Research Interests
I received my PhD in mathematics from Cardiff University at the start of 2022 under the supervision of Professor Iskander Aliev. My PhD thesis entitled "Distances to Lattice Points in Rational Polyhedra" is available below.
My current research sits broadly within discrete optimisation, number theory, and applied mathematical modelling. Much of my earlier work focused on structural questions in integer optimisation, particularly distances to lattice points, proximity bounds, and sparsity in integer linear programming. More recently, my interests have expanded to include Frobenius number bounds, weighted-sum methods for multi-criteria decision making, probabilistic and Markov Chain Monte Carlo approaches to assessment, and applications of optimisation and modelling techniques across education, sustainability, and operational research. I also maintain a strong interest in mathematics and computer science education, including assessment design, learning analytics, STEM pedagogy, and the role of AI in teaching and learning.
For those who are interested, my current Erdös Number is 3 (meaning I am a coauthor of a coauthor of a coauthor of Erdös). The specific path is A. Williams => I. Aliev => P. Gruber => P. Erdös.

Publications, Preprints & Thesis
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Markov Chain Monte Carlo Methods for Dynamic Student Assessment
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A. Williams (2025)
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[Intelligent Technology for Educational Applications (Springer) ; EdArXiv.org]
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AI and IoT for Environmental Sustainability: A Comprehensive Analysis in Line with Sustainable Development Goals
M. Bhatia and A. Williams (2025)
[Future of AI, IoT, and Sustainability (Springer)]
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Mathematics: An Important Attribute in STEM Education
M. Bhatia and A. Williams (2025)
[Canadian Journal of Science, Mathematics and Technology Education (Springer)]
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Evaluating the Sharpness and Limitations of Bounds on the Frobenius Number
A. Williams (2025)
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Insights to Weighted Sum Sampling Approaches for Multi-Criteria Decision Making Problems
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A. Williams and Y. Cai (2025)
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Considering a Classical Upper Bound on the Frobenius Number
A. Williams and D. Haijima (2024)
[Mathematics] ; [arXiv.org]
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Identifying Job Satisfaction Parameters among the Employees in Higher Educational Institutions: A Mathematical Model
M. Bhatia and A. Williams (2024)
[WSEAS Transactions on Business and Economics] ; [arXiv.org]
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Agri Supply Chain Management: An MCDM Approach towards Sustainability
M. Bhatia and A. Williams (2024)
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Selection of Criteria Using MCDM Techniques - An Application in Renewable Energy
M. Bhatia and A. Williams (2023)
[American Journal of Operations Management and Information Systems] ; [arXiv.org]
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Difference Equations, Stationary and Non-stationary Discrete Systems in Block Ciphers
R. Skuratovskii and A. Williams (2023)
[Information Systems for Intelligent Systems (Springer)]
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Target Setting: A Case Study Looking at How Greater Collaboration Can Impact the Effectiveness of Target Setting
A. Williams (2022)
[WSEAS Transactions on Business and Economics]
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Finding an Optimal Proximity Bound in a Very Special Scenario
A. Williams (2022)
[WSEAS Transactions on Mathematics]
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Distances to Lattice Points in Rational Polyhedra (PhD Thesis)
A. Williams (2022)
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Intelligent Security Control Based on the New Criterion of Edwards and Montgomery Curves, Isogenous of These Curves Supersingularity
R. Skuratovskii, A. Williams and Y. Osadchyy (2021)
[Proceedings of International Conference on Advanced Computing Applications]
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Distance-Sparsity Transference for Vertices of Corner Polyhedra
I. Aliev, M. Celaya, M. Henk and A. Williams (2021)
[SIAM Journal on Optimization] ; [arXiv.org]
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Irreducible bases and subgroups of a wreath product in applying to diffeomorphism groups acting on the Möbius band
R. Skuratovskii and A. Williams (2020)
[Rendiconti del Circolo Matematico di Palermo Series 2 (Springer)]
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Analysis of the Mel scale features using classification of big data and speech signals
V. Osadchyy, R. Skuratovskii and A. Williams (2020)
[International Journal of Applied Mathematics, Computational Science and Systems Engineering]
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Some Approach to Key Exchange Protocol Based on Non-Commutative Groups
R. Skuratovskii and A. Williams (2020)
[International Journal of Mathematical Models and Methods in Applied Sciences] ; [arXiv.org]
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A Solution of the Inverse Problem to Doubling of Twisted Edwards Curve Point over Finite Field
R. Skuratovskii and A. Williams (2019)
[Wydawnictwo Naukowe Akademii Techniczno-Humanistycznej w Bielsku-Białej]
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Minimal Generating Set and a Structure of the Wreath Product of Groups, and the Fundamental Group of the Orbit Morse Function
R. Skuratovskii and A. Williams (2019)
[Вісник Донецького національного університету. Серія А: Природничі науки] ; [arXiv.org]
Conferences & Workshops
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2nd International Conference on Intelligent Technology for Educational Application (ITEA) | Bangkok (2025)
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6th International Conference on Control, Artificial Intelligence, Robotics and Optimisation (ICCAIRO) | Institut Henri Poincaré (2025)
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International Meeting on Numerical Semigroups (IMNS) | Universidad de Cádiz (2024)
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33rd European Conference on Operational Research | Technical University of Denmark (2024)
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75th British Mathematical Colloquium (Number Theory Workshop) | University of Manchester (2024)
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Sharing Best Practices in Teaching (LSE ECR Network's Peer Learning Café) | LSE (2023)
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Seminar on Combinatorics, Games and Optimisation | LSE (2023)
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6th European Conference on Electrical Engineering and Computer Science | Bern, Switzerland (2022)
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PhD Seminar on Combinatorics, Games and Optimisation | LSE (2022)
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World Conference on Information Systems for Business Management | Bangkok, Thailand (2022)
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7th International Conference on Mathematics and Computers in Sciences and Industry | Athens, Greece (2022)
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British Early Career Mathematicians' Colloquium | University of Birmingham (2021)
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Young Researchers in Mathematics | University of Bristol (2021)
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International Conference of Young Mathematicians | Online Kiev, Ukraine (2021)
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British Early Career Mathematicians' Colloquium | University of Birmingham (2020)
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Algebraic and Geometric Methods of Analysis | Odessa, Ukraine (2020)
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Intellectual Systems and Information Technologies | Odessa, Ukraine (2019)
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British Combinatorial Conference | University of Birmingham (2019)
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SIAM-UKIE National Student Chapter Conference | University of Manchester (2019)
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International Conference of Young Mathematicians | Institute of Mathematics NAS of Ukraine (2019)
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Welsh Mathematics Colloquium | Gregynog Hall (2019)
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British Young Mathematicians Colloquium | University of Birmingham (2019)
Contributed Talk
Contributed Poster
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SIAM-UKIE National Student Chapter Conference | University of Manchester (2019)
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SIAM-IMA Student Chapter Conference | Oxford University (2019)
Society Membership
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Society for Industrial and Applied Mathematics (Discrete Mathematics, Linear Algebra, Optimisation)
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South Wales Operational Research Discussion Society (SWORDS)
Other Responsibilities
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Editorial Board Member of the American Journal of Operations Management and information Systems
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Member of the LSE Review of Books Advisory Board | London School of Economics
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Joint organiser of the Combinatorics, Games and Optimisation (CGO) Seminar | London School of Economics
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Member of the Early Career Research (ECR) Steering Group | London School of Economics
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Undergraduate Academic Mentor | London School of Economics
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WSEAS Transactions on Systems | Reviewer
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WSEAS Transactions on Business and Economics | Reviewer
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International Journal for Mathematics Teaching and Learning | Reviewer
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Canadian Journal of Science, Mathematics and Technology Education (Springer) | Reviewer

