Recent progress on the ErdosGinzburgZiv problem
Recent progress on the ErdosGinzburgZiv problem

Dmitrii Zakharaov, MIT
Fine Hall 224
InPerson Talk
In 1961, Erdos, Ginzburg and Ziv showed that among any 2n1 numbers one can find n whose sum is divisible by n. Consider a higher dimensional generalization of this fact: what is the smallest N such that among any N points in Z^d one can find n whose sum is zero mod n? This turns out to be a much more difficult question and the exact answer is only known when d =1 or 2 or n is a power of 2. I will talk about 2 new upper bounds substantially improving previously known results for most parameters (d, n). Proofs use a variety of tools coming from additive combinatorics, algebraic methods and convex geometry. Joint work with Lisa Sauermann.