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Geometry & Topology

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.

Academic staff

John Bolton

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.

John Bolton

Sophy Darwin

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.

Sophy Darwin

Anna Felikson

Anna's current research interests include cluster algebras, Coxeter groups, hyperbolic geometry, and frieze patterns.

Anna Felikson

Fernando Galaz-Garcia

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.

Fernando Galaz Garcia

Jeffrey Giansiracusa

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.

Jeffrey Giansiracusa

John Hunton

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.

John Hunton

Martin Kerin

Martin is interested in the geometry and topology of Riemannian manifolds with non-negative sectional curvature, especially in the presence of symmetries.

Martin Kerin

Wilhelm Klingenberg

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.

Wilhelm Klingenberg

Andrew Lobb

Andrew studies geometric and topological spaces, often in low dimensions.

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John Parker

John studies hyperbolic geometry and discrete groups.

John Parker

Norbert Peyerimhoff

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.

Norbert Peyerimhoff

Dirk Schütz

Dirk's current interests are mostly in knot theory and quantum topology, particularly in Khovanov homology and its generalizations.

Dirk Schütz

Pavel Tumarkin

Pavel's research mainly concerns the theory of cluster algebras and its interactions with other subjects, in particular hyperbolic geometry and Coxeter groups.

Pavel Tumarkin

Raphael Zentner

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.

Raphael Zentner

News from our department

Durham University to help deliver AI Growth Zone

Durham University will take a key role in delivering a new AI Growth Zone in North East England – an initiative that promises to create thousands of jobs.
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National Astronomy Meeting 2025 - exploring Durham’s rich astronomical research

Almost a thousand of the world’s top space scientists will visit Durham University next week (7 to 11 July) as we host the UK’s National Astronomy Meeting (NAM) 2025.
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