The typical structure of sets with small sumset


Natasha Morrison


University of Cambridge


Thu, 14/11/2019 - 11:00am


RC-4082, The Red Centre, UNSW


One of the central objects of interest in additive combinatorics is the sumset $A + B := \{ a+b : a \in A, \, b \in B \}$ of two sets $A,B \subset \mathbb{Z}$. Our main theorem, which improves results of Green and Morris, and of Mazur, implies that the following holds for every fixed $\lambda > 2$ and every $k \ge (\log n)^4$: if $\omega \to \infty$ as $n \to \infty$ (arbitrarily slowly), then almost all sets $A \subset [n]$ with $|A| = k$ and $|A + A| \le \lambda k$ are contained in an arithmetic progression of length $\lambda k/2 + \omega$. This is joint work with Marcelo Campos, Mauricio Collares, Rob Morris and Victor Souza.


Natasha Morrison is a Research Fellow at Sidney Sussex College in Cambridge. She was a Postdoctoral Research Fellow at IMPA 2018-2019 after finishing her PhD at the University of Oxford under the supervision of Alex Scott. 


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