# interactive

I have a healthy interest in mathematics on the internet:

Moreover I like interactive mathematics:

- le superficie algebriche
- An atlas for $\mathop{\mathrm{Spec}}\mathbb{Z}[x]$
- comparison of topologies on $\mathrm{Sch}/S$
- cohomology of twists of the structure sheaf and Hodge diamonds for complete intersections

## Stacks project

First and foremost, I am the developer of the Stacks project. To quote its description:

It is an open source textbook and reference work on algebraic stacks and the algebraic geometry needed to define them.

I am responsible for the website, which contains some (in my opinion) exciting features, such as the LaTeX preview (including commutative diagrams) and dependency graphs.

`ncag.info`

`ncag.info`

aims to be something like a portal website for noncommutative algebraic geometry. At the moment it consists of a regularly updated list of conferences in the field.

## le superficie algebriche

le superficie algebriche is a tool to study the Enriques–Kodaira classification of compact complex surfaces. It is joint with Johan Commelin. If you feel like contributing, see GitHub.

## Various

I also have smaller 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, ...)