Kyle Yip

Given a prime power q≡1(mod4), the Paley graph of order q is the graph defined over 𝔽q (the finite field with q elements), such that two vertices are adjacent if and only if their difference is a square in 𝔽q. A clique in the Paley graph over 𝔽q is a...

The celebrated Erdõs similarity problem asks if it is always possible to construct a set of positive Lebesgue measure that does not contain any (nontrivial) affine copy of a given infinite set. The problem remains widely open. In this talk, I will...

A set of positive integers is called a Diophantine tuple if the product of any two distinct elements in the set is one less than a square. There is a long history and extensive literature on the study of Diophantine tuples and their generalizations...

Let q=1 mod 4 be a prime power and let F_q be the finite field of q elements. The Paley graph of order q is the graph with vertex set F_q, such that two vertices are adjacent if and only if their difference is a square in F_q. Paley graphs play an...

A set {a1,a2,…,am} of distinct positive integers is a Diophantine m-tuple if the product of any two distinct elements in the set is one less than a square. There is a long history and extensive literature on the study of Diophantine tuples and their...

In this talk, we will discuss how to improve the trivial upper bound on the clique number of Paley graphs and generalized Paley graphs using a different method. I will revisit the direction set determined by a Cartesian product in an affine Galois...