Department of

April 2020 May 2020June 2020Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th FrSa1 2 3 4 1 2 1 2 3 4 565 6 7 8 9 10 11 3 4 5 6 7 8 9 7 8 9 10 11 12 13 12 13 14 15 16 17 18 10 11 12 13 14 15 16 14 15 16 17 18 19 20 19 20 21 22 23 24 25 17 18 19 20 21 22 23 21 22 23 24 25 26 27 26 27 28 29 30 24 25 26 27 28 29 30 28 29 30 31

Tuesday, May 12, 2020

**Abstract:** A difference basis with respect to $n$ is a subset $A \subseteq \mathbb{Z}$ such that $A - A \supseteq [n]$. Rédei and Rényi showed that the minimum size of a difference basis with respect to $n$ is $(c+o(1))\sqrt{n}$ for some positive constant $c$. The precise value of $c$ is not known, but some bounds are available, and I will discuss them in this talk. This is joint work with Michael Tait (Villanova University).

For the Zoom ID and password, please email Sean at SEnglish@illinois.edu.