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I edit here and on the French wikipedia (though mostly here right now), mostly on mathematics articles with a particular focus on geometry ("geometric geometry", that is geometric group theory, differential geometry) and dabbling a bit in neighbouring areas of mathematics (number theory, probability, algebraic groups...).
My overall project would be to improve the coverage of geometric group theory (understood in the largest sense possible) on Wikipedia, and for this I am trying to both add new articles concerning recent directions in research (in pure math, taken charitably this means less than 20 years old) and to improve the coverage of the foundations and "entry-level" articles. There is currently not one page on "advanced" mathematics that is a featured article, and a obvious goal of my editing would be to try and bring Geometric group theory to this status. On the other hand I doubt that we can currently do this, since this would need both a well-written coverage of the field depending on solid detailed pages on the various sub-topics, contributors and results that would be useful to a mathematician from a neighbouring field, and a description of what this is about that would be readable by a curious undergraduate or a person stumbling on, the page from the (currently in much better state) page on Group theory.
As (laughably small) parts in this effort I have seriously worked on the following pages (list is mostly here for me to remember wher I am in this project):
- Lattices in topological groups, Arithmetic group and the more topic-specific congruence subgroup, arithmetic Fuchsian group and arithmetic Kleinian group; related pages are Local rigidity, Kazhdan-Margulis theorem, Trace field, Mostow rigidity.
- Gromov hyperbolic space, Hyperbolic group and Real tree.
- Teichmüller space, Thurston compactification, Mapping class group of a surface, Curve complex, Translation surface and Pair of pants (mathematics).
- Hyperbolic 3-manifold, Thurston norm.
- Finiteness properties of groups.
- and some others: (G,X)-manifold, Algebraic torus, Margulis lemma, Poisson boundary, Approximate group...
