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Creators/Authors contains: "Robertson, Donald"

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  1. ; ; ; (, Communications of the American Mathematical Society)
    We show that every set A A of natural numbers with positive upper Banach density can be shifted to contain the restricted sumset { b 1 + b 2 : b 1 , b 2 ∈<#comment/> B  and  b 1 ≠<#comment/> b 2 } \{b_1 + b_2 : b_1, b_2\in B \text { and } b_1 \ne b_2 \} for some infinite set B ⊂<#comment/> A B \subset A . 
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  2. ; ; ; (, Journal of the American Mathematical Society)
    Motivated by questions asked by Erdős, we prove that any set A ⊂<#comment/> N A\subset \mathbb {N} with positive upper density contains, for any k ∈<#comment/> N k\in \mathbb {N} , a sumset B 1 + ⋯<#comment/> + B k B_1+\cdots +B_k , where B 1 B_1 , …, B k ⊂<#comment/> N B_k\subset \mathbb {N} are infinite. Our proof uses ergodic theory and relies on structural results for measure preserving systems. Our techniques are new, even for the previously known case of k = 2 k=2 . 
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    Full Text Available 
  3. ; ; ; (, Notices of the American Mathematical Society)
    Flapan, Erica (Ed.)
    Since 2012 the University of North Carolina at Greensboro (UNCG) has held an annual summer school in computational number theory aimed at first- and second-year graduate students. In 2020 we were in charge of running the school, entitled An Introduction to Ergodic Theory via Continued Fractions. Given the ongoing COVID-19 outbreak, we decided, in mid-March 2020, to run the school entirely online. In this article we will describe how we carefully tried to preserve as many desirable features of an intensive summer school experience as we could online. Since surveys indicated that the participants were uniformly pleased with their experiences, we hope that our account will help others who wish to organize similar online events. 
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  4. (, Ergodic Theory and Dynamical Systems)
    We prove that irreducible, linearly recurrent, type W interval-exchange transformations are always mild mixing. For every irreducible permutation, the set of linearly recurrent interval-exchange transformations has full Hausdorff dimension. 
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    Full Text Available 
  5. ; (, Journal of Modern Dynamics)
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  6. ; ; (, Annals of Mathematics)
    Full Text Available 
  7. ; ; (, Annals of mathematics)
    In this paper we show that every set A⊂ℕ with positive density contains B+C for some pair B,C of infinite subsets of ℕ, settling a conjecture of Erd\H os. The proof features two different decompositions of an arbitrary bounded sequence into a structured component and a pseudo-random component. Our methods are quite general, allowing us to prove a version of this conjecture for countable amenable groups. 
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    Accepted Manuscript Full Text Available
  8. ; (, Journal of the London Mathematical Society)