Research

For you Simpsons fans out there, I like to think of myself as a hyperbolic topologist. The terminology comes from the following Professor Frink quote: "Well, it should be obvious to even the most dim-witted individual who holds an advanced degree in hyperbolic topology, that Homer Simpson has stumbled into... the third dimension!"

Research Interests

Preprints

Publications

(You can also see a list of all my publications/preprints on the arXiv here.)

Denotes an undergraduate author.

Notes

These are notes on the open problem session run by Priyam Patel and Nicholas Vlamis for the infinite-type surfaces group at the 2021 Nearly Carbon Neutral Geometric Topology conference. The notes have been typed by Yassin Chandran.


These notes stem from discussions at the AIM workshop "Surfaces of infinite type".  In particular, they give proofs that big mapping class groups are not locally compact, not compactly generated, homeomorphic to the irrational numbers, and give an infinite family of mapping class groups that are generated by coarsely bounded sets (and hence have a well-defined quasi-isometry class).

Update 2/21/2020: Proposition 18 is now Conjecture 18 (and the following corollary was removed).  An error was pointed out to me: please see document for a discussion.  Also, added the new and very relevant reference to the paper "Large scale geometry of big mapping class groups" by Mann-Rafi.  This paper supercsedes the section of the notes on coarse boundedness, but I still think the explicit examples given in the notes are valuable.

Other sources for this information: