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Dr Martin Crossley

Dr Martin Crossley

Associate Professor, Mathematics

Telephone number

+44 (0) 1792 602759
Office - 304
Third Floor
Computational Foundry
Bay Campus


Dr Martin Crossley is an Associate Professor at Swansea University, specializing in algebra and algebraic topology. He is Deputy Head of the Mathematics Department, and a Senior Fellow of the Higher Education Academy.

Prior to arriving in Swansea Martin worked in universities and research institutes in Spain, France and Germany, giving him a very international perspective on mathematics and mathematics education.

Areas Of Expertise

  • Hopf algebras
  • Modular representation theory
  • Cohomology operations
  • Algebraic completions
  • Algebraic combinatorics

Career Highlights

Teaching Interests

Martin’s teaching interests focus on algebra and topology, and their inter-relations with other areas of mathematics and applications.  His book “Essential Topology” has been adopted by universities across the world, and commended for its accessible style.


Martin’s research has focussed on the Steenrod algebra, and connections with modular representation theory, cohomology operations in K-theory, and related completions, and the role of Hopf algebras in these areas and related algebraic combinatorics

Award Highlights

Martin is a Senior Fellow of the Higher Education Academy, and has been nominated for a Distinguished Teaching Award for his mathematics teaching for engineering students.