The primary source code repository for Macaulay2, a system for computing in commutative algebra, algebraic geometry and related fields.

Comprehensive open source book on basic topology, smooth manifolds, differential geometry, Lie theory, homological algebra, and index theory.

CAP project -- Categories, Algorithms, and Programming

Deposited packages of the homalg project

Notes for the lecture course “Foundations in Representation Theory”.

Typst Lecture Notes for University of Oxford course C2.2 Homological Algebra (Michaelmas, 2023-24)

A GAP framework for categorical homological algebra with special focus on homotopy categories and tilting equivalences

The homalg project compatibility package for Julia

Equivalent definitions of flatness

A rewrite of the Quiver frontend to use Bootstrap CSS so that it can be used as a diagram editor on all platforms having a web browser.

Homological Algebra

Using chain complexes to enforce clean information flow in neural networks.

Chain complexes in Julia

Category theory & homological algebra lecture notes (HSE, Spring 2025)

Program (still in progress) for calculating resolutions of modules over the truncated Steenrod algebra 𝓐(1) at p = 2.

My math publications

A short seminar I gave in Padova, in January 2020, dealing with the proof of De Rham theorem for singular and De Rham cohomology.

Lecture notes from APMA 2811X: Finite Element Exterior Calculus by Johnny Guzman at Brown University for the Spring 2024 semester.

An algorithm that computes the twisted L^2-Euler characteristic.

Notes written for (lazy) lectures.