# interactive

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

## Online mathematics

I maintain the (infrastructure for) the following websites:

## 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

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

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, ...)