Bremner's research is in the area of Diophantine analysis, which occurs in many areas of pure mathematics and in the last couple of decades has seen applications in cryptography and cybersecurity.

Childress works in algebraic number theory and p-adic analysis.

Jones is an algebraic number theorist interested in number fields, local fields, and Artin representations.

Sprung likes to explore mysterious relationships between algebra and analysis, such as Iwasawa theory.