Thank you for visiting! I am currently a Heibronn Fellow at the University of Bristol. I was previously a postdoc at ICMAT in Madrid, and before that a postdoc at UPV/EHU supervised by Ilya Kazachkov. I received a PhD in May 2016 from Vanderbilt University under the advisement of Mark Sapir. My Erdos is 2. A recent fascination has been the construction of unusual objects. These include
- (w/ Saharon Shelah) many infinite groups which can only act on a metric space by bounded orbits (see here, for locally indicable examples see here);
- groups which are freely indecomposable, whose subgroups of smaller cardinality are free, but whose abelianization is free and of maximum possible rank (see here);
- Jonsson groups (every proper subgroup is of strictly smaller cardinality) at arbitrarily large cardinalities (see here);
- an isomorphism between the fundamental group of the harmonic archipelago and that of the Griffiths double cone (see here);
- a topological space which is “just barely connected” and satisfying some other strange properties (see here);
- a model of ZF + [ultrafilter lemma] in which there is a metric space which is not paracompact (the axiom of choice implies that no such space exists, see here);
- a model of ZF + [dependent choice] in which there is a torsion-free abelian group which is not bi-orderable (the ultrafilter lemma implies that no such group exists, see here).
Other papers deal with automatic continuity (w/ various coauthors including Oleg Bogopolski, Greg Conner, Ilya Kazachkov, Saharon Shelah, Olga Varghese). As some examples, any abstract group homomorphism from a
- completely metrizable topological group to Thompson’s group F, or to a torsion-free word hyperbolic group, or to a braid group, has an open kernel;
- locally compact topological group to a group which has no torsion nor a subgroup isomorphic to or to a p-adic integer group, has an open kernel;
- locally countably compact topological group to the mapping class group of a connected compact surface, will map some open normal subgroup of the domain to a finite subgroup of the codomain.
Still other papers analyze fundamental groups of wild topological spaces.
On the right you will find links to a CV and other web pages, also links to my papers in the reverse chronological order in which they appeared on arXiv. A few blog posts are below.