Program Overview

This programme aims to engage energetic and motivated Mathematics students in innovative research in pure Mathematics and its application in Computer Science. The programme is suitable for students with a solid background in Mathematics or in a closely related discipline. This programme, in particular, is a stepping stone for students to join research institutes and universities as PhD students and researchers.

Some of our research projects will seek new directions towards neural networks and AI, and potentially towards industrial application. The significance of interdisciplinary research is emphasised in the UK’s Research and Development Roadmap, which includes innovative proposals for interactions between mathematical sciences, biomedical research, and the Computing industry.

The main research areas of interest include, but are not limited to:

• Model theory is a branch of mathematical logic, and its applications in a wide range of subjects such as algebra, topological dynamics, combinatorics, and theoretical Computer Science. Specifically, the projects are focused on Fraïssé construction method, automorphism groups of countable homogeneous structures, structural Ramsey theory, asymptotic classes, ultraproducts, and infinite constraint satisfaction problems in theoretical Computer Science. Research proposals in a wider range of areas in mathematical logic, philosophy of Mathematics, pure Mathematics and theoretical Computer Science are also welcome. These include research areas such as formal methods, type theory, set theory, higher-order logics and fuzzy logics.
• Applied Computational Topology and Geometry is a relatively recent and fast-growing field of mathematics that emerged from applying well-established theories in algebraic topology and geometry. Specific projects focus on applications of data-driven Machine Learning and Artificial Intelligence in the fields of computer vision, medical diagnostics, and multimedia security for image tampering and fake videos. These applications employ Topological Data Analysis (TDA) and its growing list of tools (Persistent Homology, Mapper, etc.) to infer relevant (topological) class discriminating features from high dimensional and complex data. Other projects involve the use of TDA for interpreting Deep Learning (DL) decisions and dealing with the problem of overfitting of DL models.

Throughout the project, students will interact and be encouraged to work with other researchers at the University of Buckingham and other leading research universities in the UK. The students will be part of research networks such as BPGMTC, SEEMOD, MODNET and Data Science groups.