Jordan Ellenberg's research is in arithmetic algebraic geometry: his
specific interests include rational points on varieties over number fields,
enumeration of number fields and other arithmetic objects, Galois
representations attached to varieties and their etale fundamental groups,
non-abelian Iwasawa theory, automorphic forms, Hilbert-Blumenthal abelian
varieties, Q-curves, geometry of moduli spaces, curves of low genus, Serre's
conjecture, the ABC conjecture, and Diophantine problems related to all of the
above.