Qianhe Qin

Ma 109 abc. Introduction to Geometry and Topology. 9 units (3-0-6); first, 2026-27. Prerequisites: Ma 2 or equivalent. We recommend Ma 5 a and Ma 108 a be taken previously or concurrently. First term: aspects of point set topology, and an introduction to geometric and algebraic methods in topology. Second term: the differential geometry of curves and surfaces in two- and three-dimensional Euclidean space. Third term: an introduction to differentiable manifolds. Transversality, differential forms, and further related topics.
Instructor: Qin

Ma 151 abc. Geometry and Topology. 9 units (3-0-6); first, second, third terms, 2026-27. Prerequisites: Ma 109 abc or equivalent. Part a: Homology Theory. CW complexes, homology and calculation of homology groups, exact sequences, cohomology rings, Poincare duality. Part b: Homotopy Theory and K-theory. Fibrations, higher homotopy groups, and exact sequences of fibrations. Fiber bundles, Eilenberg-MacLane spaces, classifying spaces. K-theory, generalized cohomology theory, Bott periodicity. Part c: Basic Riemannian geometry: geometry of Riemannian manifolds, connections, curvature, Bianchi identities, completeness, geodesics, exponential map, Gauss's lemma, Jacobi fields, comparison theorems, relation between curvature and topology.
Instructors: Ni, Qin