1. Why this blog exists
Most of my work lives in papers, talks, and code repositories. That is great for finished results, but not so great for the messy in-between stage where ideas are tried, broken, and slowly improved.
This blog is a space for that in-between stage. Here I want to record small computational experiments, derivations, and observations that connect topological data analysis (TDA), topological deep learning, and physical systems across scales – from gravitational waves and galaxy morphology to dynamical systems and condensed-matter toy models.
Posts are intentionally informal. They are closer to research notes than to polished articles, and I expect many of them to evolve as projects move forward.
2. What you will find here
2.1 Conceptual notes
Short explanations of ideas that I use frequently in my work, such as:
- Intuition behind persistent homology and persistence diagrams;
- How Mapper and related constructions help summarize complex state spaces;
- Connections between TDA, graphs, and representations used in ML models.
2.2 Computational experiments
Many posts will include small Python scripts or Jupyter-style snippets where I try things out on synthetic or real data. Examples include:
- Topological summaries of gravitational-wave-like time series at low SNR;
- Simple models for galaxy morphology using self-supervised representations;
- Diagnostics of neural networks trained on physical simulations.
Whenever possible, I will link to the corresponding code repositories or notebooks so that you can reproduce or modify the experiments.
2.3 Teaching and learning material
I also plan to use the blog to share material that may be useful for students:
- Notes that complement my courses or seminars;
- Step-by-step introductions to tools I use frequently (Python, TDA libraries, etc.);
- Annotated references and reading suggestions for people entering the area.
3. Who this blog is for
The primary audience I have in mind is:
- Students and researchers in physics or astronomy curious about TDA and ML;
- People from the TDA / ML community interested in physical applications;
- Anyone who enjoys seeing how mathematical ideas meet real data.
I will try to keep posts as self-contained as reasonably possible, but some familiarity with basic calculus, linear algebra, and programming will certainly help.
4. How to read and use these posts
You should think of these posts as invitations rather than final answers. Feel free to:
- Reuse snippets of code or ideas in your own projects (with attribution, if relevant);
- Disagree, extend, or correct what you find – and let me know when you do;
- Contact me if a note sparks an idea for a collaboration or project.
If you notice any errors or have suggestions for topics, feel free to send me an email. I am always happy to discuss physics, topology, and machine learning.