We will start by presenting a combinatorial problem about square binary matrices called the Erikson matrix problem, proposed by Martin Erikson in 1996. The problem and its solution (given in 2010 by Bacher and Eliahou) represent a prototype result in Ramsey Theory. We will explore natural variations of the Erikson matrix problem where we seek zero-sum squares instead of constant squares. Meanwhile, we take the opportunity to present the philosophies behind Ramsey theory and zero-sum Ramsey theory, emphasizing its differences and similarities. We prove that every f􀀀1; 1g-matrix where the difference between the number of 1’s and -1’s is bounded contains a zero-sum (also called balanced) square except for a particular matrix. This is joint work with Edgardo Roldan-Pensado and Alma Arevalo.

This is a hybrid talk. The speaker will present remotely, but the talk will be displayed on the screen in Hylan 1106A.