Our PhD Program offers research training in a wide variety of topics in mathematics. **Major areas of research specialization** include algebra, number theory, algebraic geometry, analysis, differential geometry and physics, topology, dynamical systems, partial differential equations, scientific computing, and stochastic processes. There are strong groups in mathematical biology, and in the analysis of high-dimensional data using ideas from topology and harmonic analysis. These and other research efforts often include collaborations with researchers in the medical school and other Duke departments. These opportunities for interdisciplinary research and the breadth of research areas in the department make the Duke math department an ideal place to prepare for a job inside or outside of academia.