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.
Teaching and Supervision
In Wintersemester 2019 (WS2019) I will be teaching parts of the advanced course on Cryptography, run by Prof. Goulnara Arzhantseva. The course material for the previous course is still available here.
I have successfully supervised two masters students. The first, in conjunction with Prof. Goulnara Arzhantseva and Prof. Andrea Lucchini, was Stefania Ebli. She successfully defended her thesis in 2016 at the University of Padova.
The second, in conjunction with Prof. Goulnara Arzhantseva, was Leonhard Katzlinger, who defended his Thesis in the summer semester 2019 at the University of Vienna. His wonderful survey on topological full groups of Cantor groupoids can be found on the arXiv, here.
Preprints and Publications
You can find my up to date publication history through my ORCID:
My preprints are available on the arXiv. The versions of these articles are the same as their corresponding journal versions where possible, and this source may contain more recent work than my ORCID suggests.
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 .