About me

I am currently undertaking my master’s degree in Mathematics & Computer Science at the Technical University of Munich.
My professional interests include Software Engineering, Machine Learning — particularly applied uses of numerical solutions — and my newly founded interest in applied topology. I am motivated by projects that bridge rigorous mathematical theory with practical, high‑performance computational systems.

Pure Mathematics

My primary interests are in modern functional analysis and differential geometry.
In functional analysis, I am particularly drawn to operator theory and reproducing kernel Hilbert spaces (RKHS), especially in the context of their applications to machine learning. For example, the study of spectral properties of integral operators and their approximation theory has direct relevance to kernel methods, Gaussian processes, and graph‑based learning algorithms.

I have also worked on a project in manifold deflation, which takes a manifold — possibly non‑convex — and algorithmically “flattens” it into a lower‑dimensional representation while preserving key geometric and topological features. This work connects geometric analysis with computational techniques for data representation and dimensionality reduction.

I continue to explore aspects of geometric analysis that intersect with topology and data science — such as persistent homology and manifold learning — to better understand the shape and structure of complex datasets.

Applied Mathematics

I am interested in machine learning topics that benefit from mathematically grounded numerical methods, with a focus on:

• Quantum mechanical solutions — developing and implementing algorithms for simulating quantum systems, including tensor network methods and resource monotone calculations, and exploring their potential in quantum‑enhanced learning.
• Probability theory in algorithmic trading — applying probabilistic reasoning, statistical inference, and law‑of‑large‑numbers principles to design and evaluate deterministic trading systems.
• Numerical stability and reproducibility — ensuring that algorithms for large‑scale or real‑time applications maintain accuracy under computational constraints.

My work often combines these areas — for example, using probability‑driven decision rules in trading algorithms informed by clustering, data mining and feature engineering, or applying topological data analysis to detect structural changes in time‑series data.

Irish

I am interested in Connemara Irish, especially Árainn Irish and Cois Fharraige Irish.
I have made a hobby of translating common everyday things into Irish and publish translations for games, books, and TV shows. You can see more of my work here.

Note that I also go by my Irish Gaelic surname “Cinnsealach”.