Dr Alastair Litterick
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Email
a.litterick@essex.ac.uk -
Telephone
+44 (0) 1206 874731
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Location
2.525, Colchester Campus
Profile
Biography
I am an algebraist, interested in linear algebraic groups, finite groups of Lie type and everything related to these, including algebraic geometry, representation theory, Lie algebras, computational algebra, geometric invariant theory, Lie theory, combinatorics and more besides. I joined the University of Essex in 2019. Before this, I held a Humboldt Fellowship at Bielefeld University and the Ruhr-University Bochum, Germany, and prior to this I held other postdoctoral positions in Bielefeld and Bochum, and at the University of Auckland, New Zealand. I completed my MSci and PhD degrees at Imperial College London, and I originally hail from Essex, having grown up here and attended Colchester Royal Grammar School from 1998 to 2005. As an alumnus of the Humboldt Foundation, I am eligible to host postdoctoral researchers from Germany for up to two years as Feodor Lynen Research Fellows, funded by the Humboldt Foundation. Click the link below for more information, and send me an email if you are interested in this opportunity.
Qualifications
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PhD Pure Mathematics Imperial College London, (2013)
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MSci Mathematics Imperial College London, (2009)
Appointments
University of Essex
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Elected Member of Senate, University of Essex (1/1/2024 - 31/7/2027)
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Senior Lecturer in Mathematics, School of Mathematics, Statistics and Actuarial Science, University of Essex (1/10/2023 - present)
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Lecturer in Mathematics (R), Department of Mathematical Sciences, University of Essex (1/9/2019 - 30/9/2023)
Other academic
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External Examiner (Pure Algebra), Department of Mathematics, University of York (1/10/2022 - 30/9/2026)
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Humboldt Research Fellowship for Postdoctoral Researchers, Faculty of Mathematics, Bielefeld University and Ruhr-University Bochum (1/10/2017 - 31/8/2019)
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Postdoctoral Researcher, Faculty of Mathematics, Ruhr University Bochum (1/4/2017 - 30/9/2017)
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Postdoctoral Researcher, Faculty of Mathematics, Bielefeld University (1/1/2016 - 31/3/2017)
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Postdoctoral Research Fellow, Department of Mathematics, University of Auckland (1/7/2013 - 31/12/2016)
Research and professional activities
Research interests
Reductive algebraic groups
The structure of reductive algebraic groups is an active research area with several open areas of enquiry. Open questions exist concerning their subgroup structure, representation theory, Lie algebra structure and geometry.
Finite groups of Lie type
Finite groups of Lie type arise as the finite analogues of reductive linear algebraic groups, and the theories of these objects are closely intertwined. Finite groups of Lie type give rise to most finite simple groups, in an appropriate sense, which makes them fundamental objects of study in group theory. These groups are therefore objects of intensive study, and there are many open problems to investigate.
Representation varieties
There is a natural geometric structure on the collection of homomorphisms from a fixed finitely generated group into a fixed linear algebraic group. Studying this structure can provide insights into the structure of each group.
Conferences and presentations
Varying Flavours of Complete Reducibility
Invited presentation, Keynote presentation, London Algebra Colloquium, London Algebra Colloquium (Imperial), London, United Kingdom, 21/11/2024
Complete Reducibility: The Good, the Bad and the Conjugacy
Invited presentation, Workshop on Algebraic Groups and Representation Theory, Ruhr-University Bochum, Bochum, Germany, 4/12/2023
Finitely-generated groups and representation varieties
Invited presentation, Future directions in algebraic groups and Lie algebras in the UK, Birmingham, United Kingdom, 5/1/2022
Geometric invariant theory and Generating Sets in Finite Simple Groups
Invited presentation, Groups in Galway, Galway, Ireland, 2/12/2021
History, current and future trends of algebra
Invited presentation, Summer School on Future Mathematics and its Applications, Bandung, Indonesia, 27/7/2021
Teaching and supervision
Current teaching responsibilities
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Number Theory (MA220)
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Group Theory (MA301)
Previous supervision
Degree subject: Mathematics
Degree type: Doctor of Philosophy
Awarded date: 14/4/2023
Publications
Publications (3)
Bate, M., Böhm, S., Litterick, A., Martin, B. and Roehrle, G., (2024). $G$-complete reducibility and saturation
Litterick, AJ. and Thomas, AR., (2023). Complete reducibility in bad characteristic
Akello-Egwell, D., Leedham-Green, C., Litterick, A., Markström, K. and Riis, S., (2023). Condorcet Domains of Degree at most Seven
Journal articles (12)
An, J., Dietrich, H. and Litterick, A., (2024). Elementary abelian subgroups: from algebraic groups to finite groups. Transactions of the American Mathematical Society. 377 (12), 8335-8380
Akello-Egwell, D., Leedham-Green, C., Litterick, A., Markström, K. and Riis, S., (2024). Condorcet Domains of Degree at most Seven. Mathematical Social Sciences. 133 (January 2025), 23-33
Gruchot, M., Litterick, A. and Roehrle, G., (2022). Complete reducibility: Variations on a theme of Serre. Manuscripta Mathematica. 168 (3-4), 439-451
Litterick, A., Bannuscher, F. and Uchiyama, T., (2022). Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields IV: An F4 example. Journal of Group Theory. 25 (3), 527-541
Attenborough, C., Bate, M., Gruchot, M., Litterick, A. and Roehrle, G., (2020). On relative complete reducibility. Quarterly Journal of Mathematics. 71 (1), 321-334
Gruchot, M., Litterick, A. and Roehrle, G., (2020). Relative complete reducibility and normalised subgroups. Forum of Mathematics, Sigma. 8
Litterick, AJ. and Thomas, AR., (2019). Reducible subgroups of exceptional algebraic groups. Journal of Pure and Applied Algebra. 223 (6), 2489-2529
Conder, M. and Litterick, A., (2019). Further rigid triples of classes in G₂. International Journal of Group Theory. 8 (4), 5-9
Litterick, AJ. and Thomas, AR., (2018). Complete reducibility in good characteristic. Transactions of the American Mathematical Society. 370 (8), 5279-5340
Jambor, S., Litterick, A. and Marion, C., (2018). On finite simple images of triangle groups. Israel Journal of Mathematics. 227 (1), 131-162
Litterick, AJ., (2018). On non-generic finite subgroups of exceptional algebraic groups. Memoirs of the American Mathematical Society. 253 (1207), 0-0
Liebeck, MW., Litterick, AJ. and Marion, C., (2011). A rigid triple of conjugacy classes in G 2. Journal of Group Theory. 14 (1), 31-35
Conferences (1)
Litterick, AJ., Stewart, DI. and Thomas, AR., (2022). Complete reducibility and subgroups of exceptional algebraic groups
Thesis dissertation (1)
Litterick, A., (2013). Finite Simple Subgroups of Exceptional Algebraic Groups
Grants and funding
2024
AGGITatE: A conference on Groups, Representations and Cohomology
The Heilbronn Institute for Mathematical Research (University of Bristol)
INI@Essex � Algebras, Groups, Geometry, Invariants and Related Topics
The Isaac Newton Institute for Mathematical Sciences (INI)
AGGITatE: A conference on Groups, Representations and Cohomology
London Mathematical Society
2023
The Complex Structure of Random-Walk Coefficient Polynomials
London Mathematical Society
AGGITATE 2023: A Workshop on Algebraic Groups and Cremona Transformations
Foundation Compositio Mathematica
2022
AGGITATE 2023: A WORKSHOP ON ALGEBRAIC GROUPS AND CREMONA TRANSFORMATIONS
London Mathematical Society
2021
LITTERICK 210630
London Mathematical Society
2019
Algebraic Groups and Geometric Invariant Theory Day (Day2)
London Mathematical Society
Contact
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