Pure & Applied Topology

The research area in Pure and Applied Topology covers includes algebraic topology, low-dimensional topology, the theory of knots and braids, homological algebra, contact geometry, and computational topology, as well as applications in topological data analysis and mathematical physics. We run a regular seminar and routinely host visiting and postdoctoral researchers.

Capabilities

• Vigleik Angeltveit: algebraic topology, stable homotopy theory, algebraic K-theory, Ramsey theory.
• Asilata Bapat: geometric and categorical representation theory, homological algebra, with connections to topology, combinatorics, and algebraic geometry.
• Joan Licata: low-dimensional topology and contact geometry, knot theory, Floer-theoretic invariants.
• Brett Parker: symplectic geometry, Gromov-Witten and related invariants using exploded manifolds.
• Katharine Turner: computational topology, topological data analysis.