王进一 (Wang Jinyi), SimplicialCat

Maths

My supervisor is Prof. Lin Chen.

My mathematical interests lie in

• initially, differential geometry, algebraic topology;
• later, category theory, topos theory, categorical logic,
• homotopy theory, homotopy type theory;
• and recently, the geometric Langlands program.

Some of my talks are on Bilibili.

Some of my notes are on Zhihu.

Here are my Github repositories.

Selected works

These are in Chinese unless specified otherwise.

盲人摸象 (Blind men touching an elephant)

A basic introduction to topos theory.

Book on Github (>300 pages)

单纯百科 Simplopedia

A forest-style site personal encyclopedia of mathematics.

Site

Nonabelian Cohomology English

A short note on nonabelian cohomology, using the language of ∞-toposes.

Notes

Sketches of an Elephant English

A short talk on topos theory (name borrowed from P. Johnstone)

Notes

Interview with Prof. Laurent Lafforgue English

Video 1: From Langlands program to topos theory

Video 2: The future of topos theory

Category Theory in Differential Geometry

A short talk on the use of sheaves and stacks in differential geometry.

Notes

Quillen's 1969 paper explained English

A presentation of Quillen's 1969 paper on formal group laws.

Notes

Survey on Atiyah–Singer index theorem English

Article

Spin geometry and Dirac operators

Notes

Notes on Categorical Logic Summer School 2025

Notes 1: Posets and propositional logic

Notes 2: Lex categories, algebraic theories and locally finitely presentable categories

Notes 3: Sketches

Principal bundles in an ∞-topos

Video and Slides English

All concepts are Kan extensions

Video

Non-maths

Selected musical works

Que le Vent Soit Doux

An improvised piano re-arrangement of a beautiful background music in Genshin Impact.

Video