Arithmetic algebraic geometry (Diophantine geometry) Arithmetic and non-Archimedean dynamical systems Diophantine approximation Diophantine equations Dynamical systems and ergodic theory Elementary number theory Elliptic curves over global fields Finite fields and commutative rings (number-theoretic aspects) Instructional exposition (textbooks, tutorial papers, etc.) Number theory Polynomial and rational maps Polynomials Probabilistic theory: distribution modulo $1$; metric theory of algorithms