Computations in geometric group theory, hyperbolic geometry, and the mapping class group — interactive tools alongside the notebooks and source they grew out of.
Professor and Chair, School of Mathematics, Korea Institute for Advanced Study (KIAS), and affiliate professor at the Graduate School of AI4Math, KAIST. Since 2025 also working with the Superhuman Reasoning team at Google DeepMind on AI for mathematical research.
Publications, research in geometric group theory and low-dimensional topology, activities, and full academic background.
Visit kimsh.kr →Interactive mathematics across space, flow, quantum, sense, machine, and mechanics — 37 chapters of explorable explanations, in English and Korean.
Visit edu.kimsh.kr →These run entirely client-side — nothing to install.
Decides whether a given graph embeds as an induced subgraph of the curve graph of the five-punctured sphere. Since the complexity is ξ(S0,5) = 2, the Aougab–Biringer–Gaster theorem forces any such graph to be simple and strictly triangle-free. Offers a practical certificate search and an exact certified mode, with built-in examples.
An illustrated tour of what it would be like to inhabit hyperbolic space: how distance, area, and the horizon behave when the geometry curves away from you everywhere at once.
Mathematica notebooks, C++, and GAP scripts. These do not run in a browser — each link opens the folder on GitHub, where notebooks and PDFs can be previewed or downloaded.
Farey compact lists, special polygons, and binary-tree searches for full Farey numbers. Nineteen notebooks and data files, 2022–2023.
Fundamental domains for arithmetic Kleinian groups: generators, faces, edges, and quotient data computed for Bianchi orbifolds, with notebooks driving the runs and checking equivalence and volume. Builds on Aurel Page’s KleinianGroups Magma package, bundled here under the GPL v3 — the folder’s README says which files are which.
Polygonality and geometric-likeness tests: a C++ search over random and specific words, with Mathematica notebooks summarizing the runs and a reduced tiling conjecture. The largest collection here — 70 files, dating back to 2010.
Notebooks on acute angles and acute triangulations of surfaces.
The relation-number algorithm and the output of a full run.
Early GAP working notes.