Professor Kamienny will work on extending his recent work on the uniform boundedness theorem to other fields then Quadratic. He will also be working on isogenies of elliptic curves over fields of degree d. This project falls into the general area of Number theory - more specifically the theory of elliptic curves. Often called "the Queen of mathematics", number theory, is along with Euclidean geometry, the oldest field in mathematics. Yet, it is one that has shown its freshness anew in each generation. This has been shown most dramatically with the astonishing connections of elliptic curves to cryptography and coding theory.
