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 currently holds 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) and previously a CoDiMa Workshop “Tools for Discrete Computational Mathematics”. In addition to sole supervisions in their areas of expertise, members have co-supervised PhD students working on problems in geometric invariant theory (Dr Litterick, Dr Martinez-Garcia), finite quotients of infinite groups (Dr Litterick, Prof. Williams), and algebraic invariants of graphs (Dr Penman, Prof. Williams).