interactive
I have a healthy interest in using computers for mathematics, in different ways.
Online mathematics
I've created interactive classifications:
fanography.info
a tool to visually study the geography of Fano 3-foldsgrassmannian.info
a periodic table of (generalised) Grassmannianshyperkaehler.info
the geography of irreducible holomorphic symplectic (or hyperkähler) varietiesmgnbar.info
the geometry of $\overline{\mathrm{M}}_{g,n}$superficie.info
interactive geography of (minimal) complex algebraic smooth surfacescubics.fanography.info
cubic fourfolds and their associated K3 surfaces
I also maintain the (infrastructure for) the following websites:
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stacks.math.columbia.edu
an open source textbook and reference work on algebraic geometry ncag.info
a website for things related to noncommutative algebraic geometrykerodon.net
an online resource for homotopy-coherent mathematics
Implementations
I've implemented the following (hopefully useful) tools:
hodge-diamond-cutter
, Sage library to compute Hodge numbers for many classes of smooth projective varietiessee also its online documentation
twisted-hodge
, Sage library to compute twisted Hodge numbers of complete intersections, joint with Piet Glasgerby-project
, the system underlying the Stacks project, Kerodon, and other large online mathematical texts
currently not functioning:
bibgetter
, automatically resolve MathSciNet and arXiv identifiers in LaTeX for bibliography management(after the MathSciNet update this no longer works, I will look into it in due time)
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
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