Alex Iosevich and Jonathan Pakianathan awarded joint NSA Grant

Professors Alex Iosevich and Jonathan Pakianathan have been awarded a joint NSA Mathematical Sciences Grant titled Group Actions and Erdos Problems in Discrete, Continuous and Arithmetic Settings.

Their study addresses questions in extremal combinatorics such as, “How big does a set have to be (either in the sense of dimension or point-count) in order to guarantee the existence of a certain type of configuration?” For example, what is the minimum Hausdorff dimension of subset of a given Euclidean space so that it is guaranteed to contain an equilateral triangle? Or what is the minimum number of distinct distances that n points in some given Euclidean space must determine?

These questions are extremal in nature as the generic situation is understood and must instead address the worst-case scenarios. For a general discussion of extremal combinatorics see Extremal and Probabilistic Combinatorics (PDF file).