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BEGIN:VEVENT
SUMMARY:Mohan (BK Birla Institute of Engineering and Technology\, India)
DTSTART:20250520T110000Z
DTEND:20250520T112500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/1/">Special additive complements of a set of natural numbers</a>\nby M
 ohan (BK Birla Institute of Engineering and Technology\, India) 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 $A$ be 
 a set of natural numbers.	A set $B$ of natural numbers is said to be an ad
 ditive 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 d
 escribe various types of additive complements of the set $A$ such as those
  additive complements of $A$  that do or do not intersect  $A$\, additive 
 complements which are the union of disjoint infinite arithmetic progressio
 ns\, and additive complements having various densities etc. We estabilish 
 that if   $A=\\{a_i: i\\in \\mathbb{N}\\}$ is a set of natural numbers suc
 h that  $a_{i} < a_{i+1} $ for $i \\in \\mathbb{N}$ and $\\liminf_{n\\righ
 tarrow \\infty } (a_{n+1}/a_{n})>1$\, then there exists a set $B\\subset \
 \mathbb{N}$  such that $B\\cap A = \\varnothing$ and $B$ is a sparse addit
 ive complement of the set $A$.  Besides this\,  for a given positive real 
 number $\\alpha \\leq 1$ and a finite set $A$\, we investigate a set $B$ s
 uch that $B$ can be written as a union of disjoint infinite arithmetic pro
 gressions with the natural density of $A+B$ equal to $\\alpha$.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harald Helfgott (CNRS/Institut de Math\\' ematiques de Jussieu)
DTSTART:20250520T113000Z
DTEND:20250520T115500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/2/">Explicit estimates for sums of arithmetic functions\, or the optim
 al use of finite information on Dirichlet series</a>\nby Harald Helfgott (
 CNRS/Institut de Math\\' ematiques de Jussieu) 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\nLet $F(s) = \\sum_n a_n n^{-
 s}$ be a Dirichlet series. Say we have an analytic continuation of $F(s)$\
 , and information on the poles of $F(s)$ with $|\\Im s|\\leq T$ for some l
 arge constant $T$. \n What is the best way to use this information to give
  explicit estimates on sums $\\sum_{n\\leq x} a_n$? \n\n  The problem of g
 iving explicit bounds on the Mertens function $M(x) = \\sum_{n\\leq x} \\m
 u(n)$ illustrates how open this basic question was.\n  One might think tha
 t bounding $M(x)$ is essentially equivalent to estimating $\\psi(x) = \\su
 m_{n\\leq x} \\Lambda(n)$ or the number of primes $\\leq x$.\n  However\, 
 we have long had fairly satisfactory explicit bounds on $\\psi(x)-x$\, whe
 reas bounding $M(x)$ well was a notoriously recalcitrant problem.\n\nWe gi
 ve an optimal 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 stro
 nger than those in the literature\, while also substantially improving on 
 estimates on $\\psi(x)$.\n\n We use functions of "Beurling-Selberg" type -
 - namely\, an optimal approximant due to Carneiro-Littmann and an optional
  majorant/minorant due to Graham-Vaaler. Our procedure has points of conta
 ct \n with Wiener-Ikehara and also with work of Ramana and Ramaré\, but d
 oes not rely on results in the explicit analytic-number-theory literature.
  \n\n(joint work with Andrés Chirre)\n
LOCATION:https://stable.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:20260404T094912Z
UID:CANT2025/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/3/">Variants of Raimi's theorem</a>\nby Norbert Hegyvari (E\\"otv\\"os
  University  and R\\'enyi Institute) as part of Combinatorial and additive
  number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Scien
 ce Center (4th floor).\n\nAbstract\nThere exists $E\\subseteq \\mathbb{N}$
  such that\, whenever $r\\in \\mathbb{N}$ and $\\mathbb{N}=\\bigcup_{i=1}^
 rD_i$ there exist\n$i\\in\\{1\,2\,\\ldots\,r\\}$ and $k\\in \\mathbb{N}$ s
 uch that $(D_i+k)\\cap E$ is\ninfinite and $(D_i+k)\\setminus E$ is infini
 te.\n\nA new proof of the theorem is due to N. Hindman\, then to Bergelson
  and Weiss\, and the generalization to the author.\nIn the present talk\, 
 we give an outline of the new proofs and the generalization and some varia
 tions are discussed in different structures (e.g. in $\\Z_n^k$\, in $SL_2(
 \\mathbb F_p)$.)\n\nThese variations are joint work with J\\'anos Pach and
  Thang Pham.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alisa Sedunova (Purdue University)
DTSTART:20250521T133000Z
DTEND:20250521T135500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/4/">The multiplication table constant and sums of two squares</a>\nby 
 Alisa Sedunova (Purdue University) as part of Combinatorial and additive n
 umber theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science
  Center (4th floor).\n\nAbstract\nLet $r_1(n)$ be the number of representa
 tions of $n$ as the sum of a square and a square of a prime. We discuss th
 e erratic behavior of $r_1$\, which is similar to the one of the divisor f
 unction. \nWe will show that the number of integers up to $x$ that have at
  least one such representation \nis asymptotic to $(\\pi/2) x \\log x$ min
 us a secondary term of size $x/(\\log x)^{1+d+o(1)}$\, \nwhere $d$ is the 
 multiplication table constant. Detailed heuristics suggest very precise as
 ymptotic \nfor the secondary term as well. In particular\, our proofs impl
 y that the main contribution to the mean \nvalue of $r_1(n)$ comes from in
 tegers with “unusual” number of prime factors\, i.e. those with\n $\\o
 mega(n) \\sim 2 \\log \\log x$ (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 i
 nclude a recent joint preprint with Andrew Granville and Cihan Sabuncu and
  my paper from 2022 as well as some work in progress.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinhui Fang (Nanjing Normal University\, China)
DTSTART:20250522T130000Z
DTEND:20250522T132500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/5/">On  bounded unique representation bases</a>\nby Jinhui Fang (Nanji
 ng Normal University\, China) as part of Combinatorial and additive number
  theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Cent
 er (4th floor).\n\nAbstract\nFor a nonempty set $A$ of integers and an int
 eger $n$\,  let $r_{A}(n)$ be the number of representations of $n=a+a'$ w
 ith $a\\le a'$ and $a\, a'\\in A$\, and let $d_{A}(n)$ be the number of re
 presentations of $n=a-a'$ with $a\, a'\\in A$. In 1941\, Erd\\H{o}s and Tu
 r\\'{a}n posed the profound conjecture: If $A$ is a set of positive intege
 rs such that $r_A(n)\\ge 1$ for all sufficiently large $n$\, then $r_A(n)$
  is unbounded. In 2004\, Ne\\v{s}et\\v{r}il and Serra introduced the notio
 n of bounded sets and confirmed the Erd\\H{o}s-Tur\\'{a}n conjecture for a
 ll bounded bases. In 2003\, Nathanson considered the existence of the set 
 $A$ with logarithmic growth such that $r_A(n)=1$ for all integers $n$. Rec
 ently\, we prove that\, for any positive function $l(x)$ with $l(x)\\right
 arrow 0$ as $x\\rightarrow \\infty$\,  there is a bounded set $A$ of inte
 gers such that $r_A(n)=1$ for all integers $n$ and $d_A(n)=1$ for all posi
 tive integers $n$\, and $A(-x\,x)\\ge l(x)\\log x$ for all sufficiently la
 rge $x$\, where $A(-x\,x)$ is the number of elements $a\\in A$ with $-x\\l
 e a\\le x$.  \nThis is joint work with Prof. Yong-Gao Chen.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gergo Kiss (Budapest Corvinus University and R\\' enyi Institute)
DTSTART:20250522T130000Z
DTEND:20250522T132500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/6/">Weak tiling and the Coven-Meyerowitz conjecture</a>\nby Gergo Kiss
  (Budapest Corvinus University and R\\' enyi Institute) as part of Combina
 torial and additive number theory (CANT 2025)\n\nLecture held in CUNY Grad
 uate Center - Science Center (4th floor).\n\nAbstract\nThe concept of weak
  tiling was originally introduced in $\\mathbb{R}^n$ by Lev and Matolcsi\,
  and has proven to be an essential tool in addressing Fuglede's conjecture
  for convex domains. In this talk\, we extend the notion of weak tiling to
  the setting of cyclic groups and further generalize it using a natural av
 eraging process. As a result\, the tiles are no longer sets\, \nbut rather
  become step functions--a framework we refer to as functional tiling.\n\nO
 ne advantage of this approach is that the cyclotomic divisors of the funct
 ions involved in a functional tiling remain the same as those of the chara
 cteristic functions of the original sets. Another is that functional tilin
 gs can be studied using the well-established tools and objective functions
  of linear programming\, which is computationally efficient due to its pol
 ynomial-time solvability.\n\nI will introduce the key quantities involved 
 and present basic connections between functional and classical tilings. Fi
 nally\, I will provide a counterexample to the Coven-Meyerowitz conjecture
  within the context of functional tilings. It is important to note\, howev
 er\, that none of the counterexamples we constructed in this setting corre
 spond to tiling pairs of sets. Thus\, the Coven-Meyerowitz conjecture for 
 tiling sets remains open.\nThis is joint work with Itay Londner\, M\\' at\
 \' e Matolcsi\, and G\\' abor Somlai.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salvatore Tringali (Hebei Normal University\, China)
DTSTART:20250523T130000Z
DTEND:20250523T132500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/7/">Power monoids and the Bienvenu-Geroldinger problem for torsion gro
 ups</a>\nby Salvatore Tringali (Hebei Normal University\, China) as part o
 f Combinatorial and additive number theory (CANT 2025)\n\nLecture held in 
 CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nLet $M$ be
  a (multiplicatively written) monoid with identity element $1_M$.  \nEndow
 ed with the operation of setwise multiplication induced by $M$\, the colle
 ction \nof finite subsets of $M$ containing $1_M$ forms a monoid in its ow
 n right\, denoted \nby $\\mathcal{P}_{\\mathrm{fin}\,1}(M)$ and called the
  reduced finitary power monoid of $M$.\n \nIt is natural to ask whether\, 
 for all $H$ and $K$ in a given class of monoids\, \n$\\mathcal{P}_{\\mathr
 m{fin}\,1}(H)$ is isomorphic to $\\mathcal{P}_{\\mathrm{fin}\,1}(K)$ \nif 
 and only if $H$ is isomorphic to $K$. Originating from a conjecture of Bie
 nvenu and \nGeroldinger recently settled by Yan and myself\, the problem -
 -- together with its numerous \nvariants and ramifications --- has non-tri
 vial connections to additive number theory and related fields.\nIn this ta
 lk\, I will present a positive solution for the class of torsion groups.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehdi Makhul (London School of Economics)
DTSTART:20250523T133000Z
DTEND:20250523T135500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/8/">Web geometry and the orchard problem</a>\nby Mehdi Makhul (London 
 School of Economics) as part of Combinatorial and additive number theory (
 CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th f
 loor).\n\nAbstract\nLet $P$ be a set of $n$ points in the plane\, not all 
 lying on a single line. \nThe orchard planting problem asks for the maximu
 m number of lines passing through exactly three points of $P$. Green and T
 ao showed that the maximum possible number of such lines \nfor an $n$-elem
 ent set is~$\\lfloor \\frac{n(n-3)}{6} \\rfloor+1$. Lin and Swanepoel also
  investigated a generalization of the orchard problem in higher dimensions
 . \nSpecifically\, if $P$ is a set of $n$ points \nin $d$-dimensional spac
 e\, they established an upper bound for the maximum number of hyperplanes 
 passing through exactly $d+1$ points of $P$. Our goal is to describe the s
 tructural properties of configurations that achieve near-optimality in the
  asymptotic regime. \nLet $C \\subset \\mathbb{R}^d$ be an algebraic curve
  of degree~$r$\, and suppose that $P \\subset C$ is a set of $n$ points.  
 If $P$ determines at least~$cn^d$ hyperplanes\, each passing through exact
 ly $d+1$ points of $P$\, then the following must hold: The degree of $C$ m
 ust be $d+1$\; and the curve $C$ is the complete intersection of ${d\\choo
 se 2}-1$ quadric hypersurfaces. Our approach relies on the theory of web g
 eometry and the Elekes-Szab\\'o Theorem-a cornerstone of incidence geometr
 y-both of which provide the structural basis for our analysis. \nJoint wor
 k with Konrad Swanepoel.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shashi Chourasiya (University of New South Wales\, Australia)
DTSTART:20250520T120000Z
DTEND:20250520T122500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/9/">Power-free palindromes and reversed primes</a>\nby Shashi Chourasi
 ya (University of New South Wales\, Australia) 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\nSeveral long-standing conjec
 tures in number theory are related to the digital properties of integers. 
 Historically\, such problems have been confined to the realm of elementary
  number theory\, but recently huge breakthroughs have been made by applyin
 g deep analytical techniques. In this talk\, we discuss some very recent r
 esults on this topic\, focusing on palindromes and reversed primes. We fir
 st establish that for all bases $b \\geq 26000$\, there exist infinitely m
 any prime numbers $p$ for which $\\{ \\overleftarrow{p} \\}$ is square-fre
 e. Furthermore\, we demonstrate the existence of infinitely many palindrom
 es (with $n= \\overleftarrow{n}$) that are cube-free.  \nThis is based on 
 joint work with Daniel R. Johnston.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vjekoslav Kovac (University of Zagreb)
DTSTART:20250520T123000Z
DTEND:20250520T125500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/10
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/10/">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 Cent
 er (4th floor).\n\nAbstract\nProving (ir)rationality of infinite series of
  distinct unit fractions has been an active topic of research for decades\
 , with numerous occasional breakthroughs. We will investigate what can be 
 obtained using elementary techniques (such as iterative constructions and 
 the probabilistic method) and address several problems posed by Paul Erdos
  throughout the 1980s. In particular\, we will study one type of irrationa
 lity sequences introduced by Erdos and Graham\, (almost entirely) resolve 
 a question by Erdos on simultaneous rationality of two or more "consecutiv
 e" series\, and give a negative answer to an "infinite-dimensional" conjec
 ture by Stolarsky. This is joint work with Terence Tao (UCLA).\n\nOnline o
 nly. Link: https://www.theoryofnumbers.com/cant/\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Konieczny (University of Oxford)
DTSTART:20250520T130000Z
DTEND:20250520T132500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/11/">Multiplicative generalised polynomial sequences</a>\nby Jakub Kon
 ieczny (University of Oxford) as part of Combinatorial and additive number
  theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Cent
 er (4th floor).\n\nAbstract\nGeneralised polynomials are sequences constru
 cted from polynomial sequences using the integer part function\, addition\
 , and multiplication. Determining whether a given sequence is a generalise
 d polynomial is often a non-trivial task. In joint work with J. Byszewski 
 and B. Adamczewski\, we have discovered both surprising examples of such s
 equences and developed criteria to disprove that a given sequence is a gen
 eralised polynomial. More broadly\, given a family of sequences\, one can 
 pose a classification problem: Which sequences in the family are generaliz
 ed polynomials? In this talk\, I will present a complete resolution of thi
 s problem for the family of multiplicative sequences\, as well as partial 
 results for (non-completely) multiplicative sequences.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro A. Garcia-Sanchez (Universidad de Granada)
DTSTART:20250520T133000Z
DTEND:20250520T135500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/12/">Some problems related to the ideal class monoid of a numerical se
 migroup</a>\nby Pedro A. Garcia-Sanchez (Universidad de Granada) as part o
 f Combinatorial and additive number theory (CANT 2025)\n\nLecture held in 
 CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nLet $S$ be
  a numerical semigroup (a submonoid of the set of non-negative integers un
 der addition such that $\\max(\\mathbb{Z}\\setminus S)$ exists). A non-emp
 ty 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 mono
 id of $S$ is defined as the set of ideals of $S$ modulo this relation\, wh
 ere addition 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 normalized if $\\min(I)=0$. The set of normalized ideals of $S$\, deno
 ted by $\\mathfrak{I}_0(S)$\, is a monoid isomorphic to the ideal class mo
 noid of $S$ [1]. \n\nIt is known that if $S$ and $T$ are numericals semigr
 oups for 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 $\\math
 frak{I}_0(S)$ 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 i
 f $S$ and $T$ are numerical semigroups with multiplicity three such that t
 he poset $(\\mathfrak{I}_0(S)\,\\preceq)$ is isomorphic to the poset $(\\m
 athfrak{I}_0(T)\,\\preceq)$\, then $S$ and $T$ are the same numerical semi
 group [3]. However\, if we remove the multiplicity three condition\, this 
 poset isomorphsm problem is still open. \n\nIn [4]\, we study the case whe
 n the poset $(\\mathfrak{I}_0(S)\,\\preceq)$ is a lattice. We show that th
 is is the case if and only if the multiplicity of $S$ is at most four. \n\
 nReferences:\n\n1.  L. Casabella\, M. D'Anna\, P. A. García-Sánchez\, Ap
 éry sets and the ideal class monoid of a numerical semigroup\, Mediterr. 
 J. Math. 21\, 7 (2024). \n\n2. P. A. García-Sánchez\, The isomorphism pr
 oblem for ideal class monoids of numerical semigroups\, Semigroup Forum 10
 8 (2024)\, 365--376. \n\n3. S. Bonzio\, P. A. García-Sánchez\, The poset
  of normalized ideals of numerical semigroups with multiplicity three\, to
  appear in Comm. Algebra. \n\n4. S. Bonzio\, P. A. García-Sánchez\, When
  the poset of the ideal class monoid of a numerical \nsemigroup is a latti
 ce\, arXiv:2412.07281.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Val Gladkova (University of Cambridge)
DTSTART:20250520T140000Z
DTEND:20250520T142500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/13
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/13/">A lower bound for the strong arithmetic regularity lemma</a>\nby 
 Val Gladkova (University of Cambridge) 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 strong  regularity lemma is a co
 mbinatorial tool originally introduced by Alon\, Fischer\, Krivelevich\, a
 nd Szegedy in order to prove an induced removal lemma for graphs. Conlon a
 nd Fox showed that for some graphs\, the strong regularity lemma must prod
 uce partitions of wowzer-type size. This talk will sketch a proof that a c
 omparable lower bound must hold for the arithmetic analogue of this lemma\
 , in the setting of vector spaces over finite fields.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debyani Manna (Indian Institute of Technology Roorkee)
DTSTART:20250520T143000Z
DTEND:20250520T145500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/14
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/14/">Some results on the extended inverse problem of $A+2 \\cdot A$</a
 >\nby Debyani Manna (Indian Institute of Technology Roorkee) as part of Co
 mbinatorial and additive number theory (CANT 2025)\n\nLecture held in CUNY
  Graduate Center - Science Center (4th floor).\n\nAbstract\nLet $A$ be a f
 inite set of integers and $A+ 2 \\cdot A= \\{a+2a': a\,a' \\in A\\}$.  An 
 extended inverse problem associated with the sumset  $A+2 \\cdot A$ is to 
  determine the underlying set $A$ when the size of the sumset $A+2 \\cdot 
 A$ deviates from the minimum possible size.\nWe find all possible arithmet
 ic structures of $A$ for certain cardinalities of $A + 2 \\cdot A$ and use
  them to address extended inverse problems in the Baumslag-Solitar group $
 BS(1\,2)$. \nThis is joint work with Ram Krishna Pandey.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Huczynska (University of St. Andrews\,)
DTSTART:20250520T150000Z
DTEND:20250520T152500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/15
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/15/">Additive triples in groups of odd prime order</a>\nby Sophie Hucz
 ynska (University of St. Andrews\,) as part of Combinatorial and additive 
 number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Scienc
 e Center (4th floor).\n\nAbstract\nFor a subset $A$ of an additive group $
 G$\,  a Schur triple in $A$ is a triple of the form $(a\,b\,a+b) \\in A^3$
 .  Denote 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 vario
 us authors. When $r(A)=0$\, $A$ is sum-free. The question of minimum and m
 aximum $r(A)$ for $A$ of fixed size in $\\mathbb{Z}_p$ was resolved by Huc
 zynska\, Mullen and Yucas (2009) and independently by Samotij and Sudakov 
 (2016).  Several generalisations of the Schur triple problem have received
  attention.  In this talk\, I will present recent work (with Jonathan Jedw
 ab and Laura Johnson) on the generalisation to triples $(a\,b\,a+b) \\in A
  \\times B \\times B$\, where $A\,B \\subseteq \\mathbb{Z}_p$.  Denote by 
 $r(A\,B\,B)$ the number of triples of this form\; we obtain a precise desc
 ription of its full spectrum of values and show constructively that each v
 alue in this spectrum can be realised when $B$ is an interval of consecuti
 ve elements in $\\mathbb{Z}_p$.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshiharu Kohayakawa (University of São Paulo\, Brazil)
DTSTART:20250520T160000Z
DTEND:20250520T162500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/16
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/16/">Arithmetic progressions in subsetsums of sparse random sets of in
 tegers</a>\nby Yoshiharu Kohayakawa (University of São Paulo\, Brazil) as
  part of Combinatorial and additive number theory (CANT 2025)\n\nLecture h
 eld in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nGiv
 en a set $S\\subset\\mathbb{N}$\, its sumset $S+S$ is the set of all\nsums
  $s+s'$ with both $s$ and $s'$ elements of $S$.  Given\n$p \\colon \\mathb
 b{N}\\to [0\,1]$\, 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 enou
 gh $n$.  We prove\nthat\, then\, with high probability\, long arithmetic p
 rogressions exist\nin the sumset of any positive density subset of $A_n$\,
  that is\, with\nprobability approaching $1$ as $n\\to\\infty$\, for any s
 ubset $S$\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://stable.researchseminars.org/talk/CANT2025/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandor Kiss (Budapest University of Technology and Economics)
DTSTART:20250520T153000Z
DTEND:20250520T155500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/17
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/17/">Generalized Stanley sequences</a>\nby Sandor Kiss (Budapest Unive
 rsity of Technology and Economics) as part of Combinatorial and additive n
 umber theory (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 d
 oes not contain an arithmetic progression of length $k$. The set $S(A)$ is
  defined by the following greedy algorithm. If $s \\ge t$ and $a_{1}\, \\d
 ots{} \,a_{s}$ have already been defined\, then\n$a_{s+1}$ is the smallest
  integer $a > a_{s}$ such that $\\{a_{1}\, \\dots{} \,a_{s}\\} \\cup \\{a\
 \}$ also 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. Stanley and Odlyzko tried to generate arithmetic progression-free sets
  by using the greedy algorithm. In 1999\, Erd\\H{o}s\, Lev\, Rauzy\, S\\'a
 ndor and S\\'ark\\"ozy extended the notion of Stanley sequence to other in
 itial sets $A_{0}$. In my talk I investigate some further generalizations 
 of Stanley sequences and I give some density type results about them.  \nT
 his is a joint work with Csaba S\\'andor and Quan-Hui Yang.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Chapman (University of Warwick)
DTSTART:20250520T173000Z
DTEND:20250520T175500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/19
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/19/">Counting commuting integer matrices</a>\nby Jonathan Chapman (Uni
 versity of Warwick) 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\nConsider the set of pairs of $d\\times d$ matrices $(A\
 ,B)$ whose entries are all integers with absolute value at most $N$. We ca
 ll $(A\,B)$ a \\emph{commuting pair} if $AB=BA$. Browning\, Sawin\, and Wa
 ng recently 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
  $\\Omega_d(N^{d^2 + 1})$\, which comes from letting $A$ or $B$ be a multi
 ple of the identity matrix\, should be sharp. In this talk\, I will discus
 s progress on the cases $d=2$ and $d=3$\, where we show that this conjectu
 re holds. I will also demonstrate how our approach relates counting commut
 ing pairs of matrices to the study of restricted divisor correlations in n
 umber theory.\\\\\nJoint work with Akshat Mudgal (University of Warwick)\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josiah Sugarman (Hebrew University of Jerusalem)
DTSTART:20250520T180000Z
DTEND:20250520T182500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/20
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/20/">Explicit spectral gap for the quaquaversal operator</a>\nby Josia
 h Sugarman (Hebrew University of Jerusalem) as part of Combinatorial and a
 dditive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center 
 - Science Center (4th floor).\n\nAbstract\nThe spectral gap of an operator
  is the gap between the largest eigenvalue and the rest of the spectrum. I
 n the mid 90s\, John Conway and Charles Radin introduced a three dimension
 al substitution tiling\, the Quaquaversal Tiling\, with the property that 
 the orientations of its tiles equidistribute faster than what is possible 
 for two dimensional substitution tilings. Conway and Radin showed that the
  orientations of the tiles were dense in $SO(3)$ and implicity introduced 
 an operator (later explicitly studied by Draco\, Sadun\, and Van Wieren) w
 hose spectral gap controls the equidistribution rate.\nDraco\, Sadun\, and
  Van Wieren studied the eigenvalues of this operator numerically and conje
 ctured that it has a spectral gap bounded below by approximately $0.006169
 7$. \nWe exploit a fact\, due to Serre\, that the group of orientations fo
 r this tiling is $2$-arithmetic and follow a strategy similar to Lubotzky\
 , Phillips\, and Sarnak's in order to obtain a lower bound of about $0.006
 1711$\,  resolving the conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Leonetti (Universit\\` a degli Studi dell'Insubria)
DTSTART:20250520T183000Z
DTEND:20250520T185500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/21
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/21/">On the completeness induced by densities on natural numbers</a>\n
 by Paolo Leonetti (Universit\\` a degli Studi dell'Insubria) as part of Co
 mbinatorial and additive number theory (CANT 2025)\n\nLecture held in CUNY
  Graduate Center - Science Center (4th floor).\n\nAbstract\nLet $\\nu: \\m
 athcal{P}(\\mathbb{N}) \\to \\mathbb{R}$ be an \\textquotedblleft upper de
 nsity\\textquotedblright\\\, on the natural numbers $\\mathbb{N}$ (for ins
 tance\, $\\nu$ can be the upper asymptotic density or the upper Banach den
 sity). Then a natural pseudometric $d_\\nu$ is induced on $\\mathcal{P}(\\
 mathbb{N})$\, namely\, \n$$\n\\forall A\,B\\subseteq \\mathbb{N}\, \\quad 
 \nd_\\nu(A\,B):=\\nu(A\\bigtriangleup B)\n$$\nWe provide necessary and suf
 ficient conditions for the completeness of $d_\\nu$. \nThen  we identify i
 n which cases the latter ones are verified.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akash Singha Roy (University of Georgia)
DTSTART:20250520T190000Z
DTEND:20250520T192500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/22
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/22/">Joint distribution in residue classes of families of multiplicati
 ve functions</a>\nby Akash Singha Roy (University of Georgia) as part of C
 ombinatorial and additive number theory (CANT 2025)\n\nLecture held in CUN
 Y Graduate Center - Science Center (4th floor).\n\nAbstract\nThe distribut
 ion of values of arithmetic functions in residue classes has been a proble
 m of great interest in elementary\, analytic\, and combinatorial number th
 eory. In work studying this problem for large classes of multiplicative fu
 nctions\, Narkiewicz obtained general criteria deciding when a family of s
 uch functions is jointly uniformly distributed among the coprime residue c
 lasses to a fixed modulus. Using these criteria\, he along with \\' Sliwa\
 , Rayner\, Dobrowolski\, Fomenko\, and others\, gave explicit results on t
 he distribution of interesting multiplicative functions and their families
  in coprime residue classes.\n\nIn this talk\, we shall give best possible
  extensions of Narkiewicz's criteria (and hence also of the other aforemen
 tioned results) to moduli that are allowed to vary in a wide range. This i
 s motivated by the celebrated Siegel-Walfisz theorem on the distribution o
 f primes in arithmetic progressions\, and our results happen to be some of
  the best possible qualitative analogues of the Siegel-Walfisz theorem for
  the classes of multiplicative functions considered by Narkiewicz and othe
 rs. Our arguments blend ideas from multiple subfields of number theory\, a
 s well as from linear algebra over rings\, commutative algebra\, and arith
 metic and algebraic geometry. This talk is partly based on joint work with
  Paul Pollack.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Keith (Michigan Technical University)
DTSTART:20250520T193000Z
DTEND:20250520T195500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/23
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/23/">$s \\pmod{t}$-cores</a>\nby William Keith (Michigan Technical Uni
 versity) as part of Combinatorial and additive number theory (CANT 2025)\n
 \nLecture held in CUNY Graduate Center - Science Center (4th floor).\n\nAb
 stract\nWe consider simultaneous $(s\,s+t\,s+2t\,\\dots\,s+pt)$-cores in t
 he large-$p$ limit\, or (when $s<t$)\, partitions in which no hook may be 
 of length $s \\pmod{t}$.  As a boundary case of the general study made by 
 Cho\, Huh and Sohn\, we find special symmetries and relations\, such as ge
 nerating functions\, congruences when $s$ is not coprime to $t$\, and enum
 erations when $s$ is coprime to $t$.  Of particular interest is the compar
 ison to the behavior of simultaneous $(s\,t)$-cores and self-conjugate $(s
 \,t)$-cores.  \nJoint work with Rishi Nath  and James Sellers.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladyslav Oles (University of Idaho)
DTSTART:20250520T200000Z
DTEND:20250520T202500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/24
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/24/">Vanishing symmetric functions</a>\nby Vladyslav Oles (University 
 of Idaho) as part of Combinatorial and additive number theory (CANT 2025)\
 n\nLecture held in CUNY Graduate Center - Science Center (4th floor).\n\nA
 bstract\nWe continue an old solution by Noga Alon of conjectures of Arie B
 ialostocki. \nThe first problem deals with vanishing symmetric functions o
 n consecutive blocks \nin an arbitrary ${\\mathbb Z}_n$-coloring of the po
 sitive integers. The second problem (unpublished) deals with vanishing sym
 metric functions on grid points inside of a polygon. The problems originat
 ed from the classical Theorem of Van der Waerden. \nThis is joint work wit
 h Arie Bialostocki.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Baczkowski (University of Findlay)
DTSTART:20250520T203000Z
DTEND:20250520T205500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/25
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/25/">Diophantine equations involving arithmetic functions and factoria
 ls</a>\nby Daniel Baczkowski (University of Findlay) as part of Combinator
 ial and additive number theory (CANT 2025)\n\nLecture held in CUNY Graduat
 e Center - 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 f
 unction\, or the function counting the number of divisors\, have finitely 
 many integer solutions in~$m$ and~$n$. In joint work with Novakovi\\'{c} w
 e generalize the mentioned result and show that Diophantine equations of t
 he form $\\alpha\\\,m_1!\\cdots m_r!=f(n!)$ have finitely many integer sol
 utions\, too. In addition\, we do so by including the case $f$ is the sum 
 of $k$\\textsuperscript{th} powers of divisors function. Moreover\, the sa
 me holds by replacing some of the factorials with certain examples of Bhar
 gava factorials.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aritram Dhar (University of Florida)
DTSTART:20250520T210000Z
DTEND:20250520T212500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/26
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/26/">A bijective proof of an identity of Berkovich and Uncu</a>\nby Ar
 itram Dhar (University of Florida) as part of Combinatorial and additive n
 umber theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science
  Center (4th floor).\n\nAbstract\nThe BG-rank BG($\\pi$) of an integer par
 tition $\\pi$ is defined as $$\\text{BG}(\\pi) := i-j$$ where $i$ is the n
 umber of odd-indexed odd parts and $j$ is the number of even-indexed odd p
 arts of $\\pi$. In a recent work\, Fu and Tang ask for a direct combinator
 ial proof of the following identity of Berkovich and Uncu $$B_{2N+\\nu}(k\
 ,q)=q^{2k^2-k}\\left[\\begin{matrix}2N+\\nu\\\n+k\\end{matrix}\\right]_{q^
 2}$$ for any integer $k$ and non-negative integer $N$ where $\\nu\\in \\{0
 \,1\\}$\, $B_N(k\,q)$ is the generating function for partitions into disti
 nct parts 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 coe
 fficient. In this talk\, I will give a bijective proof of Berkovich and Un
 cu's identity along the lines of Vandervelde and Fu and Tang's idea. \nThi
 s is joint work with Avi Mukhopadhyay.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James A. Sellers (University of Minnesota Duluth)
DTSTART:20250521T140000Z
DTEND:20250521T142500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/27
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/27/">Extending congruences for overpartitions with $\\ell$-regular non
 -overlined parts</a>\nby James A. Sellers (University of Minnesota Duluth)
  as part of Combinatorial and additive number theory (CANT 2025)\n\nLectur
 e held in CUNY Graduate Center - Science Center (4th floor).\nAbstract: TB
 A\n
LOCATION:https://stable.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:20260404T094912Z
UID:CANT2025/28
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/28/">Pushing the gap between tiles and spectral sets even further</a>\
 nby Gabor Somlai (E\\" otv\\" os Lor\\' and University and  R\\' enyi Inst
 itute) as part of Combinatorial and additive number theory (CANT 2025)\n\n
 Lecture held in CUNY Graduate Center - Science Center (4th floor).\n\nAbst
 ract\nFuglede conjectured that a bounded measurable set in a locally compa
 ct topological space endowed with Haar measure is spectral if and only if 
 it is a tile and Fuglede also confirmed the conjecture for sets whose tili
 ng complement is a lattice and for spectral sets one of whose spectrums is
  a lattice.\n\nThe conjecture was disproved by Tao in the case of finite a
 belian groups where the counting measure plays the role of the Haar measur
 e. \nTao 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 Euclide
 an space\, where the original conjecture was mostly studied. \n\nLev and M
 atolcsi verified Fuglede's conjecture for convex sets in $\\mathbb{R}^n$ f
 or every positive integer $n$. The key of proving the harder direction of 
 the conjecture is to introduce the weak tiling property and prove that all
  spectral sets are weak tilings.\n\nOne of the goals of our work was to an
 swer a question of Kolountzakis\, Lev and Matolcsi\, whether there is a we
 ak tile  that is neither a tile nor spectral. There is such a set which ap
 parently makes it harder to prove the spectral-tile direction of the conje
 cture in the remaining open cases. \n\nThe other result towards structural
 ly distinguishing spectral sets and tiles was a disproof of a conjecture o
 f Greenfeld and Lev. They conjectured that the product of two sets is spec
 tral if and only if both of them are spectral. A similar property holds fo
 r tiles\, but the product of a non-spectral set with a spectral set can be
  spectral. \nFinally\, we obtain an easy characterization of tiles using t
 he spectral property.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Spiegel (Zuse Institute Berlin)
DTSTART:20250521T150000Z
DTEND:20250521T152500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/29
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/29/">An unsure talk on an un-Schur problem</a>\nby Christoph Spiegel (
 Zuse Institute 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 pose
 d the problem of determining the minimum number of monochromatic Schur tri
 ples that must appear in any 2-coloring of the first $n$ integers. This qu
 estion was subsequently resolved independently by Datskovsky\, Schoen\, an
 d Robertson and Zeilberger. Here we suggest studying a natural anti-Ramsey
  variant of this question and establish the first non-trivial bounds by pr
 oving that 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 0.666
 56. We conjecture the lower bound to be tight. This question is also motiv
 ated by a famous analogous problem in graph theory due to Erd\\H os and S\
 \' os regarding 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 Parczyk.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Trevor D. Wooley (Purdue University)
DTSTART:20250521T153000Z
DTEND:20250521T155500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/30
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/30/">Equidistribution and $L^p$-sets for $p<2$</a>\nby Trevor D. Woole
 y (Purdue University) as part of Combinatorial and additive number theory 
 (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th 
 floor).\n\nAbstract\nWe investigate subsets $\\mathcal A$ of the natural n
 umbers 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^{\\varepsilo
 n-1}.\n\\]\nExamples of such sets include (but are not restricted to) the 
 squarefree\, or more generally\, the $r$-free numbers. For polynomials \n$
 \\psi(x\;\\boldsymbol\\alpha)=\\alpha _kx^k+\\ldots +\\alpha_1x$\, having 
 coefficients $\\alpha_i$ satisfying suitable irrationality conditions\, we
  show that the sequence $(\\psi(n\;\\boldsymbol\\alpha))_{n\\in \\mathcal 
 A}$ is equidistributed modulo $1$.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Tafula (Universit\\'e de Montr\\'eal)
DTSTART:20250521T160000Z
DTEND:20250521T162500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/31
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/31/">Waring--Goldbach subbases with prescribed representation function
 s</a>\nby Christian Tafula (Universit\\'e de Montr\\'eal) 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\nWe investigate re
 presentation functions $r_{A\,h}(n)$ of subsets $A$ of \\( k \\)-th powers
  \\( \\mathbb{N}^k \\) and \\( k \\)-th powers of primes \\( \\mathbb{P}^k
  \\). Building on work of Vu\, Wooley\, and others\, we prove that for \\(
  h \\geq h_k = O(8^k k^2) \\) and regularly varying \\( F(n) \\) satisfyin
 g \\( \\lim_{n\\to\\infty} F(n)/\\log n = \\infty \\)\, there exists \\( A
  \\subseteq \\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 o
 btain analogous results for \\( F(n) = n^{\\kappa} \\). For \\( F(n) = \\l
 og 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 subbas
 es of prime powers.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hopper Clark (Bates College)
DTSTART:20250521T173000Z
DTEND:20250521T175500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/32
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/32/">Patterns among Ulam words</a>\nby Hopper Clark (Bates College) as
  part of Combinatorial and additive number theory (CANT 2025)\n\nLecture h
 eld 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 term
 s. In 2020\, the parallel notion of the set of Ulam words\, \n$\\mathcal{U
 }$\, was introduced by Bade\, Cui\, Labelle\, and Li\, which looks at conc
 atenations of words in $F_2$\, the free group on two generators. In this t
 alk\, we will discuss patterns of words in $\\mathcal{U}$\, touching on bo
 th proven results and conjectured ones. We will see how these patterns com
 e to life visually\, and see how they produce images such as the discrete 
 Sierp\\' inski triangle.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asher Roberts (St. Joseph's University New York)
DTSTART:20250521T180000Z
DTEND:20250521T182500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/33
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/33/">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 additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate C
 enter - Science Center (4th floor).\n\nAbstract\nAssuming the Riemann hypo
 thesis\, we show that for $k>0$ and $V\\sim k\\log\\log T$\,\n     \\[\n  
    \\frac{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\\log T}}.\n     \\]\n     This shows that Selberg's central limit theo
 rem persists in the large deviation regime. As a corollary\, we recover th
 e result of Soundararajan and of Harper on the moments of $\\zeta$. This d
 irectly 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://stable.researchseminars.org/talk/CANT2025/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gautami Bhowmik (Universit\\' e Lille)
DTSTART:20250521T183000Z
DTEND:20250521T185500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/34
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/34/">On the Telhcirid problem</a>\nby Gautami Bhowmik (Universit\\' e 
 Lille) as part of Combinatorial and additive number theory (CANT 2025)\n\n
 Lecture held in CUNY Graduate Center - Science Center (4th floor).\n\nAbst
 ract\nWe consider the digital reverse of integers\, in particular those of
  primes.\nA palindromic prime number is a popular example of a prime whose
  reverse is also a prime and\nthe infinitude of such primes is one among t
 he open conjectures in the area.\nWe will  discuss reversed primes in arit
 hmetic progression built on ideas of Mauduit-Rivat and Maynard. \\\\\nThis
  is joint work with Yuta Suzuki.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Allen Alexander (U.S. Securities and Exchange Commission)
DTSTART:20250521T190000Z
DTEND:20250521T192500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/35
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/35/">Hindman's theorem and the hyperreals</a>\nby Samuel Allen Alexand
 er (U.S. Securities and Exchange Commission) as part of Combinatorial and 
 additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center
  - Science Center (4th floor).\n\nAbstract\nHindman's theorem says that if
  the natural numbers are colored using finitely many colors\, then there e
 xists some color $c$ and some infinite $S\\subseteq \\mathbb N$ such that 
 for every 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 stronger version of the theorem involving hyperreal numbers. \\\\\nSome
  of this material was previously published in 2024 in the Journal of Logic
  and Analysis.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Baginski (Fairfield University)
DTSTART:20250521T193000Z
DTEND:20250521T195500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/36
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/36/">Arithmetic Progressions\, Nonunique Factorization\, and Additive 
 Combinatorics in the Group of Units Mod $n$</a>\nby Paul Baginski (Fairfie
 ld 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\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 $a^
 2\\equiv a \\mod b$. Any such multiplicatively closed arithmetic progressi
 on is called an arithmetic congruence monoid (ACM). Though these $M_{a\,b}
 $ are multiplicative submonoids of $\\mathbb{N}$\, their factorization pro
 perties differ greatly from the unique factorization one enjoys in $\\math
 bb{N}$.\n\nIn this talk we will explore the known factorization properties
  of these monoids. When $a=1$\, these monoids are Krull and behave similar
 ly to algebraic number rings\, in that they have a class group which contr
 ols all the factorization. Combinatorially\, factorization properties corr
 espond to zero-sum sequences in the group. However\, when $a\\gt 1$\, thes
 e monoids are not Krull and thus do not have a class group which fully cap
 tures the factorization behavior. Nonetheless\, an ACM can be associated t
 o a finite abelian group\, whose additive combinatorics relate to the fact
 orization properties of the ACM. We will pay particular attention to the f
 actorization property of elasticity and its connection to sequences in the
  group which attain certain sums while avoiding others.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Iosevich (University of Rochester)
DTSTART:20250523T193000Z
DTEND:20250523T195500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/37
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/37/">The Fourier uncertainty principle\, signal recovery\, and applica
 tions</a>\nby Alex Iosevich (University of Rochester) 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\nWe are going to discu
 ss the analytic\, arithmetic\, and practical aspects of exact signal recov
 ery\, with the emphasis on the role of restriction theory for the Fourier 
 transform and connections with the classical results of Bourgain\, Talagra
 nd\, and others.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven J. Miller (Williams College\, Fibonacci Association)
DTSTART:20250521T203000Z
DTEND:20250521T205500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/38
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/38/">Phase transitions for binomial sets under linear forms</a>\nby St
 even J. Miller (Williams College\, Fibonacci Association) 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\nWe generalize res
 ults on sum and difference sets of a subset S of\n$\\mathbb{N}$ drawn from
  a binomial model. Given $A \\subseteq \\{0\, 1\,\n\\dots\, N\\}$\, an int
 eger $h \\geq 2$\, and a linear form $L: \\mathbb{Z}^h \\to\n\\mathbb{Z}$ 
 $$L(x_1\, \\dots\, x_h)\\ :=\\ u_1x_1 + \\cdots + u_hx_h\, \\quad u_i\n\\i
 n \\mathbb{Z}_{\\neq 0} {\\rm\\ for\\ all\\ } i \\in [h]\,$$ we study the 
 size\nof $$L(A)\\ =\\ \\left\\{u_1a_1 + \\cdots + u_ha_h : a_i \\in A \\ri
 ght\\}$$ and\nits complement $L(A)^c$ when each element of $\\{0\, 1\, \\d
 ots\, N\\}$ is\nindependently included in $A$ with probability $p(N)$\, id
 entifying two\nphase transitions. The first global one concerns the relati
 ve sizes of\n$L(A)$ and $L(A)^c$\, with $p(N) = N^{-\\frac{h-1}{h}}$ as th
 e threshold.\nAsymptotically almost surely\, below the threshold almost al
 l 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 $L(
 A)$.\nOur asymptotic formulae substantially extends work of Hegarty and Mi
 ller\,\nresolving their conjecture. The second local phase transition conc
 erns the\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 thresh
 old and\nidentifies (in a sharp sense) when the number of such realization
 s obeys a\nPoisson limit. Our main tools are recent results on the asympto
 tic\nenumeration of partitions\, Stein's method for Poisson approximation\
 , and\nthe martingale machinery of Kim-Vu.\n
LOCATION:https://stable.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:20260404T094912Z
UID:CANT2025/39
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/39/">Iterated sums races</a>\nby Anne de Roton (Universit\\'e de Lorra
 ine\, Institut Elie Cartan) as part of Combinatorial and additive number t
 heory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center
  (4th floor).\n\nAbstract\nThis is joint work with Paul P\\' eringuey. \\\
 \\nOur work provides a solution to a question posed by M. Nathanson in lat
 e 2024\, but we later realized that this problem\, along with an even more
  challenging one\, had already been solved by N. Kravitz in a paper posted
  on arXiv in January 2025. While our construction is similar to his\, it i
 s simpler\, and we hope that it can serve as an introductory step toward u
 nderstanding the underlying ideas. \\\\\nNathanson's question is as follow
 s: \\\\\n\\textit{For every integer $m \\geq 3$\, do there exist finite se
 ts $A$ and $B$ of integers and an increasing sequence of positive integers
  $h_1 < h_2 < \\cdots < h_m$\, such that: \\\\\n$$ |h_i A| > |h_i B| \\qua
 d \\text{if } i \\text{ is odd\,} $$\n$$ |h_i A| < |h_i B| \\quad \\text{i
 f } i \\text{ is even.} $$ \\\\\nAdditionally\, do there exist such sets w
 ith $|A| = |B|$? Can such sets be constructed with $|A| = |B|$ and $\\text
 {diam}(A) = \\text{diam}(B)$?} \\\\\nWe provide a positive answer to these
  questions and propose an iterative construction of sets that satisfy thes
 e conditions.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Kowalski (ETH Zurich)
DTSTART:20250522T143000Z
DTEND:20250522T145500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/40
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/40/">Some pseudorandom graphs</a>\nby Emmanuel Kowalski (ETH Zurich) a
 s part of Combinatorial and additive number theory (CANT 2025)\n\nLecture 
 held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nA 
 classical construction associates to any Sidon set a graph without\n$4$-cy
 cles. We investigate some properties of these graphs in the case\nof the S
 idon sets constructed by Forey\, Fres\\' an and myself using methods\nof a
 lgebraic geometry. In particular\, this provides deterministic\nfamilies o
 f Ramanujan graphs with semi-circle and other interesting\nexplicit asympt
 otic eigenvalue distributions.\n \nBased on joint work with A. Forey and J
 . Fres\\' an and discussions with\nY. Wigderson and T. Schramm.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Besfort Shala (University of Bristol\, UK)
DTSTART:20250522T150000Z
DTEND:20250522T152500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/41
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/41/">Multiplicative energy in number theory</a>\nby Besfort Shala (Uni
 versity of Bristol\, UK) as part of Combinatorial and additive number theo
 ry (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4
 th floor).\n\nAbstract\nI will discuss the important role of multiplicativ
 e energy of sets in number theory\, particularly in the probabilistic theo
 ry of random multiplicative functions. The aim is to provide a survey of r
 ecent results in the area.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Shkredov (Purdue University)
DTSTART:20250522T153000Z
DTEND:20250522T155500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/42
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/42/">Some applications of the higher energy method to distribution irr
 egularitie</a>\nby Ilya Shkredov (Purdue University) as part of Combinator
 ial and additive number theory (CANT 2025)\n\nLecture held in CUNY Graduat
 e Center - Science Center (4th floor).\n\nAbstract\nWe review recent resul
 ts obtained by the method of higher sumsets \nand higher energies. \nIn pa
 rticular\, we discuss two applications: irregularities in the distribution
  of the difference \nset and irregularities in the large Fourier coefficie
 nts of sets with small sumsets.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Karam (University of  Oxford)
DTSTART:20250522T160000Z
DTEND:20250522T162500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/43
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/43/">After the cap-set problem\, and some properties of the slice rank
 </a>\nby Thomas Karam (University of  Oxford) as part of Combinatorial and
  additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Cente
 r - Science Center (4th floor).\n\nAbstract\nThe infamous cap-set problem 
 asks for the size of the largest subset $A \\subset \\mathbb{F}_3^n$ not c
 ontaining any solutions to the equation $x+y+z=0$ aside from the trivial s
 olutions $x=y=z$. A proof that that size is bounded above by $C^n$ for som
 e $C<3$\, which arose in 2016 in two breakthrough papers by Croot-Lev-Pach
  and by Ellenberg and Gijswijt (both published in the Annals of Mathematic
 s)\, was later reformulated by Tao in a more symmetric way\, leading to th
 e definition of a new notion of rank on tensors called the slice rank.\n\n
 Since then\, the slice rank has been studied further\, and the resulting p
 roperties have often found related number-theoretic applications. To take 
 the earliest and perhaps simplest example\, a key component of the argumen
 t in the proof of the original cap-set problem itself is that the slice ra
 nk of a “diagonal” tensor is equal to its number of non-zero entries\,
  mirroring the analogous property of matrix rank.\n\nAfter reviewing some 
 more such applications by other mathematicians\, we will present some resu
 lts concerning other basic properties of the slice rank\, and in particula
 r the ideas behind some of their simpler proofs in the special case where 
 the support of the tensor is contained in an antichain: there\, as establi
 shed by Sawin and Tao\, the slice rank of the tensor is equal to the small
 est number of slices that suffice to cover its support. If time allows the
 n we will also discuss how the proofs in this special case illuminate to s
 ome extent the proofs in the general case.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Chapman (Sam Houston State University)
DTSTART:20250522T173000Z
DTEND:20250522T175500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/44
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/44/">Betti elements and non-unique factorizations</a>\nby Scott Chapma
 n (Sam Houston State University) 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\nLet $M$ be a commutative cancellative redu
 ced atomic monoid with set of atoms (or irreducibles) $\\mathcal{A}(M)$.  
 Given a nonunit $x$ in $M$\, let\n$Z(x)$ represent the set of factorizatio
 ns of $x$ into atoms.  Define a graph $\\nabla_x$ whose vertex set is $Z(x
 )$ where two vertices are joined\nby an edge if these factorizations share
  an atom.  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 study of nonunique factorizations of elements in monoids.  In particul
 ar\, \nover the past several years many papers have used Betti elements to
  study factorizaton properties in \\textit{affine monoids} (i.e.\,  finite
 ly generated additive submonoids of $\\mathbb{N}_0^k$ for some positive in
 teger $k$).  Several strong results have been obtained when $M$ is a numer
 ical monoid (i.e.\, $k=1$ above).  In this talk\, we will\nreview the basi
 c properties of Betti elements and some of the results regarding affine mo
 noids mentioned above.  \nWe will then extend this study to\nmore general 
 rings and monoids which are commutative and cancellative.   We focus on tw
 o cases: (I) when the monoid $M$ has a single Betti element\, (II) when ea
 ch atom of $M$ divides every Betti element.  We call those monoids satisfy
 ing condition (II) as having \\textit{full atomic support}.  We show using
  elementary arguments that a monoid of type (I) is actually of full atomic
  support.   We close by showing for a monoid of full atomic support that t
 he catenary degree\, the tame degree\, and the omega primality constant  (
 three well studied invariants in the nonunique factorization literature) c
 an be easily computed from the monoid's set of Betti elements.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Lebowitz-Lockard
DTSTART:20250522T180000Z
DTEND:20250522T182500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/45
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/45/">Partitions and ordered products</a>\nby Noah Lebowitz-Lockard as 
 part of Combinatorial and additive number theory (CANT 2025)\n\nLecture he
 ld in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nLet 
 $g(n)$ be the number of ways to express $n$ as an ordered partition of num
 bers greater than $1$. We also let $a(n)$ be the number of partitions of $
 n$ of the 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 resea
 rch around $g(n)$\, much less is known about $a(n)$. We discuss these two 
 functions\, as well as some new asymptotics on $a(n)$.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Eichhorn (University of California Irvine)
DTSTART:20250522T183000Z
DTEND:20250522T185500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/46
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/46/">Open problems involving cranks for partition congruences</a>\nby 
 Dennis Eichhorn (University of California Irvine) as part of Combinatorial
  and additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate C
 enter - Science Center (4th floor).\n\nAbstract\nDyson famously conjecture
 d\, correctly\, that his rank statistic witnesses Ramanujan's first two co
 ngruences for $p(n)$\, and that there exists a ``crank" statistic that wit
 nesses Ramanujan's congruence modulo $11$ in a similar fashion.\nAs it tur
 ns out\, this phenomenon of congruence-witnessing statistics\, which we no
 w also call ``cranks" in homage to Dyson\, also occurs in other contexts w
 ithin partition theory.\nIn this talk\, we give several open problems and 
 conjectures in this area\, highlighting some recent developments along the
  way.\\\\\nThis talk will include joint work with several coauthors.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Mozzochi
DTSTART:20250522T190000Z
DTEND:20250522T192500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/47
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/47/">The  closest known attempted proof of  the twin prime conjectur
 e</a>\nby Jeff Mozzochi as part of Combinatorial and additive number theor
 y (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4t
 h floor).\n\nAbstract\nUsing a primitive formulation of the circle method 
 we present a sufficient condition for\nthe twin prime conjecture that miss
 es being true by just an epsilon.\nWe also show that the well-known suffic
 ient condition for the twin prime conjecture\nimplies the patently false s
 tatement that for each positive integer m\, there exists\nan infinite numb
 er of prime pairs whose difference is $m$.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johann Thiel (New York City College of Technology (CUNY))
DTSTART:20250522T193000Z
DTEND:20250522T195500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/48
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/48/">Bivariate polynomials associated with binary trees created by Qui
 ckSort</a>\nby Johann Thiel (New York City College of Technology (CUNY)) a
 s part of Combinatorial and additive number theory (CANT 2025)\n\nLecture 
 held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nIn
  this talk we describe a generating series whose coefficients are polynomi
 als that\, for a given positive integer $n$\, encode the depth at which th
 e various list entries appear as labeled nodes in the binary trees obtaine
 d by QuickSorting permutations of the list consisting of one copy of each 
 of the first $n$ non-negative integers. Extracting the appropriate coeffic
 ients yields information for the number of times a given list entry appear
 s at a given depth\, the total number of list entries that appear at a giv
 en depth\, and consequently the average number of list entries that appear
  at a given depth taken over all $n!$ permutations. Joint work with David 
 M. Bradley.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Schinina (CUNY Graduate Center)
DTSTART:20250522T200000Z
DTEND:20250522T202500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/49
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/49/">On a missing interval of integers from $\\mathcal{R}_{\\mathbf{Z}
 }(h\,4)$</a>\nby Vincent Schinina (CUNY Graduate Center) 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\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 elements 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 integer
 s that includes the endpoints. These endpoints are known to be attained. B
 y observation\, it appears that the interval of integers $[3h+2\,4h-1]$ is
  absent from $\\mathcal{R}_{\\Z}(h\,4)$. We will briefly discuss the proce
 dure used to prove that the integers in $[3h+2\,4h-1]$ are not possible si
 zes for the $h$-fold sumset of a set containing four integers. Furthermore
 \, we will confirm that this interval can't be made larger by exhibiting a
  set whose h-fold sumset has size $4h$.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Senger (Missouri State University)
DTSTART:20250522T203000Z
DTEND:20250522T205500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/50
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/50/">VC-dimension of subsets of the Hamming graph</a>\nby Steven Senge
 r (Missouri State University) as part of Combinatorial and additive number
  theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Cent
 er (4th floor).\n\nAbstract\nVapnik-Chervonenkis or VC-dimension has been 
 a useful tool in combinatorics\, machine learning\, and other areas. Given
  a graph from a well-studied family\, there has been recent activity on si
 ze thresholds for a subset of a graph to guarantee bounds on the VC-dimens
 ion of the subset. These resemble finite point configuration results\, suc
 h as the Erdos-Falconer distance problem\, both in form as well as in the 
 techniques of proof. Typically\, one looks at graphs that are highly pseud
 orandom\, such as the distance graph or the dot product graph\, but the Ha
 mming graph is quantifiably less pseudorandom\, and standard techniques se
 em to break down and yield very weak results if any. We present a suite of
  results that outperform their counterparts for the Hamming graph. The pro
 ofs are completely elementary\, and in some cases\, tight.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Jacobs (Virginia Commonwealth University)
DTSTART:20250522T210000Z
DTEND:20250522T212500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/51
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/51/">Crossword puzzles</a>\nby Robert Jacobs (Virginia Commonwealth Un
 iversity) as part of Combinatorial and additive number theory (CANT 2025)\
 n\nLecture held in CUNY Graduate Center - Science Center (4th floor).\n\nA
 bstract\nIt is known that the most words possible in a $15\\times15$ cross
 word puzzle is 96  \nif the grid is symmetrical and connected  and every w
 ord has at least 3 letters.\n In this talk\, I will prove this and find th
 e most words possible in other grids.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Hopkins (Saint Peter's University)
DTSTART:20250523T183000Z
DTEND:20250523T185500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/52
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/52/">Scaled Arndt compositions</a>\nby Brian Hopkins (Saint Peter's Un
 iversity) as part of Combinatorial and additive number theory (CANT 2025)\
 n\nLecture held in CUNY Graduate Center - Science Center (4th floor).\n\nA
 bstract\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 count
 ed by the Fibonacci numbers.  This was confirmed by the speaker and Tangbo
 onduangjit in 2022 and we explored generalizations of this pair-wise condi
 tion including $c_{2i-1} > c_{2i} + k$ for an affine parameter $k$.  In th
 e current work\, a collaboration with Augustine Munagi\, we consider scali
 ng parameters\, integers $s$ and $t$\, and resolve some cases of the gener
 al condition $sc_{2i-1} > tc_{2i} + k$.  Techniques include generating fun
 ctions and combinatorial proofs.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (Lehman College (CUNY))
DTSTART:20250521T200000Z
DTEND:20250521T202500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/53
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/53/">Sizes of sumsets of finite sets of integers</a>\nby Mel Nathanson
  (Lehman College (CUNY)) as part of Combinatorial and additive number theo
 ry (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4
 th floor).\n\nAbstract\nIn the study of sums of finite sets of integers\, 
 most attention has been paid to sets with small sumsets (Freiman's theorem
  and related work) and to sets with large sumsets (Sidon sets and $B_h$-se
 ts).  The focus of this talk is on the full range of sizes of h-fold sums 
 of a set of k integers.   New results and open problems will be presented.
 \n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Hough (Stony Brook University)
DTSTART:20250523T180000Z
DTEND:20250523T182500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/54
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/54/">Lower order terms in the shape of cubic fields</a>\nby Robert Hou
 gh (Stony Brook 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\nThe ring of integers of a degree n number field
  may be viewed as an n-dimensional lattice within the canonical embedding.
   Spectrally expanding the space of lattices\, we study the distribution o
 f lattice shapes of rings of integers when cubic fields are ordered by dis
 criminant by studying the Weyl sums testing the lattice shape against the 
 real analytic Eisenstein series and Maass cusp forms.  In the case of Eise
 nstein series we identify a lower order main term of order $X^{11/12}$ whe
 n fields of discriminant of order $X$ are counted with a smooth weight.  \
 \\\\nJoint work with Eun Hye Lee.  Recent work of Lee and Ramin Tagloo-Big
 hash promises to extend these ideas to integral orbits in general prehomog
 eneous vector spaces.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ross (University of Hawaii)
DTSTART:20250523T203000Z
DTEND:20250523T205500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/55
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/55/">Upper density and a theorem of Banach</a>\nby David Ross (Univers
 ity of Hawaii) as part of Combinatorial and additive number theory (CANT 2
 025)\n\nLecture held in CUNY Graduate Center - Science Center (4th floor).
 \n\nAbstract\nSuppose $A_n$ $(n\\in\\mathbb{N})$ is a sequence of sets in 
 a finitely-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}
 $\, where $\\{n_k\\}_k$ has upper Banach density $\\ge a$\, such that $\\m
 u\\bigcap_{k<N}A_{n_k}\\ge a$ for every $N$.  Surprisingly\, this implies 
 a density-limit version of a representation theorem of Banach:\n\n\\textbf
 {Theorem:} Let $\\{\\\,f_n : n\\in\\mathbb{N}\\}$ be a uniformly\nbounded 
 sequence of functions on a set $X$.  The following are equivalent:  (i)~$\
 \{f_n\\}_n$ weakly d-converges to $0$\; (ii)~for any sequence\n$\\{x_k : k
 \\in\\mathbb{N}\\}$ 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
  described by some as ``marvelous".\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Donley (Queens Community College (CUNY))
DTSTART:20250523T200000Z
DTEND:20250523T202500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/56
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/56/">A classification for 1-factorizations of small order</a>\nby Robe
 rt Donley (Queens Community College (CUNY)) as part of Combinatorial and a
 dditive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center 
 - Science Center (4th floor).\n\nAbstract\nA graph $G$ admits a 1-factoriz
 ation if its edge set decomposes into disjoint perfect matchings.  When $G
 $ is bipartite\, the equivalency classes of such graphs are determined by 
 orbits of 0/1-semi-magic squares under row and column permutations. By the
  Birkhoff-von Neumann theorem\, such matrices are sums of permutation matr
 ices. In a manner similar to the construction of standard Young tableaux\,
  we introduce a path model for the construction of bipartite 1-factorizati
 ons and classify those of small order.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Benjamin Flores (Purdue University)
DTSTART:20250523T190000Z
DTEND:20250523T192500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/57
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/57/">$K$-multimagic squares and magic squares of $k$th powers via the 
 circle method</a>\nby Daniel Benjamin Flores (Purdue University) as part o
 f Combinatorial and additive number theory (CANT 2025)\n\nLecture held in 
 CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nHere we in
 vestigate $K$\\emph{-multimagic squares} of order $N$. These are $N \\time
 s N$ magic squares which remain magic after raising each element to the $k
 $th power for all $2 \\le k \\le K$. Given $K \\ge 2$\, we consider the pr
 oblem of 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 p
 oses significant technical challenges for the circle method. We overcome t
 hese obstacles by generalizing the class of Diophantine systems amenable t
 o the circle method and demonstrating that the multimagic square system be
 longs to this class for all $N \\ge 4$. We additionally establish the exis
 tence of infinitely many $N \\times N$ magic squares of distinct $k$th pow
 ers 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 popula
 rized by Martin Gardner in 1996\, which asks whether a $3 \\times 3$ magic
  square of distinct squares exists.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rishi Nath (York College (CUNY))
DTSTART:20250523T173000Z
DTEND:20250523T175500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/58
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/58/">Simultaneous (co)core partitions</a>\nby Rishi Nath (York College
  (CUNY)) as part of Combinatorial and additive number theory (CANT 2025)\n
 \nLecture held in CUNY Graduate Center - Science Center (4th floor).\n\nAb
 stract\nIn the 1950s\, Littlewood and others famously showed how to decomp
 ose 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 h
 ave both empty $s$-quotient and empty $t$-quotient for $s$ and $t$ relativ
 ely prime. Here we consider a perpendicular question\, that of partitions 
 which have both empty $s$-core and $t$-core.\\\\\nThis is joint work with 
 T. Queer and A. Perez.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan McNew (Towson University)
DTSTART:20250523T210000Z
DTEND:20250523T212500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/59
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/59/">The density of covering numbers</a>\nby Nathan McNew (Towson 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\nIn 1950\, Erd\\H{o}s introduced covering systems--finite collection
 s of arithmetic progressions whose union contains every integer. They feat
 ured 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 coveri
 ng numbers: positive integers $n$ for which a covering system can be const
 ructed 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 establish an upper bound on the number of primitive covering numbers\, 
 from which it follows that the set of covering numbers has a natural densi
 ty. By refining techniques used to bound the density of abundant numbers\,
  we obtain relatively tight bounds for the density of covering numbers and
 \, in the process\, improve the bounds on the density of abundant numbers 
 as well.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Francisco E. Adajar (University of Georgia)
DTSTART:20250523T140000Z
DTEND:20250523T142500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/60
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/60/">On the distribution of $v_p(\\sigma(n))$</a>\nby Carlo Francisco 
 E. Adajar (University of Georgia) as part of Combinatorial and additive nu
 mber theory (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 diviso
 rs of $m$\, and $v_p(m) := \\max\\{ k \\in \\mathbf{Z}_{\\ge 0} : p^k \\mi
 d m \\}$ for the $p$-adic valuation of $m$\, i.e.\, the exponent of $p$ in
  the prime factorization of $m$. For each prime $p$\, we give an asymptoti
 c expression for the count\n$$ \\#\\{ n \\le x : v_p(\\sigma(n)) = k \\} $
 $\nas $x\\to\\infty$\, uniformly for $k \\ll \\log\\log{x}$. We then deduc
 e an asymptotic for the count of $n \\le x$ such that $v_p(\\sigma(n)) < v
 _p(n)$ as $x \\to \\infty$. \\\\\nThis talk is based on ongoing work with 
 Paul Pollack.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Fraser (St. Andrews University\, UK)
DTSTART:20250523T143000Z
DTEND:20250523T145500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/61
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/61/">Averages of the Fourier transform in finite fields</a>\nby Jonath
 an Fraser (St. Andrews University\, UK) as part of Combinatorial and addit
 ive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Sc
 ience Center (4th floor).\n\nAbstract\nDiscrete Fourier analysis is a usef
 ul tool in various counting problems in vector spaces over finite fields. 
  I will mention some results in this direction\, with emphasis on a new ap
 proach based on quantifying Fourier decay via a spectrum of exponents comi
 ng from certain $L^p$ averages.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taylor Daniels (Purdue University)
DTSTART:20250523T150000Z
DTEND:20250523T152500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/62
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/62/">Vanishing Legendre-$17$-signed partition numbers</a>\nby Taylor D
 aniels (Purdue University) as part of Combinatorial and additive number th
 eory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center 
 (4th floor).\n\nAbstract\nFor odd primes $p$ let $\\chi_p(r) := (\\frac{r}
 {p})$ denote the Legendre symbol. With this\, the Legendre-signed partitio
 n numbers\, denoted $\\mathfrak{p}(n\,\\chi_{p})$\, are then defined to be
  the coefficients appearing in the series expansion \n$$\\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.$$ \nIt is known that: (1) one has 
 $\\mathfrak{p}(n\,\\chi_{5}) = 0$ for all $n \\equiv 2 \\\,(\\mathrm{mod}\
 \\,10)$\; and (2) the sequences $(\\mathfrak{p}(n\,\\chi_{p}))_{n \\geq 1}
 $ do not have such a periodic vanishing whenever $p \\not\\equiv 1 \\\,(\\
 mathrm{mod}\\\,8)$ and $p \\neq 5$. In this talk we discuss the recent res
 ult that $\\mathfrak{p}(n\,\\chi_{17})$ vanishes only when the input $n$ i
 s odd and $1-24n$ is congruent to a quartic residue $(\\mathrm{mod}\\\,17)
 $\, as well as a similar vanishing in the sequence $(\\mathfrak{p}(n\,-\\c
 hi_{17}))_{n\\geq 1}$.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cihan Sabuncu (Universite de Montreal)
DTSTART:20250523T153000Z
DTEND:20250523T155500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/63
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/63/">Extreme values of $r_3(n)$ in arithmetic progressions</a>\nby Cih
 an Sabuncu (Universite de Montreal) as part of Combinatorial and additive 
 number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Scienc
 e Center (4th floor).\n\nAbstract\nA classical result of Chowla shows that
  the representation function $r_3(n)$\, which counts the number of ways $n
 $ can be expressed as a sum of three squares\, satisfies $$r_3(n) \\gg \\s
 qrt{n} \\log\\log n $$ \nfor infinitely many integers $n$. This lower boun
 d\, in turn\, also implies that $ L(1\, \\chi_D) \\gg \\log\\log |D|$ hold
 s for infinitely many fundamental discriminants $D<0$. In this talk\, we w
 ill investigate whether such extremal behavior of $r_3(n)$ persists when $
 n$ is restricted to lie in an arithmetic progression $n\\equiv a \\pmod q$
 . \\\\This is joint work with Jonah Klein and Michael Filaseta.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Firdavs Rakhmonov (University of St. Andrews\, UK)
DTSTART:20250523T160000Z
DTEND:20250523T162500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/64
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/64/">Exceptional projections in finite fields: Fourier analytic bounds
  and incidence geometry</a>\nby Firdavs Rakhmonov (University of St. Andre
 ws\, UK) as part of Combinatorial and additive number theory (CANT 2025)\n
 \nLecture held in CUNY Graduate Center - Science Center (4th floor).\n\nAb
 stract\nWe consider the problem of bounding the number of exceptional proj
 ections (projections which are smaller than typical)  of a subset of a vec
 tor space over a finite field.  We establish bounds that depend on $L^p$ e
 stimates for the Fourier transform\, improving various known bounds for se
 ts with sufficiently good Fourier analytic properties.  The special case $
 p=2$ recovers a recent result of Bright and Gan (following Chen)\, which e
 stablished the finite field analogue of Peres--Schlag's bounds from the co
 ntinuous setting.\\\\\nWe prove several auxiliary results of independent i
 nterest\, including a character sum identity for subspaces (solving a prob
 lem of Chen)\, and an analogue of Plancherel's theorem for subspaces. Thes
 e auxiliary results also have applications in affine incidence geometry\, 
 that is\, the problem of estimating the number of incidences between a set
  of points and a set of affine $k$-planes. We present a novel and direct p
 roof of a well-known result in this area that avoids the use of spectral g
 raph theory\, and we provide simple examples demonstrating that these esti
 mates are sharp up to constants.  \\\\\nThis is joint work with Jonathan F
 raser.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorg Brudern (Universitat Gottingen)
DTSTART:20250521T163000Z
DTEND:20250521T165500Z
DTSTAMP:20260404T094912Z
UID:CANT2025/65
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANT2
 025/65/">Expander estimates for cubes</a>\nby Jorg Brudern (Universitat Go
 ttingen) as part of Combinatorial and additive number theory (CANT 2025)\n
 \nLecture held in CUNY Graduate Center - Science Center (4th floor).\n\nAb
 stract\nSuppose that $\\mathcal A$ is a subset of the natural numbers. The
  supremum $\\alpha$ of all $t$ with \n$$ \\limsup N^{-t} \\#\\{a\\in{\\mat
 hcal 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\\in {\\mathbb N}\, \\\, a\\in{\\mathcal A}\\}.$$\nIt is easy to see t
 hat $\\beta_2= \\min (1\, \\frac12 +\\alpha).$ One might guess that\n$$ \\
 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 due to Davenport\, and are 80 years old. In this interim report on on
 going work with Simon Myerson\, we describe a method \nfor $k=3$ that impr
 oves Davenport's results when $\\alpha>3/5$\, and that confirms (*) in an 
 interval $(\\alpha_0\, 1]$. A concrete value for $\\alpha_0$ will be relea
 sed during the talk\, and if time permits\, we also discuss the perspectiv
 es to generalize the approach to larger values of $k$.\n
LOCATION:https://stable.researchseminars.org/talk/CANT2025/65/
END:VEVENT
END:VCALENDAR