Welcome to Topology and Group Theory

Thank you for visiting!  I am currently a Heibronn Fellow at the University of Bristol.  I received a PhD in mathematics in May 2016 from Vanderbilt University under the advisement of Mark Sapir.  My results include theorems of automatic continuity, combinatorial and geometric group theory, applications of set theory to group theory, and decompositions of fundamental groups of wild topological spaces.  I also draw some ties between geometry and axiomatic set theory as well as axiomatizability and direct limit structures.

A recent fascination has been the construction of unusual uncountable groups.  With Saharon Shelah we construct many infinite groups which can only act on a metric space by bounded orbits (see here).  I have also produced groups which are freely indecomposable, whose subgroups of smaller cardinality are free, but whose abelianization is free and of maximum possible rank (see here).

I was previously a postdoc at ICMAT in Madrid, before which a postdoc at the University of the Basque Country UPV/EHU supervised by Ilya Kazachkov.  My Erdos number is 2.  On the right you will find links to my CV and some web pages related to math that I enjoy, as well as links to my papers in the reverse chronological order in which they appeared on arXiv.  Blog posts are below.