Michigan State University has a large and active research group in topology, and closely related areas of geometry. Among the research areas represented by the group are: knot theory and 3- and 4-manifolds, Floer homology, hyperbolic geometry, quantum invariants and their categorification, equivariant stable homotopy theory, algebraic K-theory, geometric group theory, topological data analysis, symplectic geometry, geometric analysis, gauge theory, cluster algebras, and Teichmuller space and its quantization and generalizations.