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Applications of Group Theory in Virology - MAT00066M

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  • Department: Mathematics
  • Module co-ordinator: Dr. Eric Dykeman
  • Credit value: 10 credits
  • Credit level: M
  • Academic year of delivery: 2022-23
    • See module specification for other years: 2021-22

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Module will run

Occurrence Teaching period
A Spring Term 2022-23

Module aims

  • To describe cutting-edge applications of group theory in virology.

  • To introduce non-crystallographic Coxeter groups and different methodologies for their affine extension and implement this theory to model the structures of viruses.

  • To use group theoretical techniques to model genome organization in viruses.

  • To discuss applications of these results in the framework of current research topics.

Module learning outcomes

  • Apply group, tiling and representation theoretical techniques in the context of virology.

  • Understand the concepts of Coxeter groups, root systems, and their affine extensions and basic concepts in the representation theory of the icosahedral group.

  • Understand how these results are used to model virus structure.

Module content


  • Group theory, in particular the icosahedral group and its applications to the symmetries of viruses (Crick and Watson’s principle of genetic economy).

  • Tiling theory and its applications to the surface organisation of virus particles (Caspar-Klug Theory).

  • The mathematics of long-range order: quasicrystals and motivation of generalisations of Caspar-Klug theory with applications to the structure of Human Papilloma Virus (HPV).

  • Introduction to Coxeter groups (non-crystallographic versus crystallographic, root systems, associated reflection groups, their classification and properties).

  • Affine extensions of non-crystallographic Coxeter groups and basic concepts in representation theory and their applications to the modeling of the three-dimensional structure of viruses.

York Mathematics is world-leading in the field of Mathematical Virology. The department has pioneered many of the group theoretical applications in virology in an interdisciplinary research context and has organised the leading conferences in the field for over a decade. It is therefore in a unique position to offer this module to students studying for a Masters degree in Mathematics. The module provides the students with a rigorous mathematical training with cutting-edge applications in interdisciplinary research with medical impact, which will make York graduates highly employable.


Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Applications of Group Theory in Virology
2 hours 100

Special assessment rules



Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Applications of Group Theory in Virology
2 hours 100

Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

  • J E Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics, 29, Cambridge University Press, 1990.
  • P G Stockley, R Twarock, Emerging topics in physical virology, London: Imperial College Press, 2010.

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.