Arithmetic geometry is the study of number theoretic problems via a combination of techniques from algebraic number theory and differential and algebraic geometry; recent faculty research projects include Diophantine equations, elliptic curves, special values of zeta and L-functions, and motives, and motivic cohomology.

Analysis at Brown encompasses partial differential equations, complex function theory, harmonic analysis, and operator theory. The connections among all of these areas are a specialty of ours.

The faculty in geometry and topology at Brown represent a broad set of strengths, from homotopy theory, to low-dimensional topology, to geometric analysis and symplectic geometry.