Hi, I’m Justus

I like maths and code

About me

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I’m a Research Associate in Formalization of Mathematics at Imperial College London. Previously, I was a PhD student of Jürgen Hausen in Tübingen, doing algebraic geometry.

  • Formalizing maths with Lean
  • Varieties with torus action
  • Del Pezzo surfaces
  • Convex geometry, polygons
  • Writing programs that count stuff

Projects

Mathlib contributor

2021, 2025-present

In 2021, I started contributing to Lean’s official mathematics library as a hobby. After completing my PhD in 2025, I am now again a regular contributor.

Rational polygons database

2026

A searchable online database of almost 500 million rational polygons, collected from the classifications by Martin Bohnert and me and from the literature. You can search by invariants, identify a given polygon, or query it programmatically.

RationalPolygons.jl

2024-2025

During my PhD, I needed a way to do computations with large amounts of rational polygons. Unsatisfied with the existing solutions, I created RationalPolygons.jl: A pure Julia package optimized precisely for this purpose. Check out its documentation on Github and see also my joint articles with Martin Bohnert.

CStarSurfaces.jl

2023-2025

I developed this Julia package during my PhD to perform classifications of ℂ﹡-surfaces. It was redesigned multiple times, the latest iteration is documented in the appendix of my PhD thesis.

LDP database

2022-2024

I made this online search interface to showcase various classifications of log del Pezzo surfaces with torus action. It is kindly hosted by the University of Tübingen.


Publications

Generalizations of Scott's inequality and Pick's formula to rational polygons

With Martin Bohnert

Preprint

Classifying Rational Polygons with Small Denominator and Few Interior Lattice Points

With Martin Bohnert

Discrete & Computational Geometry (2026)

Classifying log del Pezzo surfaces with torus action

With Daniel Hättig, and Jürgen Hausen

Revista Matemática Complutense 39, 1–74 (2026)

Del Pezzo surfaces of Picard number one admitting a torus action

With Daniel Hättig, Beatrice Hafner, and Jürgen Hausen

Annali di Matematica Pura ed Applicata 204, 1899–1936 (2025)

The Picard index of a surface with torus action

Collectanea Mathematica 76, 515–544 (2025)

Classification and Geometry of Rational Polygons and Surfaces with Torus Action

PhD thesis, University of Tübingen (2025)


Contact

Room 758, Huxley Building, South Kensington Campus, United Kingdom

My current local time is .

j.springer@imperial.ac.uk