Why Do Finite Fields Have Prime-Power Size?
A combinatorial route from unique factorization to an Euler-product generating function, Möbius inversion, and the existence of irreducible polynomials of every degree over finite prime fields.
Notes & ideas
Blog
Short notes on physics, topological data analysis, topological machine learning, and the computational tools I use day-to-day. These posts are informal and often technical – more like research notes than polished papers.
Latest posts
Why Can't I Take My Underwear Off While Wearing Pants? (Topologically)
A playful but rigorous investigation of an everyday puzzle using pair-of-pants surfaces, fundamental groups, knot theory, spatial graphs, Alexander duality, and ambient isotopy.
Topological Representation of Exoplanet Transits
From a limb-darkened exoplanet transit light curve to a delay-coordinate point cloud and persistent homology, with an interactive demonstration and reproducible Python example.
Topological Representation of Stellar Spectra
How can an absorption spectrum be converted into a multiscale topological object? We build the construction from first principles and test it on a reproducible synthetic spectrum near the Mg I b triplet.
Topological Representation of Light Curves
A two-part note on how a one-dimensional light curve can be converted into a geometric and topological object, and how this viewpoint helps us characterize periodicity, transients, and structure beyond classical summary statistics.
Welcome to my research notes
An overview of what you can expect to find here: notes on physics, topological data analysis, machine learning, and small computational experiments that do not fit into formal papers.
About this blog
Posts here are mostly for learning and sharing ideas. They may contain incomplete results, toy models, or work-in-progress thoughts. If you spot an error or want to discuss something, feel free to send me an email.