interactive

I have a healthy interest in using computers for mathematics, in different ways.

Online mathematics

I maintain the (infrastructure for) the following websites:

• stacks.math.columbia.edu
  an open source textbook and reference work on algebraic geometry
• ncag.info
  a website for things related to noncommutative algebraic geometry
• kerodon.net
  an online resource for homotopy-coherent mathematics
• fanography.info
  a tool to visually study the geography of Fano 3-folds
• grassmannian.info
  a periodic table of (generalised) Grassmannians
• superficie.info
  interactive geography of (minimal) complex algebraic smooth surfaces

Implementations

I've implemented the following (hopefully useful) tools:

• bibgetter, automatically resolve MathSciNet and arXiv identifiers in LaTeX for bibliography management

• twisted-hodge, Sage library to compute twisted Hodge numbers of complete intersections, joint with Piet Glas

• hodge-diamond-cutter, Sage library to compute Hodge numbers for many classes of smooth projective varieties

Various

I also have smaller (and older) projects:

• An atlas for $\mathop{\mathrm{Spec}}\mathbb{Z}[x]$, a collection of pictures for the geometric intuition behind $\mathop{\mathrm{Spec}}\mathbb{Z}[x]$

• comparison of topologies on $\mathrm{Sch}/S$, an incomplete comparison of all the Grothendieck topologies on the category of schemes I could find, together with their properties

  see github.com/pbelmans/topologies-comparison

• cohomology of twists of the structure sheaf and Hodge diamonds for complete intersections: in the case of a complete intersection it is not too difficult to compute the dimensions of the cohomology spaces of (twists of) the structure sheaf, thereby visualising Serre duality, and similarly one can compute the Hodge diamond

  see github.com/pbelmans/cohomology-tables

• comparison tables for the Stacks project (work in progress): the goal is to have tables comparing properties and providing a structured means of accessing the Stacks project, the first example being properties of morphisms and their preservation properties (under composition, base change, fpqc descent, ...)

  see github.com/stacks/stacks-table