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This project started a while ago when I was an undergrad student at Ghent University (Belgium). This compendium allowed me to summarize all the topics that I found interesting. However, the initial purpose was quickly forgotten. Instead of summarizing the courses that I took, my interest in more exotic topics increased and I started to use this compendium as a means to remember what I learned. Although all chapters are mathematical in nature, most chapters are even purely focused on mathematics, the motivating force was, is and will remain the understanding of the physical laws of Nature.
After my career switch in 2020 (from the Physics department to the Bio-science department) this project got yet another purpose. Now it also served as the primary motivation for reading papers and books on exotic subjects. Currently the mathematical foundations of the project are more or less settled. The topics of interest for the (near) future are Modal Type Theory, Higher Geometry and Algebraic Quantum Field Theory (although, as in the past, the route towards attaining a decent understanding of these topics will probably lead me along a dozen other interesting areas). At some point it would also be nice if the chapters about physics reach the same level of maturity as those on mathematics, but for the time being I am still not smart enough.
Anyway, the main areas of interest are the following ones:
- Category theory
- Differential topology
- Gauge theory
- Foundations of physics
In 2014 I started an undergraduate degree at Ghent University (Belgium) in Physics & Astronomy. From the start I knew I was more interested in the theoretical side of science in general, so I mainly selected mathematics and theoretical physics courses. For my master degree (2019) I did a thesis on symmetry-protected topological states and tensor networks "Spatial Symmetries and Symmetry Breaking with Matrix Product States". In February 2020 I started a PhD at the mathematical modelling department of the Bio-Science Faculty in Ghent where I now mainly work on uncertainty estimation in machine learning problems.
The true starting date of this project has been lost to time. The first drafts were only stored offline and at the time I started using GitHub for this project, it was located on a private university GitHub. The earliest commit on that repository dates back to November 7, 2017. At that time the repository consisted of 87 files (mainly written in tex and including many redundant files due to a misconfigured .gitignore-file). The topics already included things such as Measure Theory, Differential Geometry and Quantum Mechanics. (Apparently my fascination for category theory started later.)