I am a postdoctoral research fellow at the University of Adelaide in South Australia.
Theorem A for topological categories - this is a version of Quillen’s Theorem A for categories in . As a corollary, with a condition on the unit map of the codomain we get that geometric realisation of an -equivalence is a homotopy equivalence.
Serre’s proof of the Grothendieck-Serre theorem on the Brauer group of a compact space. (to be uploaded).
I have views about the current system of academic publishing, especially how it impacts mathematics. Two links of interest:
Math2.0 - a forum on mathematical publishing and what can be done
Construction of an equivalence between crossed modules in finite groups, and crossed modules with finite homotopy groups. More generally, same thing with (finite groups) replaced with some sort of Serre class.