About

Welcome to my blog! I’m Zia Rehman, a software engineer and mathematician based in London, with a passion for blending advanced mathematics with cutting-edge technology. I hold a Master of Mathematics from the University of Nottingham, where I explored complex topics in theoretical physics and mathematics. In my professional career, I specialize in designing and developing the core software architecture that drives advanced data modeling systems. My work includes building robust libraries for various types of modelling, and complex data transformations, along with the APIs that make these capabilities accessible and scalable.

Educational Background

During my time at the University of Nottingham, I explored a range of complex topics, including:

• Quantum Information Science: Exploring the principles of quantum mechanics as they apply to information theory, including concepts such as quantum entanglement, quantum cryptography, and quantum algorithms.
• Quantum Field Theory: Studying the fundamental forces and particles that make up our universe through the lens of advanced mathematics.
• Black Holes: Investigating the physics of black holes, exploring concepts like event horizons, singularities, and Hawking radiation.
• Differential Geometry: Exploring the mathematical framework that describes the curvature and shape of spaces, essential in understanding the geometry of the universe and the foundations of general relativity.

My thesis, titled “Cohomological Techniques for Abelian Gauge Theory”, explores the relationship between cohomology, a key concept in algebraic topology, and electromagnetism, an abelian gauge theory. By reformulating Maxwell’s equations using differential forms, I demonstrated that electric and magnetic charges can be associated with de Rham cohomology classes. However, this classical formulation falls short when accounting for quantum phenomena like the Aharonov-Bohm effect, which led to the development of a more robust gauge-theoretic framework. This new approach not only recovers the classical field strength but also reveals deeper topological structures, linking gauge fields to differential cohomology groups. The thesis ultimately provides a unified perspective on electromagnetism, connecting physical phenomena to abstract mathematical concepts, and suggests future research directions in more complex spacetimes.

Professional Journey

I currently work as a software engineer, blending my mathematical background with practical software engineering. I’m proficient in a broad range of technologies, including:

• Full Stack Engineering: C# (ASP.NET Core, Entity Framework Core), Python (FastAPI, Flask), JavaScript/Typescript (Angular, React), and SQL/NoSQL databases.
• Data Science: Python (Pandas, NumPy, Scikit-learn), MATLAB, R, and data visualization tools.
• DevOps: Docker, CI/CD pipelines, Microservices, and Agile methodologies.

Why This Blog?

This blog is where I share my journey at the intersection of mathematics, software engineering, and data science. Whether it’s exploring advancements in data science, dissecting new algorithms, or providing tutorials on full-stack engineering, I aim to create content that’s both insightful and practical for all levels!

Beyond Engineering

Outside of my professional life, I’m fascinated by the field of quantitative finance and enjoying the complexities of Rust. I also maintain an active lifestyle, enjoying calisthenics, climbing and powerlifting.

Thank you for stopping by. I hope you find the content here both informative and inspiring. Feel free to connect or discuss any topics that interest you!