Mathematics · KAIST

Topology, categories,
and persistence.

I am interested in algebraic topology, category theory, and topological data analysis. In particular, I study persistence modules and categorical formulations of metric and stability phenomena.

arXiv GitHub Solutions & notes

Research

Selected publication

2025

Preprint · Algebraic Topology / TDA

Interleaving Distance as a Galois-Edit Distance

Woojin Kim, Won Seong

A Galois-edit formulation of interleaving distance for finitely presented single- and multi-parameter persistence modules, with an edit-theoretic perspective on stability and bottleneck stability.

arXiv ↗ PDF ↗

Category theory

Higher and homotopical categorical methods; categorical formulations of structure and universality.

Algebraic topology

Homotopical and stable phenomena, with an emphasis on structural explanations rather than calculation alone.

Topological data analysis

Persistence modules, interleaving distance, edit distance, and stability in multi-parameter persistence.

Talks & slides

Presentations

A compact archive for seminar slides, conference talks, and posters.

2026

Interleaving distance as a Galois-Edit distance

ATMCS 12 · Leipzig

slides

Add future talks here

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Notes & solutions

Mathematical archive

Long-form notes, exercise solutions, and material worth keeping public.

Solutions · PDF

Dummit & Foote
Partial Solutions

Selected solutions and working notes for Abstract Algebra.

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Notes

Category Theory

A home for expository notes, reading notes, and small observations.

Coming soon

Slides

Seminars & Talks

Short decks and blackboard-style summaries for talks and seminars.