Alp Müyesser

Graham's rearrangement conjecture

Graham's rearrangement conjecture from 1971 asserts the following: for any prime p, any set of integers modulo p not including 0 admits an ordering s_1,...,s_k such that all partial sums s_1+...+s_j are distinct modulo p. This conjecture has recently been resolved in the affirmative for all sufficiently large primes in a series of works using a combination of graph theoretic and additive combinatorial methods. In this talk, we will discuss some of these ideas.

Partially based on joint works with Pokrovskiy, and with Bedert, Bucić, Kravitz, and Montgomery.