{T}\\int_T^{2T}|\\zeta(1/2+{\\rm i} t)|{\\rm d}t\\leq
  C_k (\\log T)^{k^2}.\n     \\]\n     This is joint work with Louis-Pierre
  Arguin (Oxford University) and Emma Bailey (University of Bristol).\n
LOCATION:https://researchseminars.org/talk/CANT2025/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gautami Bhowmik (Universit\\' e Lille)
DTSTART:20250521T183000Z
DTEND:20250521T185500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/34/
 ">On the Telhcirid problem</a>\nby Gautami Bhowmik (Universit\\' e Lille) 
 as part of Combinatorial and additive number theory (CANT 2025)\n\nLecture
  held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nW
 e consider the digital reverse of integers\, in particular those of primes
 .\nA palindromic prime number is a popular example of a prime whose revers
 e is also a prime and\nthe infinitude of such primes is one among the open
  conjectures in the area.\nWe will  discuss reversed primes in arithmetic 
 progression built on ideas of Mauduit-Rivat and Maynard. \\\\\nThis is joi
 nt work with Yuta Suzuki.\n
LOCATION:https://researchseminars.org/talk/CANT2025/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Allen Alexander (U.S. Securities and Exchange Commission)
DTSTART:20250521T190000Z
DTEND:20250521T192500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/35/
 ">Hindman's theorem and the hyperreals</a>\nby Samuel Allen Alexander (U.S
 . Securities and Exchange Commission) as part of Combinatorial and additiv
 e number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Scie
 nce Center (4th floor).\n\nAbstract\nHindman's theorem says that if the na
 tural numbers are colored using finitely many colors\, then there exists s
 ome color $c$ and some infinite $S\\subseteq \\mathbb N$ such that for eve
 ry finite nonempty subset $\\{n_1\,\\ldots\,n_k\\}$ of $S$\, $n_1+\\cdots+
 n_k$ is color $c$. We present a proof using hyperreal numbers\, and a stro
 nger version of the theorem involving hyperreal numbers. \\\\\nSome of thi
 s material was previously published in 2024 in the Journal of Logic and An
 alysis.\n
LOCATION:https://researchseminars.org/talk/CANT2025/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Baginski (Fairfield University)
DTSTART:20250521T193000Z
DTEND:20250521T195500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/36/
 ">Arithmetic Progressions\, Nonunique Factorization\, and Additive Combina
 torics in the Group of Units Mod $n$</a>\nby Paul Baginski (Fairfield Univ
 ersity) as part of Combinatorial and additive number theory (CANT 2025)\n\
 nLecture held in CUNY Graduate Center - Science Center (4th floor).\n\nAbs
 tract\nFor integers $0\\lt a\\leq b$\, the arithmetic progression $M_{a\,b
 }=a+b\\mathbb{N}$ is closed under multiplication if and only if $a^2\\equi
 v a \\mod b$. Any such multiplicatively closed arithmetic progression is c
 alled an arithmetic congruence monoid (ACM). Though these $M_{a\,b}$ are m
 ultiplicative submonoids of $\\mathbb{N}$\, their factorization properties
  differ greatly from the unique factorization one enjoys in $\\mathbb{N}$.
 \n\nIn this talk we will explore the known factorization properties of the
 se monoids. When $a=1$\, these monoids are Krull and behave similarly to a
 lgebraic number rings\, in that they have a class group which controls all
  the factorization. Combinatorially\, factorization properties correspond 
 to zero-sum sequences in the group. However\, when $a\\gt 1$\, these monoi
 ds are not Krull and thus do not have a class group which fully captures t
 he factorization behavior. Nonetheless\, an ACM can be associated to a fin
 ite abelian group\, whose additive combinatorics relate to the factorizati
 on properties of the ACM. We will pay particular attention to the factoriz
 ation property of elasticity and its connection to sequences in the group 
 which attain certain sums while avoiding others.\n
LOCATION:https://researchseminars.org/talk/CANT2025/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Iosevich (University of Rochester)
DTSTART:20250523T193000Z
DTEND:20250523T195500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/37/
 ">The Fourier uncertainty principle\, signal recovery\, and applications</
 a>\nby Alex Iosevich (University of Rochester) as part of Combinatorial an
 d additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Cent
 er - Science Center (4th floor).\n\nAbstract\nWe are going to discuss the 
 analytic\, arithmetic\, and practical aspects of exact signal recovery\, w
 ith the emphasis on the role of restriction theory for the Fourier transfo
 rm and connections with the classical results of Bourgain\, Talagrand\, an
 d others.\n
LOCATION:https://researchseminars.org/talk/CANT2025/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven J. Miller (Williams College\, Fibonacci Association)
DTSTART:20250521T203000Z
DTEND:20250521T205500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/38/
 ">Phase transitions for binomial sets under linear forms</a>\nby Steven J.
  Miller (Williams College\, Fibonacci Association) as part of Combinatoria
 l and additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate 
 Center - Science Center (4th floor).\n\nAbstract\nWe generalize results on
  sum and difference sets of a subset S of\n$\\mathbb{N}$ drawn from a bino
 mial model. Given $A \\subseteq \\{0\, 1\,\n\\dots\, N\\}$\, an integer $h
  \\geq 2$\, and a linear form $L: \\mathbb{Z}^h \\to\n\\mathbb{Z}$ $$L(x_1
 \, \\dots\, x_h)\\ :=\\ u_1x_1 + \\cdots + u_hx_h\, \\quad u_i\n\\in \\mat
 hbb{Z}_{\\neq 0} {\\rm\\ for\\ all\\ } i \\in [h]\,$$ we study the size\no
 f $$L(A)\\ =\\ \\left\\{u_1a_1 + \\cdots + u_ha_h : a_i \\in A \\right\\}$
 $ and\nits complement $L(A)^c$ when each element of $\\{0\, 1\, \\dots\, N
 \\}$ is\nindependently included in $A$ with probability $p(N)$\, identifyi
 ng two\nphase transitions. The first global one concerns the relative size
 s of\n$L(A)$ and $L(A)^c$\, with $p(N) = N^{-\\frac{h-1}{h}}$ as the thres
 hold.\nAsymptotically almost surely\, below the threshold almost all sums\
 ngenerated in $L(A)$ are distinct and almost all possible sums are in\n$L(
 A)^c$\, and above the threshold almost all possible sums are in $L(A)$.\nO
 ur asymptotic formulae substantially extends work of Hegarty and Miller\,\
 nresolving their conjecture. The second local phase transition concerns th
 e\nasymptotic behavior of the number of distinct realizations in $L(A)$ of
  a\ngiven value\, with $p(N) = N^{-\\frac{h-2}{h-1}}$ as the threshold and
 \nidentifies (in a sharp sense) when the number of such realizations obeys
  a\nPoisson limit. Our main tools are recent results on the asymptotic\nen
 umeration of partitions\, Stein's method for Poisson approximation\, and\n
 the martingale machinery of Kim-Vu.\n
LOCATION:https://researchseminars.org/talk/CANT2025/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne de Roton (Universit\\'e de Lorraine\, Institut Elie Cartan)
DTSTART:20250522T140000Z
DTEND:20250522T142500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/39/
 ">Iterated sums races</a>\nby Anne de Roton (Universit\\'e de Lorraine\, I
 nstitut Elie Cartan) as part of Combinatorial and additive number theory (
 CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th f
 loor).\n\nAbstract\nThis is joint work with Paul P\\' eringuey. \\\\\nOur 
 work provides a solution to a question posed by M. Nathanson in late 2024\
 , but we later realized that this problem\, along with an even more challe
 nging one\, had already been solved by N. Kravitz in a paper posted on arX
 iv in January 2025. While our construction is similar to his\, it is simpl
 er\, and we hope that it can serve as an introductory step toward understa
 nding the underlying ideas. \\\\\nNathanson's question is as follows: \\\\
 \n\\textit{For every integer $m \\geq 3$\, do there exist finite sets $A$ 
 and $B$ of integers and an increasing sequence of positive integers $h_1 <
  h_2 < \\cdots < h_m$\, such that: \\\\\n$$ |h_i A| > |h_i B| \\quad \\tex
 t{if } i \\text{ is odd\,} $$\n$$ |h_i A| < |h_i B| \\quad \\text{if } i \
 \text{ is even.} $$ \\\\\nAdditionally\, do there exist such sets with $|A
 | = |B|$? Can such sets be constructed with $|A| = |B|$ and $\\text{diam}(
 A) = \\text{diam}(B)$?} \\\\\nWe provide a positive answer to these questi
 ons and propose an iterative construction of sets that satisfy these condi
 tions.\n
LOCATION:https://researchseminars.org/talk/CANT2025/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Kowalski (ETH Zurich)
DTSTART:20250522T143000Z
DTEND:20250522T145500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/40/
 ">Some pseudorandom graphs</a>\nby Emmanuel Kowalski (ETH Zurich) as part 
 of Combinatorial and additive number theory (CANT 2025)\n\nLecture held in
  CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nA classic
 al construction associates to any Sidon set a graph without\n$4$-cycles. W
 e investigate some properties of these graphs in the case\nof the Sidon se
 ts constructed by Forey\, Fres\\' an and myself using methods\nof algebrai
 c geometry. In particular\, this provides deterministic\nfamilies of Raman
 ujan graphs with semi-circle and other interesting\nexplicit asymptotic ei
 genvalue distributions.\n \nBased on joint work with A. Forey and J. Fres\
 \' an and discussions with\nY. Wigderson and T. Schramm.\n
LOCATION:https://researchseminars.org/talk/CANT2025/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Besfort Shala (University of Bristol\, UK)
DTSTART:20250522T150000Z
DTEND:20250522T152500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/41/
 ">Multiplicative energy in number theory</a>\nby Besfort Shala (University
  of Bristol\, UK) as part of Combinatorial and additive number theory (CAN
 T 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th floo
 r).\n\nAbstract\nI will discuss the important role of multiplicative energ
 y of sets in number theory\, particularly in the probabilistic theory of r
 andom multiplicative functions. The aim is to provide a survey of recent r
 esults in the area.\n
LOCATION:https://researchseminars.org/talk/CANT2025/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Shkredov (Purdue University)
DTSTART:20250522T153000Z
DTEND:20250522T155500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/42/
 ">Some applications of the higher energy method to distribution irregulari
 tie</a>\nby Ilya Shkredov (Purdue University) as part of Combinatorial and
  additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Cente
 r - Science Center (4th floor).\n\nAbstract\nWe review recent results obta
 ined by the method of higher sumsets \nand higher energies. \nIn particula
 r\, we discuss two applications: irregularities in the distribution of the
  difference \nset and irregularities in the large Fourier coefficients of 
 sets with small sumsets.\n
LOCATION:https://researchseminars.org/talk/CANT2025/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Karam (University of  Oxford)
DTSTART:20250522T160000Z
DTEND:20250522T162500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/43/
 ">After the cap-set problem\, and some properties of the slice rank</a>\nb
 y Thomas Karam (University of  Oxford) as part of Combinatorial and additi
 ve number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Sci
 ence Center (4th floor).\n\nAbstract\nThe infamous cap-set problem asks fo
 r the size of the largest subset $A \\subset \\mathbb{F}_3^n$ not containi
 ng any solutions to the equation $x+y+z=0$ aside from the trivial solution
 s $x=y=z$. A proof that that size is bounded above by $C^n$ for some $C<3$
 \, which arose in 2016 in two breakthrough papers by Croot-Lev-Pach and by
  Ellenberg and Gijswijt (both published in the Annals of Mathematics)\, wa
 s later reformulated by Tao in a more symmetric way\, leading to the defin
 ition of a new notion of rank on tensors called the slice rank.\n\nSince t
 hen\, the slice rank has been studied further\, and the resulting properti
 es have often found related number-theoretic applications. To take the ear
 liest and perhaps simplest example\, a key component of the argument in th
 e proof of the original cap-set problem itself is that the slice rank of a
  “diagonal” tensor is equal to its number of non-zero entries\, mirror
 ing the analogous property of matrix rank.\n\nAfter reviewing some more su
 ch applications by other mathematicians\, we will present some results con
 cerning other basic properties of the slice rank\, and in particular the i
 deas behind some of their simpler proofs in the special case where the sup
 port of the tensor is contained in an antichain: there\, as established by
  Sawin and Tao\, the slice rank of the tensor is equal to the smallest num
 ber of slices that suffice to cover its support. If time allows then we wi
 ll also discuss how the proofs in this special case illuminate to some ext
 ent the proofs in the general case.\n
LOCATION:https://researchseminars.org/talk/CANT2025/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Chapman (Sam Houston State University)
DTSTART:20250522T173000Z
DTEND:20250522T175500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/44/
 ">Betti elements and non-unique factorizations</a>\nby Scott Chapman (Sam 
 Houston State University) as part of Combinatorial and additive number the
 ory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (
 4th floor).\n\nAbstract\nLet $M$ be a commutative cancellative reduced ato
 mic monoid with set of atoms (or irreducibles) $\\mathcal{A}(M)$.  Given a
  nonunit $x$ in $M$\, let\n$Z(x)$ represent the set of factorizations of $
 x$ into atoms.  Define a graph $\\nabla_x$ whose vertex set is $Z(x)$ wher
 e two vertices are joined\nby an edge if these factorizations share an ato
 m.  Call $x$ a \\textit{Betti element} of $M$ if the graph $\\nabla_x$ is 
 disconnected.\nBetti elements have proven to be a powerful tool in the stu
 dy of nonunique factorizations of elements in monoids.  In particular\, \n
 over the past several years many papers have used Betti elements to study 
 factorizaton properties in \\textit{affine monoids} (i.e.\,  finitely gene
 rated additive submonoids of $\\mathbb{N}_0^k$ for some positive integer $
 k$).  Several strong results have been obtained when $M$ is a numerical mo
 noid (i.e.\, $k=1$ above).  In this talk\, we will\nreview the basic prope
 rties of Betti elements and some of the results regarding affine monoids m
 entioned above.  \nWe will then extend this study to\nmore general rings a
 nd monoids which are commutative and cancellative.   We focus on two cases
 : (I) when the monoid $M$ has a single Betti element\, (II) when each atom
  of $M$ divides every Betti element.  We call those monoids satisfying con
 dition (II) as having \\textit{full atomic support}.  We show using elemen
 tary arguments that a monoid of type (I) is actually of full atomic suppor
 t.   We close by showing for a monoid of full atomic support that the cate
 nary degree\, the tame degree\, and the omega primality constant  (three w
 ell studied invariants in the nonunique factorization literature) can be e
 asily computed from the monoid's set of Betti elements.\n
LOCATION:https://researchseminars.org/talk/CANT2025/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Lebowitz-Lockard
DTSTART:20250522T180000Z
DTEND:20250522T182500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/45/
 ">Partitions and ordered products</a>\nby Noah Lebowitz-Lockard as part of
  Combinatorial and additive number theory (CANT 2025)\n\nLecture held in C
 UNY Graduate Center - Science Center (4th floor).\n\nAbstract\nLet $g(n)$ 
 be the number of ways to express $n$ as an ordered partition of numbers gr
 eater than $1$. We also let $a(n)$ be the number of partitions of $n$ of t
 he form $n_1 + n_2 + \\cdots + n_k$\, where $n_i$ is a multiple of $n_{i +
  1}$ and the $n_i$  are distinct. Though there is substantial research aro
 und $g(n)$\, much less is known about $a(n)$. We discuss these two functio
 ns\, as well as some new asymptotics on $a(n)$.\n
LOCATION:https://researchseminars.org/talk/CANT2025/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Eichhorn (University of California Irvine)
DTSTART:20250522T183000Z
DTEND:20250522T185500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/46/
 ">Open problems involving cranks for partition congruences</a>\nby Dennis 
 Eichhorn (University of California Irvine) as part of Combinatorial and ad
 ditive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center -
  Science Center (4th floor).\n\nAbstract\nDyson famously conjectured\, cor
 rectly\, that his rank statistic witnesses Ramanujan's first two congruenc
 es for $p(n)$\, and that there exists a ``crank" statistic that witnesses 
 Ramanujan's congruence modulo $11$ in a similar fashion.\nAs it turns out\
 , this phenomenon of congruence-witnessing statistics\, which we now also 
 call ``cranks" in homage to Dyson\, also occurs in other contexts within p
 artition theory.\nIn this talk\, we give several open problems and conject
 ures in this area\, highlighting some recent developments along the way.\\
 \\\nThis talk will include joint work with several coauthors.\n
LOCATION:https://researchseminars.org/talk/CANT2025/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Mozzochi
DTSTART:20250522T190000Z
DTEND:20250522T192500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/47/
 ">The  closest known attempted proof of  the twin prime conjecture</a>\n
 by Jeff Mozzochi as part of Combinatorial and additive number theory (CANT
  2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th floor
 ).\n\nAbstract\nUsing a primitive formulation of the circle method we pres
 ent a sufficient condition for\nthe twin prime conjecture that misses bein
 g true by just an epsilon.\nWe also show that the well-known sufficient co
 ndition for the twin prime conjecture\nimplies the patently false statemen
 t that for each positive integer m\, there exists\nan infinite number of p
 rime pairs whose difference is $m$.\n
LOCATION:https://researchseminars.org/talk/CANT2025/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johann Thiel (New York City College of Technology (CUNY))
DTSTART:20250522T193000Z
DTEND:20250522T195500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/48/
 ">Bivariate polynomials associated with binary trees created by QuickSort<
 /a>\nby Johann Thiel (New York City College of Technology (CUNY)) as part 
 of Combinatorial and additive number theory (CANT 2025)\n\nLecture held in
  CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nIn this t
 alk we describe a generating series whose coefficients are polynomials tha
 t\, for a given positive integer $n$\, encode the depth at which the vario
 us list entries appear as labeled nodes in the binary trees obtained by Qu
 ickSorting permutations of the list consisting of one copy of each of the 
 first $n$ non-negative integers. Extracting the appropriate coefficients y
 ields information for the number of times a given list entry appears at a 
 given depth\, the total number of list entries that appear at a given dept
 h\, and consequently the average number of list entries that appear at a g
 iven depth taken over all $n!$ permutations. Joint work with David M. Brad
 ley.\n
LOCATION:https://researchseminars.org/talk/CANT2025/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Schinina (CUNY Graduate Center)
DTSTART:20250522T200000Z
DTEND:20250522T202500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/49/
 ">On a missing interval of integers from $\\mathcal{R}_{\\mathbf{Z}}(h\,4)
 $</a>\nby Vincent Schinina (CUNY Graduate Center) as part of Combinatorial
  and additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate C
 enter - Science Center (4th floor).\n\nAbstract\nThe set $\\mathcal{R}_{\\
 Z}(h\,4)$ consists of all possible sizes for the $h$-fold sumset of  sets 
 containing four integers. An immediate question to ask is what are the ele
 ments of this set? We know that $\\mathcal{R}_{\\Z}(h\,4)\\subseteq [3h+1\
 ,\\binom{h+3}{h}]$\, where the right side is an interval of integers that 
 includes the endpoints. These endpoints are known to be attained. By obser
 vation\, it appears that the interval of integers $[3h+2\,4h-1]$ is absent
  from $\\mathcal{R}_{\\Z}(h\,4)$. We will briefly discuss the procedure us
 ed to prove that the integers in $[3h+2\,4h-1]$ are not possible sizes for
  the $h$-fold sumset of a set containing four integers. Furthermore\, we w
 ill confirm that this interval can't be made larger by exhibiting a set wh
 ose h-fold sumset has size $4h$.\n
LOCATION:https://researchseminars.org/talk/CANT2025/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Senger (Missouri State University)
DTSTART:20250522T203000Z
DTEND:20250522T205500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/50/
 ">VC-dimension of subsets of the Hamming graph</a>\nby Steven Senger (Miss
 ouri State University) as part of Combinatorial and additive number theory
  (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th
  floor).\n\nAbstract\nVapnik-Chervonenkis or VC-dimension has been a usefu
 l tool in combinatorics\, machine learning\, and other areas. Given a grap
 h from a well-studied family\, there has been recent activity on size thre
 sholds for a subset of a graph to guarantee bounds on the VC-dimension of 
 the subset. These resemble finite point configuration results\, such as th
 e Erdos-Falconer distance problem\, both in form as well as in the techniq
 ues of proof. Typically\, one looks at graphs that are highly pseudorandom
 \, such as the distance graph or the dot product graph\, but the Hamming g
 raph is quantifiably less pseudorandom\, and standard techniques seem to b
 reak down and yield very weak results if any. We present a suite of result
 s that outperform their counterparts for the Hamming graph. The proofs are
  completely elementary\, and in some cases\, tight.\n
LOCATION:https://researchseminars.org/talk/CANT2025/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Jacobs (Virginia Commonwealth University)
DTSTART:20250522T210000Z
DTEND:20250522T212500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/51/
 ">Crossword puzzles</a>\nby Robert Jacobs (Virginia Commonwealth Universit
 y) as part of Combinatorial and additive number theory (CANT 2025)\n\nLect
 ure held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract
 \nIt is known that the most words possible in a $15\\times15$ crossword pu
 zzle is 96  \nif the grid is symmetrical and connected  and every word has
  at least 3 letters.\n In this talk\, I will prove this and find the most 
 words possible in other grids.\n
LOCATION:https://researchseminars.org/talk/CANT2025/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Hopkins (Saint Peter's University)
DTSTART:20250523T183000Z
DTEND:20250523T185500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/52/
 ">Scaled Arndt compositions</a>\nby Brian Hopkins (Saint Peter's Universit
 y) as part of Combinatorial and additive number theory (CANT 2025)\n\nLect
 ure held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract
 \nIn 2013\, Joerg Ardnt observed that integer compositions $c_1 + c_2 + \\
 cdots = n$ with $c_{2i-1} > c_{2i}$ for each positive $i$ are counted by t
 he Fibonacci numbers.  This was confirmed by the speaker and Tangboonduang
 jit in 2022 and we explored generalizations of this pair-wise condition in
 cluding $c_{2i-1} > c_{2i} + k$ for an affine parameter $k$.  In the curre
 nt work\, a collaboration with Augustine Munagi\, we consider scaling para
 meters\, integers $s$ and $t$\, and resolve some cases of the general cond
 ition $sc_{2i-1} > tc_{2i} + k$.  Techniques include generating functions 
 and combinatorial proofs.\n
LOCATION:https://researchseminars.org/talk/CANT2025/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (Lehman College (CUNY))
DTSTART:20250521T200000Z
DTEND:20250521T202500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/53/
 ">Sizes of sumsets of finite sets of integers</a>\nby Mel Nathanson (Lehma
 n College (CUNY)) as part of Combinatorial and additive number theory (CAN
 T 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th floo
 r).\n\nAbstract\nIn the study of sums of finite sets of integers\, most at
 tention has been paid to sets with small sumsets (Freiman's theorem and re
 lated work) and to sets with large sumsets (Sidon sets and $B_h$-sets).  T
 he focus of this talk is on the full range of sizes of h-fold sums of a se
 t of k integers.   New results and open problems will be presented.\n
LOCATION:https://researchseminars.org/talk/CANT2025/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Hough (Stony Brook University)
DTSTART:20250523T180000Z
DTEND:20250523T182500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/54/
 ">Lower order terms in the shape of cubic fields</a>\nby Robert Hough (Sto
 ny Brook University) as part of Combinatorial and additive number theory (
 CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th f
 loor).\n\nAbstract\nThe ring of integers of a degree n number field may be
  viewed as an n-dimensional lattice within the canonical embedding.  Spect
 rally expanding the space of lattices\, we study the distribution of latti
 ce shapes of rings of integers when cubic fields are ordered by discrimina
 nt by studying the Weyl sums testing the lattice shape against the real an
 alytic Eisenstein series and Maass cusp forms.  In the case of Eisenstein 
 series we identify a lower order main term of order $X^{11/12}$ when field
 s of discriminant of order $X$ are counted with a smooth weight.  \\\\\nJo
 int work with Eun Hye Lee.  Recent work of Lee and Ramin Tagloo-Bighash pr
 omises to extend these ideas to integral orbits in general prehomogeneous 
 vector spaces.\n
LOCATION:https://researchseminars.org/talk/CANT2025/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ross (University of Hawaii)
DTSTART:20250523T203000Z
DTEND:20250523T205500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/55/
 ">Upper density and a theorem of Banach</a>\nby David Ross (University of 
 Hawaii) as part of Combinatorial and additive number theory (CANT 2025)\n\
 nLecture held in CUNY Graduate Center - Science Center (4th floor).\n\nAbs
 tract\nSuppose $A_n$ $(n\\in\\mathbb{N})$ is a sequence of sets in a finit
 ely-additive measure space which are uniformly bounded away from $0$\, $\\
 mu{A_n}\\ge a>0$ for all $n$.  Then there is a subsequence $A_{n_k}$\, whe
 re $\\{n_k\\}_k$ has upper Banach density $\\ge a$\, such that $\\mu\\bigc
 ap_{k<N}A_{n_k}\\ge a$ for every $N$.  Surprisingly\, this implies a densi
 ty-limit version of a representation theorem of Banach:\n\n\\textbf{Theore
 m:} Let $\\{\\\,f_n : n\\in\\mathbb{N}\\}$ be a uniformly\nbounded sequenc
 e of functions on a set $X$.  The following are equivalent:  (i)~$\\{f_n\\
 }_n$ weakly d-converges to $0$\; (ii)~for any sequence\n$\\{x_k : k\\in\\m
 athbb{N}\\}$ in $X$\, $d$-$\\!\\lim\\limits_{n\\to\\infty}\\liminf\\limits
 _{k\\to\\infty}f_n(x_k)=0$.\n\nHere ``d-" denotes a density limit.  Banach
 's non-density version of this theorem (without the ``d-") has been descri
 bed by some as ``marvelous".\n
LOCATION:https://researchseminars.org/talk/CANT2025/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Donley (Queens Community College (CUNY))
DTSTART:20250523T200000Z
DTEND:20250523T202500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/56/
 ">A classification for 1-factorizations of small order</a>\nby Robert Donl
 ey (Queens Community College (CUNY)) as part of Combinatorial and additive
  number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Scien
 ce Center (4th floor).\n\nAbstract\nA graph $G$ admits a 1-factorization i
 f its edge set decomposes into disjoint perfect matchings.  When $G$ is bi
 partite\, the equivalency classes of such graphs are determined by orbits 
 of 0/1-semi-magic squares under row and column permutations. By the Birkho
 ff-von Neumann theorem\, such matrices are sums of permutation matrices. I
 n a manner similar to the construction of standard Young tableaux\, we int
 roduce a path model for the construction of bipartite 1-factorizations and
  classify those of small order.\n
LOCATION:https://researchseminars.org/talk/CANT2025/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Benjamin Flores (Purdue University)
DTSTART:20250523T190000Z
DTEND:20250523T192500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/57/
 ">$K$-multimagic squares and magic squares of $k$th powers via the circle 
 method</a>\nby Daniel Benjamin Flores (Purdue University) as part of Combi
 natorial and additive number theory (CANT 2025)\n\nLecture held in CUNY Gr
 aduate Center - Science Center (4th floor).\n\nAbstract\nHere we investiga
 te $K$\\emph{-multimagic squares} of order $N$. These are $N \\times N$ ma
 gic squares which remain magic after raising each element to the $k$th pow
 er for all $2 \\le k \\le K$. Given $K \\ge 2$\, we consider the problem o
 f establishing the smallest integer $N_0(K)$ for which there exist \\emph{
 nontrivial} $K$-multimagic squares of order $N_0(K)$. \n\nPrevious results
  on multimagic squares show that $N_0(K) \\le (4K-2)^K$ for large $K$. We 
 use the Hardy-Littlewood circle method to improve this to \n\\[N_0(K) \\le
  2K(K+1)+1.\\]\nThe intricate structure of the coefficient matrix poses si
 gnificant technical challenges for the circle method. We overcome these ob
 stacles by generalizing the class of Diophantine systems amenable to the c
 ircle method and demonstrating that the multimagic square system belongs t
 o this class for all $N \\ge 4$. We additionally establish the existence o
 f infinitely many $N \\times N$ magic squares of distinct $k$th powers as 
 soon as\n\\[N > 2\\min\\{2^k\,\\lceil k(\\log k +4.20032) \\rceil \\}.\\]\
 nThis result marks progress toward resolving an open problem popularized b
 y Martin Gardner in 1996\, which asks whether a $3 \\times 3$ magic square
  of distinct squares exists.\n
LOCATION:https://researchseminars.org/talk/CANT2025/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rishi Nath (York College (CUNY))
DTSTART:20250523T173000Z
DTEND:20250523T175500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/58/
 ">Simultaneous (co)core partitions</a>\nby Rishi Nath (York College (CUNY)
 ) as part of Combinatorial and additive number theory (CANT 2025)\n\nLectu
 re held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\
 nIn the 1950s\, Littlewood and others famously showed how to decompose an 
 integer partition into its $p$-core and $p$-quotient for positive $t$. In 
 the early 2000s\, J. Anderson began the study of partitions which have bot
 h empty $s$-quotient and empty $t$-quotient for $s$ and $t$ relatively pri
 me. Here we consider a perpendicular question\, that of partitions which h
 ave both empty $s$-core and $t$-core.\\\\\nThis is joint work with T. Quee
 r and A. Perez.\n
LOCATION:https://researchseminars.org/talk/CANT2025/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan McNew (Towson University)
DTSTART:20250523T210000Z
DTEND:20250523T212500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/59/
 ">The density of covering numbers</a>\nby Nathan McNew (Towson University)
  as part of Combinatorial and additive number theory (CANT 2025)\n\nLectur
 e held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\n
 In 1950\, Erd\\H{o}s introduced covering systems--finite collections of ar
 ithmetic progressions whose union contains every integer. They featured in
  some of his favorite problems\, many of which are still open.  In 1979\,
  answering one of Erd\\H{o}s's questions\, Haight introduced covering numb
 ers: positive integers $n$ for which a covering system can be constructed 
 with distinct moduli that are divisors of $n$. If no proper divisor of $n$
  is a covering number\, we call $n$ a primitive covering number.  We esta
 blish an upper bound on the number of primitive covering numbers\, from wh
 ich it follows that the set of covering numbers has a natural density. By 
 refining techniques used to bound the density of abundant numbers\, we obt
 ain relatively tight bounds for the density of covering numbers and\, in t
 he process\, improve the bounds on the density of abundant numbers as well
 .\n
LOCATION:https://researchseminars.org/talk/CANT2025/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Francisco E. Adajar (University of Georgia)
DTSTART:20250523T140000Z
DTEND:20250523T142500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/60/
 ">On the distribution of $v_p(\\sigma(n))$</a>\nby Carlo Francisco E. Adaj
 ar (University of Georgia) as part of Combinatorial and additive number th
 eory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center 
 (4th floor).\n\nAbstract\nFor a positive integer $m$ and a prime $p$\, we 
 write $\\sigma(m) := \\sum_{d \\mid m} d$ for the sum of the divisors of $
 m$\, and $v_p(m) := \\max\\{ k \\in \\mathbf{Z}_{\\ge 0} : p^k \\mid m \\}
 $ for the $p$-adic valuation of $m$\, i.e.\, the exponent of $p$ in the pr
 ime factorization of $m$. For each prime $p$\, we give an asymptotic expre
 ssion for the count\n$$ \\#\\{ n \\le x : v_p(\\sigma(n)) = k \\} $$\nas $
 x\\to\\infty$\, uniformly for $k \\ll \\log\\log{x}$. We then deduce an as
 ymptotic for the count of $n \\le x$ such that $v_p(\\sigma(n)) < v_p(n)$ 
 as $x \\to \\infty$. \\\\\nThis talk is based on ongoing work with Paul Po
 llack.\n
LOCATION:https://researchseminars.org/talk/CANT2025/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Fraser (St. Andrews University\, UK)
DTSTART:20250523T143000Z
DTEND:20250523T145500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/61/
 ">Averages of the Fourier transform in finite fields</a>\nby Jonathan Fras
 er (St. Andrews University\, UK) as part of Combinatorial and additive num
 ber theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science C
 enter (4th floor).\n\nAbstract\nDiscrete Fourier analysis is a useful tool
  in various counting problems in vector spaces over finite fields.  I will
  mention some results in this direction\, with emphasis on a new approach 
 based on quantifying Fourier decay via a spectrum of exponents coming from
  certain $L^p$ averages.\n
LOCATION:https://researchseminars.org/talk/CANT2025/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taylor Daniels (Purdue University)
DTSTART:20250523T150000Z
DTEND:20250523T152500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/62
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/62/
 ">Vanishing Legendre-$17$-signed partition numbers</a>\nby Taylor Daniels 
 (Purdue University) as part of Combinatorial and additive number theory (C
 ANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th fl
 oor).\n\nAbstract\nFor odd primes $p$ let $\\chi_p(r) := (\\frac{r}{p})$ d
 enote the Legendre symbol. With this\, the Legendre-signed partition numbe
 rs\, denoted $\\mathfrak{p}(n\,\\chi_{p})$\, are then defined to be the co
 efficients appearing in the series expansion \n$$\\prod_{r=1}^{p-1}\\prod_
 {m=0}^{\\infty}\\frac{1}{1-\\chi_{p}(r)q^{mp+r}} = 1 + \\sum_{n=1}^\\infty
  \\mathfrak{p}(n\,\\chi_{p})q^n.$$ \nIt is known that: (1) one has $\\math
 frak{p}(n\,\\chi_{5}) = 0$ for all $n \\equiv 2 \\\,(\\mathrm{mod}\\\,10)$
 \; and (2) the sequences $(\\mathfrak{p}(n\,\\chi_{p}))_{n \\geq 1}$ do no
 t have such a periodic vanishing whenever $p \\not\\equiv 1 \\\,(\\mathrm{
 mod}\\\,8)$ and $p \\neq 5$. In this talk we discuss the recent result tha
 t $\\mathfrak{p}(n\,\\chi_{17})$ vanishes only when the input $n$ is odd a
 nd $1-24n$ is congruent to a quartic residue $(\\mathrm{mod}\\\,17)$\, as 
 well as a similar vanishing in the sequence $(\\mathfrak{p}(n\,-\\chi_{17}
 ))_{n\\geq 1}$.\n
LOCATION:https://researchseminars.org/talk/CANT2025/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cihan Sabuncu (Universite de Montreal)
DTSTART:20250523T153000Z
DTEND:20250523T155500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/63/
 ">Extreme values of $r_3(n)$ in arithmetic progressions</a>\nby Cihan Sabu
 ncu (Universite de Montreal) as part of Combinatorial and additive number 
 theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Cente
 r (4th floor).\n\nAbstract\nA classical result of Chowla shows that the re
 presentation function $r_3(n)$\, which counts the number of ways $n$ can b
 e expressed as a sum of three squares\, satisfies $$r_3(n) \\gg \\sqrt{n} 
 \\log\\log n $$ \nfor infinitely many integers $n$. This lower bound\, in 
 turn\, also implies that $ L(1\, \\chi_D) \\gg \\log\\log |D|$ holds for i
 nfinitely many fundamental discriminants $D<0$. In this talk\, we will inv
 estigate whether such extremal behavior of $r_3(n)$ persists when $n$ is r
 estricted to lie in an arithmetic progression $n\\equiv a \\pmod q$. \\\\T
 his is joint work with Jonah Klein and Michael Filaseta.\n
LOCATION:https://researchseminars.org/talk/CANT2025/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Firdavs Rakhmonov (University of St. Andrews\, UK)
DTSTART:20250523T160000Z
DTEND:20250523T162500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/64/
 ">Exceptional projections in finite fields: Fourier analytic bounds and in
 cidence geometry</a>\nby Firdavs Rakhmonov (University of St. Andrews\, UK
 ) as part of Combinatorial and additive number theory (CANT 2025)\n\nLectu
 re held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\
 nWe consider the problem of bounding the number of exceptional projections
  (projections which are smaller than typical)  of a subset of a vector spa
 ce over a finite field.  We establish bounds that depend on $L^p$ estimate
 s for the Fourier transform\, improving various known bounds for sets with
  sufficiently good Fourier analytic properties.  The special case $p=2$ re
 covers a recent result of Bright and Gan (following Chen)\, which establis
 hed the finite field analogue of Peres--Schlag's bounds from the continuou
 s setting.\\\\\nWe prove several auxiliary results of independent interest
 \, including a character sum identity for subspaces (solving a problem of 
 Chen)\, and an analogue of Plancherel's theorem for subspaces. These auxil
 iary results also have applications in affine incidence geometry\, that is
 \, the problem of estimating the number of incidences between a set of poi
 nts and a set of affine $k$-planes. We present a novel and direct proof of
  a well-known result in this area that avoids the use of spectral graph th
 eory\, and we provide simple examples demonstrating that these estimates a
 re sharp up to constants.  \\\\\nThis is joint work with Jonathan Fraser.\
 n
LOCATION:https://researchseminars.org/talk/CANT2025/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorg Brudern (Universitat Gottingen)
DTSTART:20250521T163000Z
DTEND:20250521T165500Z
DTSTAMP:20260422T212931Z
UID:CANT2025/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/65/
 ">Expander estimates for cubes</a>\nby Jorg Brudern (Universitat Gottingen
 ) as part of Combinatorial and additive number theory (CANT 2025)\n\nLectu
 re held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\
 nSuppose that $\\mathcal A$ is a subset of the natural numbers. The suprem
 um $\\alpha$ of all $t$ with \n$$ \\limsup N^{-t} \\#\\{a\\in{\\mathcal A}
 : a\\le N\\} >0 $$\nis the {\\em exponential density} of $\\mathcal A$.\n\
 nWe examine what happens if one adds a power to $\\mathcal A$. Fix $k\\ge 
 2$\, and let $\\beta_k$ be the exponential density of\n$$ \\{ x^k+a : x\\i
 n {\\mathbb N}\, \\\, a\\in{\\mathcal A}\\}.$$\nIt is easy to see that $\\
 beta_2= \\min (1\, \\frac12 +\\alpha).$ One might guess that\n$$ \\beta_k 
 = \\min (1\, \\frac{1}{k}+\\alpha) \\eqno (*) $$\nholds for all $k$\, but 
 we are far from a proof. All current world records for this problem are du
 e to Davenport\, and are 80 years old. In this interim report on ongoing w
 ork with Simon Myerson\, we describe a method \nfor $k=3$ that improves Da
 venport's results when $\\alpha>3/5$\, and that confirms (*) in an interva
 l $(\\alpha_0\, 1]$. A concrete value for $\\alpha_0$ will be released dur
 ing the talk\, and if time permits\, we also discuss the perspectives to g
 eneralize the approach to larger values of $k$.\n
LOCATION:https://researchseminars.org/talk/CANT2025/65/
END:VEVENT
END:VCALENDAR