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.