Algebra, Geometry, and Discrete Mathematics theme

The theme’s research in algebra concerns group theory (Dr Litterick, Prof. Williams), semigroup theory (Prof. Higgins, Dr Vernitski), and meets algebraic geometry and geometric topology (Dr Gunturkun, Dr Martinez-Garcia, Dr Vernitski, Prof. Williams), graph theory and combinatorics (Dr Claridge, Prof. Higgins, Dr Penman, Dr Vernitski, Prof. Williams), computational algebra and topology (Dr Litterick, Dr Martinez-Garcia, Dr Vernitski, Prof. Williams) algebraic number theory and linear algebra (Prof. Williams), and information theory and network coding (Dr Claridge).

Some theme members also work in applications of the above areas to other subjects, such as algebraic data compression methods (Prof. Higgins, Dr Vernitski), machine learning and artificial intelligence applications to mathematics (Dr Vernitski) and communication channels and information flow through the brain (Dr Claridge).

Dr Martinez-Garcia has previously received an EPSRC Standard Grant for the project The Calabi Problem for smooth Fano Threefolds. Professor Williams and Dr Vernitski have each recently held Leverhulme Research Project Grants, for work on group presentations with cyclic symmetries and machine learning in knot theory, respectively.

The theme also carries out research bridging its distinct topics, with an annual international workshop in algebraic geometry and algebraic groups (AGGITatE). The 2026 edition of AGGITatE, “Algebraic groups, geometry, invariants and related topics” will be a month-long residency programme with over 30 researchers coming to Essex. This is funded by an Isaac Newton Institute Satellite Programme grant (PI Dr Litterick, CO-I’s Dr Gunturkun and Dr Martinez-Garcia).

Our Research Theme is always interested in having new postdocs and PhD students joining in via external competitive funding. If you are interested in applying to one of the opportunities below at Essex, you can contact a researcher in your area, or the Research Theme Leader, who is currently Jesus Martinez-Garcia. For postdocs, the following opportunities may be relevant:

• EPSRC postdoctoral fellowships.
• Two-year Newton International Fellowship for people currently based overseas that do not hold UK citizenship.
• Marie Curie fellowships, usually with deadlines in September, you should ideally contact us at least two or three months in advance.
• Royal Society University Research Fellowships 5-8 years positions leading to a permanent position.
• Royal Society Dorothy Hodgkin Fellowships, for scientists who require a flexible working pattern due to personal circumstances, such as caring responsibilities and/or health-related conditions.
• Leverhulme Trust Research Leadership Awards
• Newton Advanced Fellowships for 2-3 years visits to the UK from overseas.