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BEGIN:VEVENT
SUMMARY:Emma Bailey (CUNY Graduate Center)
DTSTART:20220524T130000Z
DTEND:20220524T132500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/1/"
 >Large deviations of Selberg's central limit theorem</a>\nby Emma Bailey (
 CUNY Graduate Center) as part of Combinatorial and additive number theory 
 (CANT 2022)\n\n\nAbstract\nSelberg's celebrated central limit theorem show
 s that $\\log\\zeta(1/2+\\rm{i} t)$ at a typical point $t$ at height $T$ b
 ehaves like a complex\, centered Gaussian random variable with variance $\
 \log\\log T$. This talk will present recent results showing that the Gauss
 ian decay persists in the large deviation regime\, at a level on the order
  of the variance\, improving on the best known bounds in that range. Time 
 permitting\, we will also present various applications\, including on the 
 maximum of the zeta function in short intervals. \n\nThis work is joint wi
 th Louis-Pierre Arguin.\n
LOCATION:https://researchseminars.org/talk/CANT2022/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorg Brudern (Universitat Gottingen)
DTSTART:20220524T133000Z
DTEND:20220524T135500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/2/"
 >Bracketed ternary additive problems</a>\nby Jorg Brudern (Universitat Got
 tingen) as part of Combinatorial and additive number theory (CANT 2022)\n\
 n\nAbstract\nThe ternary additive problems of Waring's type (that is\, sum
 s of three potentially unlike powers) have attracted many workers in the a
 dditive theory of numbers. In this talk\, we discuss several variants that
  involve brackets (that is\, the integer part of certain monomials).\n
LOCATION:https://researchseminars.org/talk/CANT2022/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gautami Bhowmik (Universite de Lille)
DTSTART:20220524T143000Z
DTEND:20220524T145500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/4/"
 >Siegel zeros under Goldbach conjectures</a>\nby Gautami Bhowmik (Universi
 te de Lille) as part of Combinatorial and additive number theory (CANT 202
 2)\n\n\nAbstract\nA Landau-Siegel zero is a possible though unwelcome  cou
 nter-example to the  Generalised Riemann Hypothesis. \nProving its absence
  unconditionally is clearly a difficult problem. We will discuss some resu
 lts by assuming plausible\nconjectures on the Goldbach problem: the  Hardy
 -Litllewood one (1923)\, a weak form due to Fei (2016)\, and a \nweaker fo
 rm that we studied more recently (Bhowmik-Halupczok\, \nin: Proceedings of
  CANT 2019 and 2020). Continuing on these lines\,\nFriedlander-Goldston-Iw
 aniec-Suriajaya (2022) showed that the assumption of Fei's conjecture is e
 nough to disprove the existence of Siegel zeros.\n
LOCATION:https://researchseminars.org/talk/CANT2022/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wijit Yangjit (University of Michigan)
DTSTART:20220527T193000Z
DTEND:20220527T195500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/5/"
 >On the Montgomery–Vaughan weighted generalization of Hilbert's inequali
 ty</a>\nby Wijit Yangjit (University of Michigan) as part of Combinatorial
  and additive number theory (CANT 2022)\n\n\nAbstract\nHilbert's inequalit
 y states that\n$$\n\\left\\vert\\sum_{m=1}^N\\sum_{n=1\\atop n\\neq m}^N\\
 frac{z_m\\overline{z_n}}{m-n}\\right\\vert\\le C_0\\sum_{n=1}^N\\left\\ver
 t z_n\\right\\vert^2\,\n$$\nwhere $C_0$ is an absolute constant. In 1911\,
  Schur showed that the optimal value of $C_0$ is $\\pi$.\n\nIn 1974\, Mont
 gomery and Vaughan proved a weighted generalization of Hilbert's inequalit
 y and used it to estimate mean values of Dirichlet series. This generalize
 d Hilbert inequality is important in the theory of the large sieve. The op
 timal constant $C$ in this inequality is known to satisfy $\\pi\\le C<\\pi
 +1$. It is widely conjectured that $C=\\pi$. In this talk\, I will describ
 e the known approaches to obtain an upper bound for $C$\, which proceed vi
 a a special case of a parametric family of inequalities. We analyze the op
 timal constants in this family of inequalities. A corollary is that the me
 thod in its current form cannot imply an upper bound for $C$ below $3.19$.
 \n
LOCATION:https://researchseminars.org/talk/CANT2022/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Trevor D. Wooley (Purdue University)
DTSTART:20220524T153000Z
DTEND:20220524T155500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/6/"
 >Shifted analogues of the divisor function</a>\nby Trevor D. Wooley (Purdu
 e University) as part of Combinatorial and additive number theory (CANT 20
 22)\n\n\nAbstract\nSuppose that $\\theta$ is irrational. Then almost all e
 lements \n$\\nu\\in \\mathbb Z[\\theta]$ that may be written as a $k$-fold
  product of the shifted integers \n$n+\\theta$ $(n\\in \\mathbb N)$ are th
 us represented essentially uniquely. We discuss this and related paucity p
 roblems. \n\nMost of this work is joint with Winston Heap and Anurag Sahay
 .\n
LOCATION:https://researchseminars.org/talk/CANT2022/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huy Pham (Stanford University)
DTSTART:20220524T170000Z
DTEND:20220524T172500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/7/"
 >Homogeneous structures in subset sums and applications</a>\nby Huy Pham (
 Stanford University) as part of Combinatorial and additive number theory (
 CANT 2022)\n\n\nAbstract\nIn recent joint works with David Conlon and Jaco
 b Fox\, we develop novel techniques which allow us to prove a diverse rang
 e of results relating to subset sums. In the one-dimensional case\, our te
 chniques imply the existence of long homogeneous arithmetic progressions i
 n the set of subset sums under a variety of assumptions. This allows us to
  resolve a number of longstanding open problems\, including: solutions to 
 the three problems of Burr and Erdos on Ramsey complete sequences\, for wh
 ich Erdos later offered a combined total of 350\; analogous results for th
 e new notion of density complete sequences\; the solution to a conjecture 
 of Alon and Erdos on the minimum number of colors needed to color the posi
 tive integers less than n so that n cannot be written as a monochromatic s
 um\; the exact determination of an extremal function introduced by Erdos a
 nd Graham on sets of integers avoiding a given subset sum\; and\, answerin
 g a question reiterated by several authors\, a homogeneous strengthening o
 f a result of Szemeredi and Vu on long arithmetic progressions in subset s
 ums. In follow-up work in the multi-dimensional case\, we show the existen
 ce of large homogeneous generalized arithmetic progressions in the set of 
 subset sums of sufficiently large subsets of [n]\, yielding a strengthenin
 g of a seminal result of Szemeredi and Vu. As an application\, we make pro
 gress on the Erdos--Straus non-averaging sets problem\, showing that every
  subset A of [n] of size at least n^{\\sqrt{2} - 1 + o(1)} contains an ele
 ment which is the average of two or more other elements of A. This gives t
 he first polynomial improvement on a result of Erdos and Sarkozy from 1990
 .\n
LOCATION:https://researchseminars.org/talk/CANT2022/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krystian Gajdzica (Jagiellonian University\, Poland)
DTSTART:20220524T173000Z
DTEND:20220524T175500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/8/"
 >Some inequalities for the multicolor restricted partition function $p_\\m
 athcal{A}(n\,k)$</a>\nby Krystian Gajdzica (Jagiellonian University\, Pola
 nd) as part of Combinatorial and additive number theory (CANT 2022)\n\n\nA
 bstract\nFor a non-decreasing sequence of positive integers $\\mathcal{A}=
 \\left(a_i\\right)_{i=1}^\\infty$ and a fixed integer $k\\geqslant1$\, the
  multicolor restricted partition function $p_\\mathcal{A}(n\,k)$ counts th
 e number of partitions of $n$ with parts in the multiset $\\{a_1\,a_2\,\\l
 dots\,a_k\\}$. The talk is devoted to some multiplicative inequalities rel
 ated to $p_\\mathcal{A}(n\,k)$. Among other things\, we will examine: the 
 Bessenrodt-Ono inequality for $p_\\mathcal{A}(n\,k)$\, the $\\log$-concavi
 ty of the sequence $\\left(p_\\mathcal{A}(n\,k)\\right)_{n=1}^\\infty$\, t
 he\nhigher order Tur\\'an property and other similar phenomena.\n
LOCATION:https://researchseminars.org/talk/CANT2022/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Sellers (University of Minnesota Duluth)
DTSTART:20220524T180000Z
DTEND:20220524T182500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/9/"
 >Relating the crank of a partition and smallest missing parts</a>\nby Jame
 s Sellers (University of Minnesota Duluth) as part of Combinatorial and ad
 ditive number theory (CANT 2022)\n\n\nAbstract\nThe primary goal of this t
 alk is to demonstrate a natural connection between the smallest missing pa
 rt of an integer partition (commonly referred to as the ``mex" of the part
 ition) and the concept of the crank of a partition. After providing a brie
 f history of the crank of a partition a la Dyson as well as Andrews and Ga
 rvan\, we will utilize straightforward generating function manipulations t
 o make this connection. We will then consider additional results on the me
 x statistic based on parity\, and we will also demonstrate connections bet
 ween the crank and Frobenius symbols which satisfy certain conditions. \n\
 nThis work is joint with Brian Hopkins\, Dennis Stanton\, and Ae Ja Yee.\n
LOCATION:https://researchseminars.org/talk/CANT2022/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Guo (Rutgers University - Newark)
DTSTART:20220524T190000Z
DTEND:20220524T192500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/10/
 ">Renormalization of quasisymmetric functions</a>\nby Li Guo (Rutgers Univ
 ersity - Newark) as part of Combinatorial and additive number theory (CANT
  2022)\n\n\nAbstract\nThe algebra of quasisymmetric functions (QSym) has p
 layed a central role in multiple zeta values and a\nlarge class of combina
 torial algebraic structures related to symmetric functions. A natural line
 ar basis of QSym is the set of monomial quasisymmetric functions defined b
 y compositions\, that is\,\nvectors of positive integers.  Extending such 
 a definition for weak compositions\, that is\, vectors\nof nonnegative int
 egers\, leads to divergent expressions. This phenomenon is closely related
  to the divergency of multiple zeta values with nonpositive integer argume
 nts. \n\nWe apply\nthe method of renormalization in the spirit of Connes a
 nd Kreimer to address  \nthe divergency\, and realize weak composition\nqu
 asisymmetric functions as power series. \nThe resulting Hopf algebra has t
 he Hopf algebra of\nquasisymmetric functions as both a Hopf subalgebra and
  a Hopf quotient algebra. \n\nThis is joint work with Houyi Yu and Bin Zha
 ng.\n
LOCATION:https://researchseminars.org/talk/CANT2022/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johann Thiel (New York City College of Technology (CUNY))
DTSTART:20220524T193000Z
DTEND:20220524T195500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/11/
 ">Solving the membership problem for certain subgroups of $SL_2(\\mathbb{Z
 })$</a>\nby Johann Thiel (New York City College of Technology (CUNY)) as p
 art of Combinatorial and additive number theory (CANT 2022)\n\n\nAbstract\
 nFor positive integers $u$ and $v$\, let $L_u=\\begin{bmatrix} 1 & 0 \\\\ 
 u & 1 \\end{bmatrix}$ and $R_v=\\begin{bmatrix} 1 & v \\\\ 0 & 1 \\end{bma
 trix}$. Let $G_{u\,v}$ be the group generated by $L_u$ and $R_v$. The memb
 ership problem for $G_{u\,v}$ asks the following question: Given a 2-by-2 
 matrix $M=\\begin{bmatrix}a & b \\\\c & d\\end{bmatrix}$\, is there a rela
 tively straightforward method for determining if $M$ is a member of $G_{u\
 ,v}$? In the case where $u=2$ and $v=2$\, Sanov was able to show that simp
 ly checking some divisibility conditions for $a$\, $b$\, $c$ and $d$ is en
 ough to make this determination. We answered this question in the case whe
 re $u\,v\\geq 3$ by finding a characterization of matrices $M$ in $G_{u\,v
 }$ in terms of the short continued fraction representation of $\\frac{b}{d
 }$\, extending some results of Esbelin and Gutan. By modifying our previou
 s work\, we are able to further extend our previous result to the more dif
 ficult case where $u\,v\\geq 2$ with $uv\\neq 4$.\n\nThis is joint work wi
 th Sandie Han\, Ariane M. Masuda\, and Satyanand Singh.\n
LOCATION:https://researchseminars.org/talk/CANT2022/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi Hoi Yip (University of British Columbia)
DTSTART:20220524T200000Z
DTEND:20220524T202500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/12/
 ">Asymptotics for the number of directions determined by $[n] \\times [n]$
  in $\\mathbb{F}_p^2$</a>\nby Chi Hoi Yip (University of British Columbia)
  as part of Combinatorial and additive number theory (CANT 2022)\n\n\nAbst
 ract\nLet $p$ be a prime and $n$ a positive integer such that $\\sqrt{\\fr
 ac p2} + 1 \\leq n \\leq \\sqrt{p}$. For any arithmetic progression $A$ of
  length $n$ in $\\mathbb{F}_p$\, we establish an asymptotic formula for th
 e number of directions determined by $A \\times A \\subset \\mathbb{F}_p^2
 $. The key idea is to reduce the problem to counting the number of solutio
 ns to the bilinear Diophantine equation $ad+bc=p$ in variables $1\\le a\,b
 \,c\,d\\le n$\; our asymptotic formula for the number of solutions is of i
 ndependent interest. \n\nJoint work with Greg Martin and Ethan White.\n
LOCATION:https://researchseminars.org/talk/CANT2022/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ethan Patrick White (University of British Columbia)
DTSTART:20220524T203000Z
DTEND:20220524T205500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/13/
 ">Erdos' minimum overlap problem</a>\nby Ethan Patrick White (University o
 f British Columbia) as part of Combinatorial and additive number theory (C
 ANT 2022)\n\n\nAbstract\nIn 1955 Erd\\H{o}s posed the following problem. L
 et $n$ be a positive integer and $A\,B \\subset [2n    A weighted generali
 zation of classical zero-sum constants\nwas introduced by Adhikari {\\it e
 t al.} in 2006 and has been an active area of research since then. In the 
 last fifteen years\, weighted zero-sum constants for $\\mathbb {Z}_n$ with
  several interesting weight sets have been found.\nIn this talk\, we take 
 up the problem of determining the exact values and providing bounds of the
  weighted Davenport constant of $\\mathbb {Z}_n$  \nwith some new weight s
 ets.\n\nNext\, we consider a weighted generalization of the {\\it the Erd\
 \H{o}s-Ginzburg-Ziv constant}. \nLet $G$ be a  finite abelian group with $
 \\exp(G)=n$. For a positive integer $k$ and a non-empty subset $A$ of $[1\
 , n-1]$\,\nthe arithmetical invariant $\\mathsf s_{kn\,A}(G)$  is defined 
 to be the  least positive integer $t$ such that\nany sequence $S$ of $t$ e
 lements in $G$ has an $A$-{\\it weighted zero-sum subsequence} of  length 
 $kn$.\nWe give the exact value of $\\mathsf s_{kq\,A}(G)$\, for integers $
 k\\geq 2$ and $A=\\{1\,2\\}$\,\nwhere $G$ is an abelian $p$-group with $ra
 nk(G)\\leq 4$\, $p$ is an odd prime  and $exp(G)=q$.\nOur method consists 
 of a modification of a polynomial method \nof R\\'onyai.\n\nLastly\, we co
 nsider the questions regarding inverse problems for the weighted zero-sum 
 constants of $\\mathbb {Z}_n$. An inverse problem is the problem of charac
 terizing all the weighted {\\it zero-sum free sequences} over $\\mathbb {Z
 }_n$ of specific lengths for the particular weight sets under consideratio
 n.\n\nThis work was joint with Sukumar Das Adhikari and partly with Md Ibr
 ahim Molla and Subha Sarkar.\n]$ be a partition of $[2n]$ such that $|A|=|
 B| = n$. For any such partition and integer $-2n<k<2n$\, define $M_k$ to b
 e the number of solutions $(a\,b) \\in A  \\times B$ to $a-b = k$. Estimat
 e the size of the function\n\\[ M(n) = \\min_{A\\cup B = [2n]} \\max_{-2n<
 k<2n} M_k\,\\]\nwhere the minimum is taken over all partitions of $[2n]$ i
 nto equal-sized sets. Many upper and lower estimates were obtained over th
 e following decades\, and the state of the art is $0.356 < M(n)/n < 0.381$
 . We use elementary Fourier analysis to translate the problem to a convex 
 optimization program and obtain the new lower bound $M(n)/n>0.379$.\n
LOCATION:https://researchseminars.org/talk/CANT2022/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Baily (Williams College)
DTSTART:20220524T183000Z
DTEND:20220524T185500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/14/
 ">Large sets are sumsets</a>\nby Benjamin Baily (Williams College) as part
  of Combinatorial and additive number theory (CANT 2022)\n\n\nAbstract\nLe
 t $[n] :=\\{0\,1\,2\,\\dots\,n\\}$. Intuitively\, all large subsets of $[n
 ]$ have additive structure\, and Roth famously made this precise by\nfindi
 ng constants $c$\, $N > 0$ such that for $n \\geq N$\, any subset of $[n]$
  containing more than $\\frac{cn}{\\log\\log n}$ elements must contain an\
 narithmetic progression of length $3$. We establish a different interpreta
 tion of the intuition by finding explicit constants $\\alpha = \\frac{1}{\
 \log\n2}$ and $\\beta = \\frac{1}{\\log 1.325}$ such that\, for sufficient
 ly large $n$\, we have:\n\\begin{enumerate}\n\\item[(i)] any subset of $[n
 ]$ with more than $n-\\alpha \\log n$ elements has a nontrivial decomposit
 ion as the sum of two sets\, and\n\n\\item [(ii)]there exists a subset of 
 $[n]$ of size $n - \\beta \\log n$ at least  that has no such decompositio
 n.\n\n\\end{enumerate} We also prove\, using these methods\, a higher-dime
 nsional\nanalogue of results (i) and (ii). Notably\, our threshold at whic
 h\nstructure appears is far higher than Roth's.\n\nThis work was joint wit
 h Justine Dell\, Sophia Dever\, Adam Dionne\, Faye\nJackson\, Leo Goldmakh
 er\, Gal Gross\, Steven J. Miller\, Ethan Pesikoff\, Huy\nTuan Pham\, Luke
  Reifenberg\, and Vidya Venkatesh.     \\\\\n
LOCATION:https://researchseminars.org/talk/CANT2022/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shruti S Hegde (Ramakrishna Mission Vivekananda Educational and Re
 search Institute\, India)
DTSTART:20220525T130000Z
DTEND:20220525T132500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/15/
 ">Weighted zero-sum constants and inverse results</a>\nby Shruti S Hegde (
 Ramakrishna Mission Vivekananda Educational and Research Institute\, India
 ) as part of Combinatorial and additive number theory (CANT 2022)\n\n\nAbs
 tract\nA weighted generalization of classical zero-sum constants\nwas intr
 oduced by Adhikari et al. in 2006 and has been an active area of research 
 since then. In the last fifteen years\, weighted zero-sum constants for $\
 \mathbb {Z}_n$ with several interesting weight sets have been found.\nIn t
 his talk\, we take up the problem of determining the exact values and prov
 iding bounds of weighted Davenport constant of $\\mathbb {Z}_n$  \nwith so
 me new weight sets.\n\nNext\, we consider a weighted generalization of the
  Erd\\H{o}s-Ginzburg-Ziv constant. \nLet $G$ be a  finite abelian group wi
 th $\\exp(G)=n$. For a positive integer $k$ and a non-empty subset $A$ of 
 $[1\, n-1]$\,\nthe arithmetical invariant $\\mathsf s_{kn\,A}(G)$  is defi
 ned to be the  least positive integer $t$ such that\nany sequence of $t$ e
 lements in $G$ has an $A$- weighted zero-sum subsequence of  length $kn$.\
 nWe give the exact value of $\\mathsf s_{kq\,A}(G)$\, for integers $k\\geq
  2$ and $A=\\{1\,2\\}$\,\nwhen $G$ is an abelian $p$-group with $rank(G)\\
 leq 4$\, $p$ is an odd prime  and $exp(G)=q$.\nOur method consists of a mo
 dification of a polynomial method \nof R\\'onyai.\n\nLastly\, we consider 
 the questions regarding inverse problems for the weighted zero-sum constan
 ts of $\\mathbb {Z}_n$. An inverse problem is a problem of characterizing 
 all the weighted {\\it zero-sum free sequences} over $\\mathbb {Z}_n$ of s
 pecific lengths for the particular weight sets under consideration.\n\nThi
 s work was joint with Sukumar Das Adhikari and partly with Md Ibrahim Moll
 a and Subha Sarkar.\n
LOCATION:https://researchseminars.org/talk/CANT2022/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Somlai (Eotvos Lorand University and   Alfred Renyi Institut
 e of Mathematics)
DTSTART:20220525T133000Z
DTEND:20220525T135500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/17/
 ">Fuglede's conjecture\, the one dimensional case</a>\nby Gabor Somlai (Eo
 tvos Lorand University and   Alfred Renyi Institute of Mathematics) as par
 t of Combinatorial and additive number theory (CANT 2022)\n\n\nAbstract\nF
 uglede conjectured that a bounded measurable set (in $\\mathbb{R}^n$) is s
 pectral if and only if it is a tile. The conjecture was also confirmed by 
 Fuglede for sets whose tiling complement is lattice and for spectral sets 
 one of whose spectrums is a lattice. \nThe conjecture was disproved by Tao
  by constructing a spectral set in $\\mathbb{Z}_3^5$\, which is not a tile
  and lifted it to the $5$ dimensional Euclidean space. \n\nThe conjecture 
 is open only in dimensions 1 and 2. The 1 dimensional case is directly con
 nected with the one of finite cyclic groups and to the so called Coven-Mey
 erowitz conjecture. One of the main aims of the talk is to present some of
  the methods developed that lead to our recent results.\n
LOCATION:https://researchseminars.org/talk/CANT2022/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Fel (Technion -- Israel Institute of Technology\, Israel)
DTSTART:20220525T140000Z
DTEND:20220525T142500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/18/
 ">Commutative monoid of self-dual symmetric polynomials</a>\nby Leonid Fel
  (Technion -- Israel Institute of Technology\, Israel) as part of Combinat
 orial and additive number theory (CANT 2022)\n\n\nAbstract\nWe consider a 
 set ${\\mathfrak R}{\\mathfrak S}\\left(\\lambda\,S_n\\right)$ of self-\na
 nd skew-reciprocal polynomials in $\\lambda$\, of degree $mn$\, where $m\\
 in{\n\\mathbb Z}_{\\geq}$\, $n\\in{\\mathbb Z}_>$\, based on polynomial in
 variants $I_{n\,\nr}({\\bf x}^n)$ of symmetric group $S_n$\, acting on the
  Euclidean space ${\\mathbb\nE}^n$ over the field of real numbers ${\\math
 bb R}$\, where ${\\bf x^n}=\\{x_1\,\n\\ldots\,x_n\\}\\in{\\mathbb E}^n$. W
 e prove that ${\\mathfrak R}{\\mathfrak S}\\left(\n\\lambda\,S_n\\right)$ 
 exhibits a commutative monoid under multiplication. Real\nsolutions $\\lam
 bda\\left({\\bf x^n}\\right)$ of skew-reciprocal equations have\nmany rema
 rkable properties: a homogeneity of the 1st order\, a duality under\ninver
 sion of variables $x_i\\to x_i^{-1}$ and function $\\lambda\\to\\lambda^{-
 1}$\,\na monotony of $\\lambda\\left({\\bf x^n}\\right)$ with respect to e
 very $x_i$ and\nothers. We find the bounds of $\\lambda\\left({\\bf x^n}\\
 right)$ which are given \nby arithmetic and harmonic means of the set $\\{
 x_1\,\\ldots\,x_n\\}$.\n
LOCATION:https://researchseminars.org/talk/CANT2022/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Konieczny (Claude Bernard University Lyon 1\, France)
DTSTART:20220525T143000Z
DTEND:20220525T145500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/19/
 ">Automatic semigroups</a>\nby Jakub Konieczny (Claude Bernard University 
 Lyon 1\, France) as part of Combinatorial and additive number theory (CANT
  2022)\n\n\nAbstract\nAutomatic sequences\, that is\, sequences computable
  by finite automata\, have been extensively studied from a variety of pers
 pectives\, including combinatorics\, number theory\, dynamics and theoreti
 cal computer science. Classification problems are a natural class of quest
 ions in the theory of automatic sequences. In particular\, the problem of 
 classifying automatic multiplicative sequences has attracted considerable 
 attention\, culminating in complete classification which we obtained in jo
 int work with Clemens M\\"{u}llner and Mariusz Lema\\'{n}czyk. The subject
  of my talk will be an extension of this line of inquiry\, which we pursue
  in joint work with Oleksiy Klurman. Under mild technical assumptions\, we
  classify all automatic multiplicative semigroups\, that is\, all sets $E$
  of integers which are closed under multiplication and such that the indic
 ator function $1_E$ is automatic. Additionally\, we show (again\, under mi
 ld technical assumptions) that if $E\,F$ are automatic sets with $E \\cdot
  F \\subset E$ then $E$   must contain a large essentially periodic compon
 ent. This leads to potentially interesting open problems concerning produc
 ts of automatic sets.\n
LOCATION:https://researchseminars.org/talk/CANT2022/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Pal Pach (TU Budapest)
DTSTART:20220525T150000Z
DTEND:20220525T152500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/20/
 ">Colouring the smooth numbers</a>\nby Peter Pal Pach (TU Budapest) as par
 t of Combinatorial and additive number theory (CANT 2022)\n\n\nAbstract\nF
 or a given $n$\, can we colour the positive integers using precisely $n$ c
 olours in such a way that for any $a$\, the numbers $a\, 2a\, \\dots\, na$
  all get different colours? This question is still open in general. I will
  present a survey of known results and some other problems it leads to. \n
 \nThis is joint work with Andros Caicedo and Thomas Chartier.\n
LOCATION:https://researchseminars.org/talk/CANT2022/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Duker Lichtman (University of Oxford)
DTSTART:20220525T153000Z
DTEND:20220525T155500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/21/
 ">A proof of the Erdos primitive set conjecture</a>\nby Jared Duker Lichtm
 an (University of Oxford) as part of Combinatorial and additive number the
 ory (CANT 2022)\n\n\nAbstract\nA set of integers greater than 1 is primiti
 ve if no member in the set divides another. Erdos proved in 1935 that the 
 series of $1/(n\\log n)$\, ranging over $n$ in $A$\, is uniformly bounded 
 over all choices of primitive sets $A$. In 1988 he asked if this bound is 
 attained for the set of prime numbers. In this talk we describe recent wor
 k which answers Erdos' conjecture in the affirmative. We will also discuss
  applications to old questions of Erdos\, Sarkozy\, and Szemeredi from the
  1960s.\n
LOCATION:https://researchseminars.org/talk/CANT2022/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Wenqiang Xu (Stanford University)
DTSTART:20220525T170000Z
DTEND:20220525T172500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/22/
 ">On a Turan conjecture and random multiplicative functions</a>\nby Max We
 nqiang Xu (Stanford University) as part of Combinatorial and additive numb
 er theory (CANT 2022)\n\n\nAbstract\nWe show that if $f$ is the random com
 pletely multiplicative function\, \nthe probability that $\\sum_{n\\le x}\
 \frac{f(n)}{n}$ is positive for every $x$ is at least \\\\\n$1-10^{-40}$. 
 For large $x$  we prove an asymptotic upper bound of \\\\\n$O(\\exp(-\\exp
 ( \\frac{\\log x}{C\\log \\log x })))$ on the probability that a particula
 r truncation is negative. 	\nThis is joint work with Rodrigo Angelo.\n
LOCATION:https://researchseminars.org/talk/CANT2022/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Miska (Jagiellonian University\, Krakow\, Poland)
DTSTART:20220525T173000Z
DTEND:20220525T175500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/23/
 ">On (non-)realizibility of Stirling numbers</a>\nby Piotr Miska (Jagiello
 nian University\, Krakow\, Poland) as part of Combinatorial and additive n
 umber theory (CANT 2022)\n\n\nAbstract\nWe say that a sequence $(a_n)_{n\\
 in\\mathbb{N}_+}$ of non-negative integers is realizable if there exists a
  set $X$ and a mapping $T : X \\to X$ such that $a_n$ is the number of fix
 ed points of $T^n$. For each $k \\in\\mathbb{N}_+$ and $j \\in \\{1\,2\\}$
  we define a sequence $S^{(j)}_k =(S^{(j)}(n+k -1\,k))_{n\\in\\mathbb{N}_+
 }$ \, where $S^{(j)}(n\,k)$ is the Stirling number of the $j$-th kind (in 
 case of $j = 1$ we consider unsigned Stirling numbers). The aim of the tal
 k is to prove that $S^{(2)}_k$ is realizable if and only if $k \\in \\{1\,
 2\\}$\, while for $k \\geq 3$ the sequence $S^{(2)}_k$ is almost realizabl
 e with a failure $(k-1)!$\, i. e. $(k-1)!S^{(2)}_k$ is realizable. Moreove
 r\, I will show that for each $k \\in\\mathbb{N}_+$ the sequence $S^{(1)}_
 k$ is not almost realizable\, i. e. for any $r \\in\\mathbb{N}_+$ the sequ
 ence $rS^{(1)}_k$ is not realizable. \n\nThe talk is based on a joint work
  with Tom Ward (Newcastle\, UK).\n
LOCATION:https://researchseminars.org/talk/CANT2022/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qinghai Zhong (University of Graz\, Austria)
DTSTART:20220525T180000Z
DTEND:20220525T182500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/24/
 ">On monoids of  weighted zero-sum sequences</a>\nby Qinghai Zhong (Univer
 sity of Graz\, Austria) as part of Combinatorial and additive number theor
 y (CANT 2022)\n\n\nAbstract\nLet $G$ be an additive finite abelian group a
 nd $\\Gamma \\subset \\operatorname{End} (G)$ be a subset of the endomorph
 ism group of $G$. A sequence $S = g_1 \\cdot \\ldots \\cdot g_{\\ell}$ ove
 r $G$ is a ($\\Gamma$-)weighted zero-sum sequence if there are $\\gamma_1\
 , \\ldots\, \\gamma_{\\ell} \\in \\Gamma$ such that $\\gamma_1 (g_1) + \\l
 dots + \\gamma_{\\ell} (g_{\\ell})=0$.  We study  algebraic and arithmetic
  properties of  monoids of weighted zero-sum sequences.\n
LOCATION:https://researchseminars.org/talk/CANT2022/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sinai Robins (University of Sao Paulo\, Brazil)
DTSTART:20220525T183000Z
DTEND:20220525T185500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/25/
 ">The covariogram and an extension of Siegel's formula</a>\nby Sinai Robin
 s (University of Sao Paulo\, Brazil) as part of Combinatorial and additive
  number theory (CANT 2022)\n\n\nAbstract\nWe extend a formula of Carl Ludw
 ig Siegel in the geometry of numbers.\nSiegel's original formula assumed t
 hat there is exactly one lattice point in the interior of the body\, while
  here\nwe relax that condition\, so that the body may contain an arbitrary
  number of interior lattice points.  Our extension involves a lattice sum 
 of the covariogram for any compact set  $\\mathcal K \\subset \\mathbb{R}^
 d$\,  where the covariogram of $\\mathcal K$ at  $x \\in \\mathbb R^d$ is 
 defined by $\\rm{vol}$$( \\mathcal K \\cap (\\mathcal K + x))$.   \nThe pr
 oof hinges on a variation of the Poisson summation formula which we derive
  here\, and the Fourier methods herein also allow for more general admissi
 ble sets.  One of the consequences of these results is a new characterizat
 ion of multi-tilings of Euclidean space by translations\, using the lower 
 bound on lattice sums of such covariograms.  The classical result known as
  Van der Corput's inequality\, also follows immediately from the main resu
 lt\, as well as a new spectral formula for the volume of a compact set.  \
 n\nThis is joint work with Michel Faleiros Martins.\n
LOCATION:https://researchseminars.org/talk/CANT2022/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (Lehman College (CUNY))
DTSTART:20220525T190000Z
DTEND:20220525T192500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/26/
 ">Multiplicity interpolation of polynomials</a>\nby Mel Nathanson (Lehman 
 College (CUNY)) as part of Combinatorial and additive number theory (CANT 
 2022)\n\n\nAbstract\nInterpolation problems related to the theorems of Des
 cartes\, Budan-Fourier\, and Sturm in the theory of equations.\n
LOCATION:https://researchseminars.org/talk/CANT2022/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Kravitz (Princeton University)
DTSTART:20220525T193000Z
DTEND:20220525T195500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/27/
 ">Zero patterns of derivatives of polynomials</a>\nby Noah Kravitz (Prince
 ton University) as part of Combinatorial and additive number theory (CANT 
 2022)\n\n\nAbstract\nMotivated by recent work of Nathanson\, we study the 
 zero patterns of derivatives of polynomials.  For $P$ a polynomial of degr
 ee $n$ and $\\Lambda=(\\lambda_1\, \\ldots\, \\lambda_m)$ an $m$-tuple of 
 distinct complex numbers\, we consider the $m \\times (n+1)$ \\emph{dope m
 atrix} $D_P(\\Lambda)$ whose $ij$-entry equals $1$ if $P^{(j)}(\\lambda_i)
 =0$ and equals $0$ otherwise (for $1 \\leq i \\leq m$\, $0 \\leq j \\leq n
 $).  We address several natural questions: When $m$ is $1$ or $2$\, what d
 o the possible dope matrices look like\, and how many are there?  What can
  we say about general upper bounds on the number of $m \\times (n+1)$ dope
  matrices?  For which $m$-tuples $\\Lambda$ is the number of $m \\times (n
 +1)$ dope matrices maximized?  Does every $\\{0\,1\\}$-matrix appear as th
 e left-most portion of some dope matrix?  \n\nBased on joint work with Nog
 a Alon and Kevin O'Bryant.\n
LOCATION:https://researchseminars.org/talk/CANT2022/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Yan (Texas A&M University)
DTSTART:20220525T200000Z
DTEND:20220525T202500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/28/
 ">Multivariate  Goncarov polynomials and integer sequences</a>\nby Catheri
 ne Yan (Texas A&M University) as part of Combinatorial and additive number
  theory (CANT 2022)\n\n\nAbstract\nUnivariate delta Gon\\v{c}arov polynomi
 als arise when the classical Gon\\v{c}arov interpolation problem in numeri
 cal analysis is modified by replacing derivatives with delta operators. Wh
 en the delta operator under consideration is the backward difference opera
 tor\, we acquire the univariate difference Gon\\v{c}arov polynomials\, whi
 ch have a combinatorial relation to lattice paths in the plane with a give
 n right boundary. In this talk\, we extend several algebraic and analytic 
 properties of univariate  Gon\\v{c}arov polynomials to the multivariate ca
 se with both the derivative and backward difference operators. We then est
 ablish a combinatorial interpretation of multivariate  Gon\\v{c}arov polyn
 omials in terms of certain constraints on $d$-tuples of integer sequences.
  This motivates a connection between multivariate  Gon\\v{c}arov polynomia
 ls and a higher-dimensional generalized parking function\, the $\\mathbf{U
 }$-parking function\, from which we derive several enumerative results bas
 ed on the theory of delta operators.   \n\nThis talk is based on joint wor
 k with Ayo Adeniran and Lauren Snider.\n
LOCATION:https://researchseminars.org/talk/CANT2022/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yin Choi Cheng (CUNY Graduate Center)
DTSTART:20220525T203000Z
DTEND:20220525T205500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/29/
 ">Order type of shifts of morphic words</a>\nby Yin Choi Cheng (CUNY Gradu
 ate Center) as part of Combinatorial and additive number theory (CANT 2022
 )\n\n\nAbstract\nThe shifts of an infinite word $W=a_0a_1\\cdots$ are the 
 words $W_i=a_ia_{i+1}\\cdots$. As a measure of the complexity of a word $W
 $\, we consider the order-type of the set of shifts\, ordered lexicographi
 cally. We will look at the order-type of shifts of morphic words over a fi
 nite alphabet that are not ultimately periodic. As a concrete example\, we
  give the explicit ordering among shifts of the Thue-Morse word. The order
  type of shifts of the Fibonacci word will be discussed. We then give spec
 ial consideration to uniform morphisms on 3 letters.\n
LOCATION:https://researchseminars.org/talk/CANT2022/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Trudgian (UNSW Canberra at the Australian Defence Force Academ
 y)
DTSTART:20220525T210000Z
DTEND:20220525T212500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/30/
 ">Don’t believe the Fake Mu’s!</a>\nby Tim Trudgian (UNSW Canberra at 
 the Australian Defence Force Academy) as part of Combinatorial and additiv
 e number theory (CANT 2022)\n\n\nAbstract\nPerhaps your favourite sum is b
 iased \\ldots leaning a little towards the negative\, perhaps? Perhaps you
 r sum is suspiciously similar to the Moebius function $\\mu(n)$? What can 
 we do with such fake mu’s? Come along to find out\, and together\, we ca
 n make arithmetic great again!\n\nThis is joint work with Greg Martin (UBC
 ) and Mike Mossinghoff (CCR\, Princeton).\n
LOCATION:https://researchseminars.org/talk/CANT2022/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jin-Hui Fang (Nanjing University of Information Science and Techno
 logy)
DTSTART:20220526T130000Z
DTEND:20220526T132500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/31/
 ">Representation functions avoiding integers with density zero</a>\nby Jin
 -Hui Fang (Nanjing University of Information Science and Technology) as pa
 rt of Combinatorial and additive number theory (CANT 2022)\n\n\nAbstract\n
 For a nonempty set $A$ of integers and any integer $n$\, denote $r_{A}(n)$
  by the number of representations of $n$ of the form $n=a+a'$\, where $a\\
 le a'$ and $a\,a'\\in A$ and $d_{A}(n)$ by the number of pairs $(a\,a')$ w
 ith $a\,a'\\in A$ such that $n=a-a'$. In 2008\, Nathanson considered the r
 epresentation function with infinitely many zeros. Following Nathanson's w
 ork\, we proved that\, for any set $T$ of integers with density zero\, the
 re exists a sequence $A$ of integers such that $r_A(n)=1$ for all integers
  $n\\not\\in T$ and $r_A(n)=0$ for all integers $n\\in T$\, and $d_A(n)=1$
  for all positive integers $n$. We will also present our recent results on
  representation functions.\n
LOCATION:https://researchseminars.org/talk/CANT2022/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Sanna (Politecnico di Torino\, Italy)
DTSTART:20220526T133000Z
DTEND:20220526T135500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/32/
 ">Membership in random ratio sets</a>\nby Carlo Sanna (Politecnico di Tori
 no\, Italy) as part of Combinatorial and additive number theory (CANT 2022
 )\n\n\nAbstract\nLet $\\mathcal{A}$ be a random set constructed by picking
  independently each element of $\\{1\, \\dots\, n\\}$ with probability $\\
 alpha \\in (0\, 1)$.\nSeveral authors studied combinatorial/number-theoret
 ic objects involving $\\mathcal{A}$\, including the sum set $\\mathcal{A} 
 + \\mathcal{A}$\, the product set $\\mathcal{A}\\mathcal{A}$\, and the rat
 io set $\\mathcal{A} /\\! \\mathcal{A}$.\nGeneralizing a previous result o
 f Cilleruelo and Guijarro-Ord\\'{o}\\~{n}ez\, we give a formula for the pr
 obability that a rational number $q$ belongs to the ratio set $\\mathcal{A
 } /\\! \\mathcal{A}$.\nMoreover\, we give some results about formulas for 
 the probability of the event $\\bigvee_{i=1}^k\\!\\big(q_i \\in \\mathcal{
 A} /\\! \\mathcal{A}\\big)$\, where $q_1\, \\dots\, q_k$ are rational numb
 ers\, showing that they are related to the study of the connected componen
 ts of certain graphs.\nFinally\, we provide some open question for future 
 research.\n
LOCATION:https://researchseminars.org/talk/CANT2022/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norbert Hegyvari (Eotvos Lorand University and   Alfred Renyi Inst
 itute of Mathematics\, Hungary)
DTSTART:20220526T140000Z
DTEND:20220526T142500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/33/
 ">Boolean functions defined on pseudo-recursive sequences</a>\nby Norbert 
 Hegyvari (Eotvos Lorand University and   Alfred Renyi Institute of Mathema
 tics\, Hungary) as part of Combinatorial and additive number theory (CANT 
 2022)\n\n\nAbstract\nWe define Boolean functions on hypergraphs with edges
  having big intersections\, and an opposite situation\, \nhypergraphs whic
 h are thinly intersective induced by pseudo-recursive sequences. As a main
  result\, we estimate the cardinality of their supports.\nA sequence $X$ i
 s said to be pseudo-recursive (or pesudo-linear) sequence if the identity\
 n$x_{n+1}=M\\cdot x_n+ b_{j_{n+1}}$ holds\, where $ b_{j_{n+1}}\\in \\{b_1
 \,b_2\, \\dots b_k\\}$) for $n \\geq 0$ and $M$ is a positive integer. (Th
 is type of sequences have a long list in the combinatorial number theory a
 nd other areas too\, e.g. in random walk theory). \n\n The tools come from
  additive combinatorics and the uncertainty inequality.\n
LOCATION:https://researchseminars.org/talk/CANT2022/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Senger (Missouri State University)
DTSTART:20220526T143000Z
DTEND:20220526T145500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/34/
 ">Distinct dot products\, convexity\, and AA+1</a>\nby Steven Senger (Miss
 ouri State University) as part of Combinatorial and additive number theory
  (CANT 2022)\n\n\nAbstract\nWe discuss recent developments in estimating t
 he number of distinct dot products determined by a large finite set of $n$
  points in the plane. The improvement comes from improved understanding of
  the multiplicative structure of an additively shifted product set\, $AA+1
 \,$ when $A$ is a large finite subset of the real numbers. This breakthrou
 gh was made possible by new additive combinatorial results about convex se
 ts of numbers.\n
LOCATION:https://researchseminars.org/talk/CANT2022/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gergely Kiss (Alfred Renyi Institute of Mathematics\, Hungary)
DTSTART:20220526T150000Z
DTEND:20220526T152500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/35/
 ">Fuglede's conjecture on the direct product of finite abelian groups</a>\
 nby Gergely Kiss (Alfred Renyi Institute of Mathematics\, Hungary) as part
  of Combinatorial and additive number theory (CANT 2022)\n\n\nAbstract\nWe
  investigate Fuglede's conjecture on the direct product of abelian groups 
 and its connection to the conjecture in $\\mathbb{R}^n$ for $n\\ge 2$. We 
 overview the earlier results: Some important constructions will be shown\,
  which disproves the conjecture in higher dimensions\, and some techniques
  and ideas will be presented\, which serves to prove the conjecture for ce
 rtain abelian groups. Finally we will discuss some developments of the mos
 t recent directions of research. This talk is closely related to the talk 
 of Gábor Somlai's about Fuglede's conjecture in the cyclic group and the 
 one dimensional cases.\n
LOCATION:https://researchseminars.org/talk/CANT2022/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renling Jin (College of Charleston)
DTSTART:20220526T153000Z
DTEND:20220526T155500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/36/
 ">Hyper-hyper-hyper-integers</a>\nby Renling Jin (College of Charleston) a
 s part of Combinatorial and additive number theory (CANT 2022)\n\n\nAbstra
 ct\nIn a conference five years ago\, T. Tao reported \nhis effort to simpl
 ify Szemer\\'{e}di's original combinatorial proof of \nSzemer\\'{e}di's th
 eorem using nonstandard analysis. \nWe continued his effort and presented 
 a simple proof of\nthe theorem for $k=4$ in CANT 2020. In this talk\, we w
 ill present \na simple proof of the theorem for all $k$. One of the main s
 implifications\nis that a Tower of Hanoi type induction used by Szemer\\'{
 e}di as well as Tao\nis replaced by a straightforward induction. In the pr
 oof the integers with\nthree levels of infinities are used.\n
LOCATION:https://researchseminars.org/talk/CANT2022/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Greenfeld (UCLA)
DTSTART:20220526T170000Z
DTEND:20220526T172500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/37/
 ">Translational tilings</a>\nby Rachel Greenfeld (UCLA) as part of Combina
 torial and additive number theory (CANT 2022)\n\n\nAbstract\nTranslational
  tiling is a covering of a space using translated copies of some building 
 blocks\, called the "tiles" without any positive measure overlaps. Which a
 re the possible ways that a space can be tiled? In the talk\, we will disc
 uss the study of this question as well as its applications\, and report on
  recent progress\, joint with Terence Tao.\n
LOCATION:https://researchseminars.org/talk/CANT2022/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thai Hoang Le (University of Mississippi)
DTSTART:20220526T173000Z
DTEND:20220526T175500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/38/
 ">Bohr sets in sumsets in countable abelian groups</a>\nby Thai Hoang Le (
 University of Mississippi) as part of Combinatorial and additive number th
 eory (CANT 2022)\n\n\nAbstract\nA \\textit{Bohr set} in an abelian topolog
 ical group $G$ is a subset of the form\n\\[\nB(K\, \\epsilon) = \\{ g \\in
  G: |\\chi(g) - 1| < \\epsilon \\\, \\forall \\chi \\in K \\}\n\\]\nwhere 
 $K$ is a finite subset of the dual group $\\widehat{G}$. A classical theor
 em of Bogolyubov says that if $A \\subset \\mathbf{Z}$ has positive upper 
 density $\\delta$\, then $A+A-A-A$ contains a Bohr set $B(K\, \\epsilon)$ 
 where $|K|$ and $\\epsilon$ depend only on $\\delta$. While the same state
 ment for $A-A$ is not true (a result of K\\v{r}\\'i\\v{z})\, Bergelson and
  Ruzsa proved that if $r+s+t=0$\, then $rA + sA+tA$ contains a Bohr set (h
 ere $rA = \\{ ra: a \\in A \\}$). \nWe   investigate this phenomenon in mo
 re general groups $G$\, where $rA\, sA\, tA$ are replaced by images of $A$
  under certain endomomorphisms of $G$. It is also natural to ask for parti
 tion analogues of the Bergelson-Ruzsa theorem. In CANT 2021\, I discussed 
 our results in compact abelian groups (generalizations of $\\mathbf{R} /\\
 mathbf{Z}$). \\\nIn this talk\, I will discuss our progress on countable d
 iscrete abelian groups (generalizations of $\\mathbf{Z}$). The key ingredi
 ents are certain transference principles which allow us to transfer the re
 sults from compact groups to discrete countable groups. \nThis talk is bas
 ed on joint works with Anh Le\, and with Anh Le and John Griesmer.\n
LOCATION:https://researchseminars.org/talk/CANT2022/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Pollack (University of Georgia)
DTSTART:20220526T180000Z
DTEND:20220526T182500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/39/
 ">Weak uniform distribution of certain arithmetic functions</a>\nby Paul P
 ollack (University of Georgia) as part of Combinatorial and additive numbe
 r theory (CANT 2022)\n\n\nAbstract\nFor any fixed integer $q$\, it is a cl
 assical result (implicit in work of Landau\, and perhaps known earlier) th
 at Euler's function $\\phi(n)$ is a multiple of $q$ asymptotically 100\\% 
 of the time. Thus\, $\\phi(n)$ is very far from being uniformly distribute
 d mod $q$ in the usual sense (unless $q=1$ !). On the other hand\, Narkiew
 icz has proved that $\\phi(n)$ is weakly uniformly distributed mod $q$ whe
 never $q$ is coprime to 6\; “weakly” means that every coprime residue 
 class mod $q$ gets its fair share of values $\\phi(n)$\, from among the $n
 $ with $\\phi(n)$ coprime to $q$. In fact\, Narkiewicz proves this not jus
 t for $\\phi$ but for a wide class of “polynomially-defined” multiplic
 ative functions. In this talk\, we will consider these weak uniform distri
 bution problems with an eye towards obtaining wide ranges of uniformity in
  the modulus $q$. \n\nThis is joint work with Noah Lebowitz-Lockard and Ak
 ash Singha Roy.\n
LOCATION:https://researchseminars.org/talk/CANT2022/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junxuan Shen (California Institute of Technology)
DTSTART:20220526T183000Z
DTEND:20220526T185500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/40/
 ">The structural incidence problem for cartesian products</a>\nby Junxuan 
 Shen (California Institute of Technology) as part of Combinatorial and add
 itive number theory (CANT 2022)\n\n\nAbstract\nWe prove new structural res
 ults for point-line incidences. An incidence is a pair of one point and on
 e line\, where the point is on the line. The Szemer\\'{e}di-Trotter theore
 m states that $n$ points and $n$ lines form $O(n^{4/3})$ incidences. This 
 bound has been used to obtain many results in combinatorics\, number theor
 y\, harmonic analysis\, and more. While the Szemer\\'{e}di-Trotter bound h
 as been known for several decades\, the structural problem remains wide-op
 en. This problem asks to characterize the point-line configurations with $
 \\Theta(n^{4/3})$ incidences. \nWe prove that when the point set $\\mathca
 l{P}$ is a Cartesian product where only one axis of it behaves like a latt
 ice\, the line set must contain many families of parallel lines to achieve
  the maximal incidence bound.\n\nTheorem: \nConsider $1/3<\\alpha<2/3$. Le
 t $A\,B\\subset\\RR$ satisfy that $A=\\{1\,2\,\\cdots\, n^{\\alpha}\\}$ an
 d $|B|=n^{1-\\alpha}$. Let $\\mathcal{L}$ be a set of $n$ lines in $\\RR^2
 $\, such that $I(A\\times B\,\\mathcal{L})=\\Theta(n^{4/3})$. Then $\\math
 cal{L}$ contains $\\Omega(n^{1-\\beta}/\\log n)$ disjoint families of $\\T
 heta(n^{\\beta})$ parallel lines for $1-2\\alpha\\le\\beta\\le 2/3$.\n\nWh
 en $\\alpha<1/3$ or $\\alpha>2/3$\, it is impossible to have $\\Theta(n^{4
 /3})$ incidences. We also completely characterize the line set when the po
 int set is a lattice.\n\nJoint work with Adam Sheffer. \\\\\n
LOCATION:https://researchseminars.org/talk/CANT2022/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Fleischmann (University of Michigan)
DTSTART:20220526T190000Z
DTEND:20220526T192500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/41/
 ">Angle variants of the Erd\\H{o}s distinct distance problem</a>\nby Henry
  Fleischmann (University of Michigan) as part of Combinatorial and additiv
 e number theory (CANT 2022)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CANT2022/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Rice (Millsaps College)
DTSTART:20220526T193000Z
DTEND:20220526T195500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/42/
 ">New results in classical and arithmetic Ramsey theory</a>\nby Alex Rice 
 (Millsaps College) as part of Combinatorial and additive number theory (CA
 NT 2022)\n\n\nAbstract\nFor $r\,k\\in \n$\, Ramsey's Theorem says that the
 re exists a least positive integer $R_r(k)$ such that every $r$-coloring o
 f the edges of a complete graph on $N\\geq R_r(k)$ vertices yields a monoc
 hromatic complete subgraph on $k$ vertices. This fact can be applied to de
 duce Schur's Theorem\, which says that there exists a least positive integ
 er $S_r(k)$ such that every $r$-coloring of $\\{1\,2\,\\dots\,N\\}$ for $N
 \\geq S_r(k)$ yields a monochromatic solution to the equation $x_1+x_2+\\c
 dots+x_{k-1}=x_k$. Here we discuss new findings related to these two class
 ical results. First\, we derive explicit upper bounds on $R_r(k)$\, establ
 ished through the pigeonhole principle and careful bookkeeping\, that impr
 ove upon previously documented bounds. Second\, we present an extension of
  Schur's Theorem to higher-dimensional integer lattices\, with the additio
 nal restriction that the vectors on the left hand side of the equation are
  linearly independent. \n\nThis includes joint work with six (at the time)
  Millsaps College undergraduate students: Vishal Balaji\, Powers Lamb\, An
 drew Lott\, Dhruv Patel\, Sakshi Singh\, and Christine Rose Ward.\n
LOCATION:https://researchseminars.org/talk/CANT2022/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Russell Jay Hendel (Towson University)
DTSTART:20220526T200000Z
DTEND:20220526T202500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/43/
 ">A system of 4 simultaneous recursions: Generalization of  Ledin-Shannon-
 Ollerton</a>\nby Russell Jay Hendel (Towson University) as part of Combina
 torial and additive number theory (CANT 2022)\n\n\nAbstract\nThis paper fu
 rther generalizes a recent result of Shannon and Ollerton who resurrected 
 an old identity due to Ledin.  \nThis paper generalizes the Ledin-Shannon-
 Ollerton result to all metallic sequences. The results give closed formula
 s for the sum of products of powers of the first $n$ integers with the fir
 st $n$ members of the metallic sequence. \nThree key innovations of this p
 aper are (i) reducing the proof of the generalization to the solution of  
 a system of 4 simultaneous recursions\;\n(ii) skillful use of the shift op
 eration to prove equality of polynomials\; and (iii) new OEIS sequences\na
 rising from the coefficients of  the four polynomial\nfamilies satisfying 
 the four simultaneous recursions.\n
LOCATION:https://researchseminars.org/talk/CANT2022/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ariane Masuda (New York City College of Technology\, CUNY)
DTSTART:20220526T203000Z
DTEND:20220526T205500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/44/
 ">Redei permutations with the same cycle structure</a>\nby Ariane Masuda (
 New York City College of Technology\, CUNY) as part of Combinatorial and a
 dditive number theory (CANT 2022)\n\n\nAbstract\nPermutation polynomials o
 ver finite fields have been extensively studied over the past decades. Amo
 ng the major challenges in this area are the questions concerning their cy
 cle structures as they capture relevant properties\, both theoretically an
 d practically. In this talk we focus on a family of permutation polynomial
 s\, the so called R\\'edei permutations. Although their cycle structures a
 re known\, there are other related questions that can be investigated. For
  example\, when do two R\\'edei permutations have the same cycle structure
 ? We give a characterization of such pairs\, and present explicit families
  of R\\'edei permutations with the same cycle structure. We also discuss s
 ome results regarding R\\'edei permutations with a particularly simple cyc
 le structure\, consisting of $1$- and $j$-cycles only\, when $j$ is $4$ or
  a prime number. The case $j = 2$ is specially important in some applicati
 ons. We completely describe R\\'edei involutions with a prescribed cycle s
 tructure\, and show that the only R\\'edei permutations with a unique cycl
 e structure are the involutions. \n\nThis is joint work with Juliane Capav
 erde and Virg\\'inia Rodrigues.\n
LOCATION:https://researchseminars.org/talk/CANT2022/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Prendiville (Lancaster University\, UK)
DTSTART:20220527T130000Z
DTEND:20220527T132500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/45/
 ">Adapting the circle method for colourings</a>\nby Sean Prendiville (Lanc
 aster University\, UK) as part of Combinatorial and additive number theory
  (CANT 2022)\n\n\nAbstract\nFix your favourite Diophantine equation. If ea
 ch integer is coloured red\, blue or green\, how many solutions to your eq
 uation have all variables the same colour? We discuss how to adapt the Har
 dy-Littlewood circle method to yield a lower bound in certain problems of 
 this flavour.\n
LOCATION:https://researchseminars.org/talk/CANT2022/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ajmain Yamin (CUNY  Graduate Center)
DTSTART:20220527T133000Z
DTEND:20220527T135500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/46/
 ">The exceptional automorphism of $S_6$ explained with colored maps</a>\nb
 y Ajmain Yamin (CUNY  Graduate Center) as part of Combinatorial and additi
 ve number theory (CANT 2022)\n\n\nAbstract\nAmong all symmetric groups\, $
 S_6$ is the only one with a nontrivial outer automorphism\, \nIn this talk
 \, I will describe a new way to understand the exotic embedding of $S_5 \\
 hookrightarrow S_6$ in terms of $5$-colored complete regular maps on the t
 orus.  This provides a visual explanation for the existence of the excepti
 onal automorphism of $S_6$.\n
LOCATION:https://researchseminars.org/talk/CANT2022/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Leonetti (Universita ``Luigi Bocconi''\, Milano\, Italy)
DTSTART:20220527T140000Z
DTEND:20220527T142500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/47/
 ">The G.C.D. of $n$ and the $n$th Fibonacci number</a>\nby Paolo Leonetti 
 (Universita ``Luigi Bocconi''\, Milano\, Italy) as part of Combinatorial a
 nd additive number theory (CANT 2022)\n\n\nAbstract\nLet $(F_n)_{n \\geq 1
 }$ be the sequence of Fibonacci numbers\, defined as usual by $F_1 = F_2 =
  1$ and $F_{n + 2} = F_{n + 1} + F_n$ for all positive integers $n$\; and 
 let $\\mathcal{A}$ be the set of all integers of the form $\\gcd(n\, F_n)$
 \, for some positive integer $n$.\nIn this talk we shall illustrate the fo
 llowing result on $\\mathcal{A}$.\n\n\\noindent\n\\textbf{Theorem.} \\text
 it{For all $x \\geq 2$\, we have\n\\begin{equation*}\n\\#\\mathcal{A}(x) \
 \gg \\frac{x}{\\log x} .\n\\end{equation*}\nOn the other hand\, $\\mathcal
 {A}$ has zero asymptotic density.}\nThe proofs rely on a result of Cubre a
 nd Rouse (PAMS\, 2014) which gives\, for each positive integer $n$\, an ex
 plicit formula for the density of primes $p$ such that $n$ divides the ran
 k of appearance of $p$\, that is\, the smallest positive integer $k$ such 
 that $p$ divides $F_k$.\n
LOCATION:https://researchseminars.org/talk/CANT2022/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bartosz Sobolewski (Jagiellonian University\, Krakow\, Poland)
DTSTART:20220527T150000Z
DTEND:20220527T152500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/48/
 ">Monochromatic arithmetic progressions in binary words associated with pa
 ttern sequences</a>\nby Bartosz Sobolewski (Jagiellonian University\, Krak
 ow\, Poland) as part of Combinatorial and additive number theory (CANT 202
 2)\n\n\nAbstract\nLet $e_v(n)$ denote the number of occurrences of a patte
 rn $v$ in the binary expansion of $n \\in \\mathbb{N}$. In the talk we con
 sider monochromatic arithmetic progressions in the class of words $(e_v(n)
  \\bmod{2})_{n \\geq 0}$ over $\\{0\,1\\}$\, which includes the Thue--Mors
 e word $\\mathbf{t}$ ($v=1$) and a variant of the Rudin--Shapiro word $\\m
 athbf{r}$ ($v=11$). So far\, the problem of exhibiting long progressions a
 nd finding an upper bound on their length has mostly been studied for $\\m
 athbf{t}$ and certain generalizations. We show that analogous results hold
  for $\\mathbf{r}$. In particular\, we prove that a monochromatic arithmet
 ic progression of difference $d \\geq 3$ starting at $0$ in $\\mathbf{r}$ 
 has length at most $(d+3)/2$\, with equality infinitely often. We also com
 pute the maximal length of progressions of differences $2^k-1$ and $2^k+1$
 .\nSome weaker results for a general pattern $v$ are provided as well.\n
LOCATION:https://researchseminars.org/talk/CANT2022/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maciej Ulas (Jagiellonian University\, Krakow\, Poland)
DTSTART:20220527T153000Z
DTEND:20220527T155500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/49/
 ">Solutions of certain meta-Fibonacci recurrences</a>\nby Maciej Ulas (Jag
 iellonian University\, Krakow\, Poland) as part of Combinatorial and addit
 ive number theory (CANT 2022)\n\n\nAbstract\nWe investigate the solutions 
 of certain meta-Fibonacci recurrences of the form $f(n)=f(n-f(n-1))+f(n-2)
 $ for various sets of initial conditions. In the case when $f(n)=1$ for $n
 \\leq 1$\, we prove that the resulting integer sequence is closely related
  to the function counting binary partitions of a certain type (independent
 ly of the value of $f(2)\\in\\mathbb{N}$). \n\nThe talk is based on a join
 t work with Bartosz Sobolewski.\n
LOCATION:https://researchseminars.org/talk/CANT2022/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daodao Yang (Graz University of Technology\, Austria)
DTSTART:20220527T170000Z
DTEND:20220527T172500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/50/
 ">Extreme values of derivatives of the Riemann zeta function\, log-type GC
 D sums\, and spectral norms</a>\nby Daodao Yang (Graz University of Techno
 logy\, Austria) as part of Combinatorial and additive number theory (CANT 
 2022)\n\n\nAbstract\nFirst I will recall the research on greatest common d
 ivisor (GCD) sums and   extreme values of  the Riemann zeta function. The 
 motivation for the study and the connection between the two problems will 
 be discussed.\n Then I will explain how to establish lower bounds for maxi
 mums of $|\\zeta^{(\\ell)}\\left(\\sigma+it\\right)|$ when $\\sigma \\in [
 \\frac{1}{2}\, 1]$\, $\\ell \\in \n$.  One of my results states that   as 
 $T \\to \\infty$\,  uniformly for all positive integers $\\ell \\leqslant 
 (\\log_3 T) / (\\log_4 T)$\, we have\n$  \n\\max_{T\\leqslant t\\leqslant 
 2T}\\left|\\zeta^{(\\ell)}\\left(1+it\\right)\\right| \\geqslant \\left(\\
 mathbf Y_{\\ell}+ o\\left(1\\right)\\right)\\left(\\log_2 T \\right)^{\\el
 l+1} $\, where $\\mathbf Y_{\\ell} = \\int_0^{\\infty} u^{\\ell} \\rho (u)
  du$\, and $\\rho(u)$ denotes the Dickman function. This  generalizes resu
 lts of Bohr-Landau and Littlewood on $\\left|\\zeta\\left(1+it\\right)\\ri
 ght|$ in 1910s.  The tools are Soundararajan's resonance methods and ingre
 dients are certain combinatorial optimization problems. On the other hand\
 , assuming the Riemann hypothesis\, we have $|\\zeta^{(\\ell)}\\left(1+it\
 \right)| \\ll_{\\ell}\\left(\\log \\log t\\right)^{\\ell+1}$.\nThen I will
  talk on the log-type GCD sums $\\Gamma^{(\\ell)}_{\\sigma}(N)$\, which I 
 define it as $\\Gamma_{\\sigma}^{(\\ell)}(N):\\\,= \\sup_{|\\mathcal{M}| =
  N} \\frac{1}{N}\\sum_{m\, n\\in \\mathcal{M}} \\frac{(m\,n)^{\\sigma}}{[m
 \,n]^{\\sigma}}\\log^{\\ell} \\left(\\frac{m}{(m\,n)}\\right)\\log^{\\ell}
 \\left(\\frac{n}{(m\,n)}\\right)\,$\nwhere the supremum is taken over all 
 subsets   $\\mathcal{M} \\subset \\mathbb N$ with size $N$.\nI will explai
 n how $\\Gamma^{(\\ell)}_{\\sigma}(N)$ can be related to $|\\zeta^{(\\ell)
 }(1+it)|$ and how to prove that $\\left(\\log\\log N\\right)^{2+2\\ell} \\
 ll _{\\ell}\\Gamma^{(\\ell)}_1(N)\\ll_{\\ell} \\left(\\log \\log N\\right)
 ^{2+2\\ell}$\, which generalizes Gál's theorem (corresponding to the case
  $\\ell = 0$). The lower bounds could be used to produce large values of $
 |\\zeta^{(\\ell)}\\left(1+it\\right)|$.   Using a random model for the zet
 a function via methods  of Lewko-Radziwiłł\,   upper bounds for spectral
  norms on $\\alpha$-line are established\,  when $\\alpha \\to 1^{-}$ with
  certain fast rates. As a corollary\,  upper bounds of correct order of   
 the log-type GCD sums are established.\n
LOCATION:https://researchseminars.org/talk/CANT2022/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Filip Gawron (Jagiellonian University\, Poland)
DTSTART:20220527T173000Z
DTEND:20220527T175500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/51/
 ">Sign behavior of sums of weighted numbers of partitions</a>\nby Filip Ga
 wron (Jagiellonian University\, Poland) as part of Combinatorial and addit
 ive number theory (CANT 2022)\n\n\nAbstract\nLet $A$ be a subset of the po
 sitive integers. By an $A$-partition of $n$ we\nunderstand the representat
 ion of $n$ as a sum of elements from the set $A$. For\ngiven $i$\, $n\\in 
 \\mathbb{N}$\, by $c_A(i\,n)$ we denote the number of $A$-partitions of $n
 $ with\nexactly $i$ parts. In the talk I will describe several results con
 cerning the sign behaviour\nof the sequence $S_{A\,k}(n) = \\sum_{i=0}^n(-
 1)^i i^k c_A(i\, n)$\, for fixed $k\\in \\mathbb{N}$.   I will focus on th
 e periodicity of the sequence of signs for different forms of $A$. Finally
 \, I will also mention some conjectures and questions that arose naturally
  during our research.\n\nThe talk is based on a joint work with Maciej Ula
 s (Jagiellonian University).\n
LOCATION:https://researchseminars.org/talk/CANT2022/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anurag Sahay (University of Rochester)
DTSTART:20220527T180000Z
DTEND:20220527T182500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/52/
 ">Moments of the Hurwitz zeta function with rational shifts</a>\nby Anurag
  Sahay (University of Rochester) as part of Combinatorial and additive num
 ber theory (CANT 2022)\n\n\nAbstract\nThe Hurwitz zeta function is a shift
 ed integer analogue of the Riemann zeta function\, for shift parameters $0
  < \\alpha \\leqslant 1$. We consider the moments of the Hurwitz zeta func
 tion on the critical line $\\Re{s} = 1/2$ for rational shifts $\\alpha = a
 /q$. In this case\, the Hurwitz zeta function decomposes as a linear combi
 nation of Dirichlet $L$-functions\, which leads us into investigating mome
 nts of products of $L$-functions.\n\nIf time permits\, we will briefly dis
 cuss these moments for irrational shift parameters $\\alpha$\, which shall
  dovetail into Trevor Wooley's talk on our joint work with Winston Heap.\n
LOCATION:https://researchseminars.org/talk/CANT2022/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ognian Trifonov (University of South Carolina)
DTSTART:20220527T183000Z
DTEND:20220527T185500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/53/
 ">Lattice points close to ovals\, arcs\, and helixes</a>\nby Ognian Trifon
 ov (University of South Carolina) as part of Combinatorial and additive nu
 mber theory (CANT 2022)\n\n\nAbstract\nIn 1972 Schinzel showed that the la
 rgest distance between three lattice points on a circle of radius $R$ \nis
  at least $\\sqrt[3]{2} R^{1/3}$. We generalize Schinzel's result to ovals
  and arcs with bounded curvature in the plane  and lattice points close to
  the curve.\nFurthermore\, we extend the result to the case of affine latt
 ices. Finally\, we obtain similar results when the curve is a helix in thr
 ee dimensional space.\n
LOCATION:https://researchseminars.org/talk/CANT2022/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brad Isaacson (New York City College of Technology (CUNY))
DTSTART:20220527T190000Z
DTEND:20220527T192500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/54/
 ">On a polynomial reciprocity theorem of Carlitz</a>\nby Brad Isaacson (Ne
 w York City College of Technology (CUNY)) as part of Combinatorial and add
 itive number theory (CANT 2022)\n\n\nAbstract\nCarlitz proved a powerful r
 eciprocity theorem for generalized Dedekind-Rademacher sums.  Among its ma
 ny consequences was an interesting polynomial reciprocity theorem which ho
 lds under a certain restriction of its parameters.  Carlitz remarked that 
 it was unclear how this restriction could be removed.  In this talk\, we r
 emove this restriction and obtain a generalization of Carlitz's polynomial
  reciprocity theorem.\n
LOCATION:https://researchseminars.org/talk/CANT2022/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Faye Jackson (University of Michigan)
DTSTART:20220527T200000Z
DTEND:20220527T202500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/56/
 ">The Generalized Bergman game</a>\nby Faye Jackson (University of Michiga
 n) as part of Combinatorial and additive number theory (CANT 2022)\n\n\nAb
 stract\nP. Baird-Smith A. Epstein\, K. Flint\, and S. J. Miler\n(2018) cre
 ated the \\emph{Zeckendorf Game}\, a two-player game which takes\nas an in
 put a positive integer $n$ and\, using moves related to the\nFibonacci rec
 urrence relation\, outputs the unique decomposition of $n$\ninto a sum of 
 non-consecutive Fibonacci numbers. Following this work and\nthat of G. Ber
 gman (1957)\, which proved the existence and uniqueness of\nsuch $\\varphi
 $-decompositions\, we formulate the \\emph{Bergman Game} which\noutputs th
 e unique decomposition of $n$ into a sum of non-consecutive\npowers of $\\
 varphi$\, the golden mean.\n\nWe then formulate \\emph{Generalized Bergman
  Games}\, which use moves based\non an arbitrary non-increasing positive l
 inear recurrence relation and\noutput the unique decomposition of $n$ into
  a sum of non-adjacent powers\nof $\\beta$\, where $\\beta$ is the dominat
 ing root of the characteristic\npolynomial of the chosen recurrence relati
 on. We prove that the longest\npossible Generalized Bergman game on an ini
 tial state $S$ with $n$\nsummands terminates in $\\Theta(n^2)$ time\, and 
 we also prove that the\nshortest possible Generalized Bergman game on an i
 nitial state terminates\nbetween $\\Omega(n)$ and $O(n^2)$ time. We also s
 how a linear bound on the\nmaximum length of the tuple used throughout the
  game.\n\nThis is joint work with Benjamin Baily\, Justine Dell\, Irfan Du
 rmic\, Henry\nFleischmann\, Isaac Mijares\, Steven J. Miller\, Ethan Pesik
 off\, Alicia Smith\nReina\, and Yingzi Yang.\n
LOCATION:https://researchseminars.org/talk/CANT2022/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gabdullin (Steklov Mathematical Institute\, Moscow\, Russi
 a)
DTSTART:20220527T143000Z
DTEND:20220527T145500Z
DTSTAMP:20260422T215726Z
UID:CANT2022/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/57/
 ">A conjecture of Cilleruelo and Cordoba and divisors in a short interval<
 /a>\nby Mikhail Gabdullin (Steklov Mathematical Institute\, Moscow\, Russi
 a) as part of Combinatorial and additive number theory (CANT 2022)\n\n\nAb
 stract\nLet $E(A)=\\#\\{(a_1\,a_2\,a_3\,a_4)\\in A^4: a_1+a_2=a_3+a_4\\}$ 
 denote the additive energy of a set $A\\subset \n$\, and let $\\mathbb{T}=
 \\R/\\Z$ and $\\|f\\|_4=\\left(\\int_{\\mathbb{T}}|f(t)|^4dt\\right)^{1/4}
 $. It is well-known that \n$$\nE(\\{n^2: n\\leq N\\})=\\left\\|\\sum_{n\\l
 eq N}e^{2\\pi in^2x}\\right\\|_4^4 \\asymp N^2\\log N\,\n$$\nwhile we triv
 ially have $E(A)\\geq |A|^2$. In 1992\, J. Cilleruelo and A. Cordoba prove
 d that $E(\\{n^2: N\\leq n\\leq N+N^{\\gamma}\\})\\asymp N^{2\\gamma}$ for
  any $\\gamma\\in (0\,1)$\, and conjectured a much more general bound (aga
 in\, for any $\\gamma\\in(0\,1)$)\n$$\n\\left\\|\\sum_{N\\leq n\\leq N+N^{
 \\gamma}}a_ne^{2\\pi in^2x}\\right\\|_4\\leq C(\\gamma)\\left(\\sum_{N\\le
 q n\\leq N+N^{\\gamma}}|a_n|^2\\right)^{1/2}.\n$$\nWhile this bound is eas
 y to prove for $\\gamma\\leq 1/2$\, it seems to be open for any $\\gamma>1
 /2$. We prove this for all $\\gamma<\\frac{\\sqrt5-1}{2}=0.618...$ and pre
 sent a connection between this problem and a conjecture of I. Ruzsa: for a
 ny $\\epsilon>0$ there exists $C(\\epsilon)>0$ such that any positive inte
 ger $N$ has at most $C(\\epsilon)$ divisors in the interval $[N^{1/2}\, N^
 {1/2}+N^{1/2-\\epsilon}]$.\n
LOCATION:https://researchseminars.org/talk/CANT2022/57/
END:VEVENT
END:VCALENDAR