Runqi Liu
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Email
rl24056@essex.ac.uk -
Location
Colchester Campus
Profile
- Algebraic groups
- Exceptional groups, especially E8(q)
- Root systems and Dynkin diagrams
- Maximal subgroups
- Representation theory
- Redctive group theory
Biography
I am a Postgraduate Research Student in the School of Mathematics, Statistics and Actuarial Science at the University of Essex. My research interests are in group theory and representation theory, especially algebraic groups, finite groups of Lie type, and the classification of maximal subgroups. My PhD project focuses on the maximal subgroup structure of exceptional groups of Lie type, in particularly? E8(q), and on the structural, geometric, and representation-theoretic methods used to study these groups.
Qualifications
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Master of Science in Mathematics The University of Sheffield (2024)
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Bachelor of Science in Mathematics The University of Sheffield (2021)
Research and professional activities
Thesis
Classification of the Maximal Subgroups of E8(q)
My PhD research concerns the maximal subgroup structure of the finite exceptional group E8(q). The main problem is to determine which subgroups of a given isomorphism type can occur, and which of them can occur maximally. The project studies this through the relation between E8(q) and the ambient algebraic group of type E8. The work is guided by modern approaches to maximal subgroup classification in exceptional groups, especially the organisation of the problem into broad subgroup families.
Supervisor: Dr Alastair James Litterick
Research interests
Maximal subgroups of finite groups of Lie type
I am interested in the classification of maximal subgroups of finite groups of Lie type, especially exceptional groups. My current work focuses in particular on E8(q), with emphasis on the methods used to determine which subgroup types can occur and how they are constrained by the structure of the ambient algebraic group.
Algebraic groups and reductive groups
I am interested in linear algebraic groups, especially reductive groups, and in the way their structure informs the study of finite fixed-point groups. This includes parabolic subgroups, Levi subgroups, unipotent radicals, root systems, and the general structural theory underlying groups of Lie type.
Contact
Location:
Colchester Campus
Working pattern:
Full-time Postgraduate Research Student