Geometry and topology, algebra, and analysis are the three major fields of pure mathematics. It emphasizes geometric intuition and visualization, and includes active research areas such as differential geometry (geometric analysis), algebraic geometry, algebraic topology, and geometric topology (low-dimensional topology). The seminar grows out of a strong representation of the field by faculty in the Department. Relevant faculty members will take turns over semesters to organize interested students for directed reading on hot topics. Registered students will present assigned topics under supervision of the instructor, with supplementary lectures by the instructor, other relevant faculty members, as well as experts in the field from other universities. Recent proposed topics include applied and computational topology, manifolds and modular forms, the topology and geometry of four-manifolds, knot theory and algebraic number theory.