Yi Ni
Yi Ni
Professor of Mathematics
B.S., Peking University, 2001; M.S., 2003; Ph.D., Princeton University, 2007. Assistant Professor, Caltech, 2009-15; Professor, 2015-.
Research Interests: Low-dimensional geometry and topology
Overview
Yi works in Low Dimensional Geometry and Topology. His research focuses on Heegaard Floer homology and its applications, Gauge theory, Symplectic Geometry and Khovanov homology. He is also interested in hyperbolic geometry, combinatorial topology, geometric group theory, foliations and laminations, and dynamics.
Selected Awards
- NSF CAREER Award, 2013
- Five-Year Fellowship, American Institute of Mathematics, 2007
- Gold Medal, 38th International Mathematical Olympiad, Argentina, 1997
Selected Awards
- NSF CAREER Award, 2013
- Five-Year Fellowship, American Institute of Mathematics, 2007
- Gold Medal, 38th International Mathematical Olympiad, Argentina, 1997
Related Courses
Ma 151 abc. Geometry and Topology.
9 units (3-0-6); first, second, third terms, 2025-26.
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, Chen, Caniato
Instructors: Ni, Chen, Caniato