I am a postdoctoral researcher in the Geometric and Analytic Group Theory group at the University of Vienna, working with Goulnara Arzhantseva. I received my Ph.D. from the School of Mathematics of the University of Southampton. My supervisor was Nick Wright.
Fakultät für Mathematik,
|e-mail:||martin.finn-sell 'at' univie.ac.at|
I am primarily interested in the coarse geometry of metric spaces, aiming toward understanding coarse properties of discrete groups and the role they play in controlling topological and analytic aspects of group theory.
More specifically, I am currently learning about topological full groups of r-discrete groupoids, and trying to understand the connections between property A and properties of the dynamical system that can be extracted from the associated representations of the full pseudogroup. I am also interested in obtaining results, via groupoid techniques, concerning coarse properties of sofic groups, as well as doing more general coarse geometry to groupoids with metrizable fibres.
I also retain a keen interest in the Baum-Connes conjecture, and am interested in quantitative approaches to this conjecture that use old ideas from controlled topology that are now prevalent in applied topology in the guise of persistent homology.
This summer semester I am teaching assistant for two exercises classes for the undergraduate course Algebra I. The exercise sessions take place in Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock at 13.15 and 14.15 respectively. Students who've found their way here and need information should check out the Moodle for their respective class.
I am also in charge of the "geometric and analytic group theory" research seminar, which this semester is hosting introductory talks on this subject. Details can be found at the seminar webpage.
Preprints and Publications
Sofic boundaries of groups and coarse geometry of sofic approximations [2016 - with Vadim Alekseev] arXiv
Non-amenable principal groupoids with weak containment [2016 - with Vadim Alekseev, accepted, International Mathematical Research Notices] arXiv
The asymptotic dimension of box spaces for elementary amenable groups [2015 - with Jianchao Wu] arXiv
Almost quasi-isometries and more non-exact groups [2015 - accepted, Proceedings of the Cambridge Philosophic Society] arXiv
Subsemigroup, ideal and congruence growth of free semigroups [2015, with Alex Bailey and Rob Snocken - Accepted, Israel Journal of Mathematics] arXiv
On the Baum-Connes conjecture for Gromov monster groups [2015 - Published, Journal of Noncommutative Geometry] arXiv
Below are the links associated to the paper: "Subsemigroup, ideal and congruence growth of free semigroups":
- The project webpage for the paper
- A local copy of the algorithm FISOFS , taken from the link above.
- A local copy of the data up to index 7 and index 8 computed using FISOFS.
- A navigational tool (using HTML/XML) for navigating finite index subsemigroups of FS_2 using their gap sets, the shortlex tree .