2025 CMS Winter Meeting
Toronto, Dec 5 - 8, 2025
Blair Spearman Doctoral Prize
- CHI HOI YIP, Georgia Institute of Technology
Some inverse problems in arithmetic combinatorics [PDF]
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In this talk, I will give a gentle introduction to some of my favorite problems in arithmetic combinatorics and highlight some recent progress. In particular, I will discuss:
\begin{itemize}
\item A question of Erd\H{o}s on whether the set of perfect squares can be close to a sumset, and a multiplicative analogue by Hajdu and S\'{a}rk\"{o}zy.
\item A conjecture of Van Lint and MacWilliams on the characterization of maximum subsets of a finite field of square order such that pairwise differences are all squares (also known as the Erd\H{o}s-Ko-Rado theorem for Paley graphs), and its generalization.
\item Inverse sieve problems (that have been studied by Green--Harper, Helfgott--Venkatesh, Shao, and Walsh), motivated by the inverse Goldbach problem.
\end{itemize}
Joint work with Shamil Asgarli, Ernie Croot, and Junzhe Mao.