Latest Posts

Choo Choo
Today I posted my first paper, Train Tracks, Orbigraphs and CAT(0) Freebycyclic Groups to the ArXiv! In it I give an extension to automorphisms of free products of the algorithmic construction of relative train track maps for outer automorphisms of free groups. I use it to prove that mapping tori of polynomiallygrowing automorphisms of certain kinds are CAT(0) groups. I want to talk about the main ideas in the proof. I haven’t addressed the question of “why” study these groups in this post, but I will another time.

The Lay Of The Land
In a poor attempt to remain interesting to the nonmathematically inclined reader, maybe it would be good to begin with a few words about the landscape.

The Category Of Graphs
You know the sensation where a familiar word becomes suddenly completely strange for no apparent reason? Like suddenly the scales fall away from your eyes and you see how utterly weird it is that a concept has a particular name? I’ve been having that feeling with the word graph as I use it in math.

Hello World
Earlier this week, Marc Weidenbaum of disquiet.com wrote a paean to the blog that I found really inspiring. “Selfpublishing,” he writes, “is the heart of the healthy internet.”