The Geometry and Topology group at Durham has a wide range of interests. The flavours of geometry we study include complex geometry; metric and Riemannian geometry; hyperbolic geometry; and cluster algebras. In topology we have interests including Floer and gauge-theoretic invariants; aperiodic tilings; quantum topology; and computational topology.
The group is also a node in the Yorkshire Durham Geometry Days Network and the UK Metric Geometry and Analysis Network.
John has retired from active mathematical research, but still teaches undergraduate tutorials organised by the Department of Mathematical Sciences in certain areas of pure mathematics.
Sophy is on the teaching track, and lectures on discrete maths, error-correcting codes, and general topology. She likes graph theory, knots, braid groups, and aperiodic tilings, and is involved in several outreach projects.
Anna's current research interests include cluster algebras, Coxeter groups, hyperbolic geometry, and frieze patterns.
Fernando studies Riemannian and Alexandrov geometry; transformation groups; interactions between curvature, symmetry, and topology; links to data analysis via geometric statistics, topological data analysis, and Wasserstein metrics.
Jeff studies topological data analysis, phase transitions in QFT, topology and geometry in machine learning and artificial intelligence, tropical algebra and geometry, and non-Archimedean geometry.
John’s research applies methods from homotopy theory and shape theory to the study of aperiodic tilings, and more generally hyperbolic, or chaotic, attractors in topological dynamics. He works on classifications of these spaces and their embeddings.
Martin is interested in the geometry and topology of Riemannian manifolds with non-negative sectional curvature, especially in the presence of symmetries.
Wilhelm works in geometric analysis, with specific interests in those problems of differential geometry that can be addressed by methods of complex analysis, convex analysis, and partial differential equations.
Andrew studies geometric and topological spaces, often in low dimensions.
John studies hyperbolic geometry and discrete groups.
Norbert's research interests are centered around geometry. Of particular interest are relations between geometry and Laplace- and Schrödinger operators and relations between geometry and dynamical systems.
Dirk's current interests are mostly in knot theory and quantum topology, particularly in Khovanov homology and its generalizations.
Pavel's research mainly concerns the theory of cluster algebras and its interactions with other subjects, in particular hyperbolic geometry and Coxeter groups.
Raphael is interested in low-dimensional geometry and topology. One of his main topics is the use of instanton gauge theory to study 3-dimensional manifolds and the representation varieties of their fundamental groups.
Our 2025 Willmore Pure Postgraduate Day celebrated the exciting research in pure mathematics carried out by junior researchers in the Department of Mathematical Sciences.
Find out more about our research, research areas, other members of staff and more.
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