Welcome! Basic info about me and this blog can be found in the "about me and this blog" page.
- Brief Introduction (BI)
- Expanded Outline (EO)
- hyperbolicity of complexes
- Just for fun
- random walks
- Why not donating your paper to the public domain?
Category Archives: Brief Introduction (BI)
This post is about a remarkable construction due to Bestvina-Bromberg-Fujiwara. It has been first used to show that the asymptotic dimension of Mapping Class Groups is finite, and it is quite useful, for example, in this great paper by Dahmani-Guirardel-Osin … Continue reading
In this post I’ll talk about a lovely paper by Sebastian Hensel, Piotr Przytycki and Richard Webb. They show that all curve graphs are 17-hyperbolic. Hyperbolicity of curve graphs is a very very very useful* property because mapping class groups … Continue reading
In this post I’ll define finite decomposition complexity (FDC) for you, tell you what it’s good for (Stable Borel Conjecture!) and point out that an argument by Osin shows that it is preserved by relative hyperbolicity. First, the motivation. Here … Continue reading
In this post I’ll discuss a cool lemma due to Brian Bowditch (from this paper) which is very useful when you want to show that a space is hyperbolic. The most direct way of showing that is hyperbolic is trying … Continue reading
It is a remarkable fact that the group of orientation-preserving isometries of can be identified with the group of bi-holomorphisms of the unit disk in . [Fun fact: Poincaré said that he discovered (basically) this while stepping on a bus.] … Continue reading
First of all, you can read about nonstandard analysis in a slightly more famous blog than my own, for example you can check out this post. I guess I should explain the quote “a small investment” by Isaac Goldbring (afaik). … Continue reading
There are a few types of quasi-isometric rigidity results. I will talk about results of the following kinds: 1) self-quasi-isometries of such-and-such space or group (coarsely) preserve some structure, usually a collection of (left cosets) of subgroups 2) if a … Continue reading
This post contains an experimental exposition of asymptotic cones, I hope this will be vaguely understandable (feedback is warmly welcome!). Many (most?) researchers actually think of asymptotic cones in a way similar to the one I’ll present, rather than as … Continue reading