This is the personal area of Alex Hoffnung within the nLab.
I am currently working on a number of projects, which I would like to try to develop here. I list a couple to start, which will hopefully quickly take form here:
Spans in Bicategories
The first two projects will become reasonably small papers, which provide foundational results for a larger project with John Baez:
I have just posted an expository version of this paper, which reflects some early ideas on how this story should go. The next paper will likely differ to some extent in its approach to the relationship between ‘nice topoi’ and groupoids.
The newest project (or more likely, projects) has begun as a fairly regular chat over coffee with James Dolan, who is keeping some of his notes here:
John Baez has been discussing similar ideas with Dolan and has also created a page to detail some of these ideas on his personal web.
This project is a combination of abstract category theory, algebraic geometry and representation theory. This should be a great bridge to span as I go into my new job at the University of Ottawa working with Rick Blute in the Category Theory Group and Alistair Savage in the Representation Theory Group.