The Centre consists of four research groups:
- Geometric Group Theory
- Topology
- Noncommutative geometry
- Topological data analysis
Centre for Geometry, Topology, and Applications
Research areas
The main areas of research at CGTA include geometric group theory, topology, homotopy theory and noncommutative geometry, applied topology and topological data analysis.
Geometric Group Theory
Members of Geometric Group Theory are interested in problems concerning groups that can be studied through a detailed understanding of the geometric properties of spaces on which they act. A main motivation for this subject are the foundational ideas of Mikhael Gromov.
Topology
The Topology group is interested in problems in homotopy theory, classification of 4-manifolds and topological questions arising from problems in symplectic geometry.
Noncommutative geometry
Noncommutative geometry, created by Alain Connes, brings together ideas from differential geometry with analytic and algebraic methodology of operator algebras. Group members investigate problems in coarse geometry, K-theory, the Baum-Connes conjecture, and interactions with Geometric Group Theory.
Topological data analysis
Topological data analysis investigates direct applications of topology and geometry to complex, data-driven problems in medicine, the sciences. We have a strong and growing track record of interdisciplinary projects. We are always interested in possibilities of new collaborations.