David Roberts David Roberts

This is the private area of David Roberts within the nLab.

I am a visiting fellow at the University of Adelaide in South Australia, and was a postdoc there for a couple of years.

For my papers (including PhD thesis) please see here. This site is to gather teaching material, but also more ephemeral things.

• See here for a list of my talks.

• See here for a list of the courses I’ve taught as well as students who’ve worked on projects with me

• here is a list of unicode/TeX equivalents

Notes

• Theorem A for topological categories - this is a version of Quillen’s Theorem A for categories in $Top$. As a corollary, with a condition on the unit map of the codomain we get that geometric realisation of an $\mathcal{N}$-equivalence is a homotopy equivalence.

• Serre’s proof of the Grothendieck-Serre theorem on the Brauer group of a compact space. (to be uploaded).

Mathematical publishing

I have views about the current system of academic publishing, especially how it impacts mathematics. Two links of interest:

• The cost of knowledge (wiki) - a boycott of Elsevier

• Math2.0 - a forum on mathematical publishing and what can be done

Less polished ideas

• 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.

• The (n+1)-ary factorisation system on nCat

• The 2-connected cover of a 2-crossed complex

• cocompact proper Lie groupoids

• geometry on S^5

Random ideas

• list of journals publishing category theory - clearly incomplete!

• scratch - read at own risk!