# 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).