# Research

## If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

John von Neumann

I received my Ph.D. in 2007 from the University of Michigan under the supervision of Mario Bonk. I also worked closely with Juha Heinonen during my studies. During my post-doctoral years, I was mentored by Pekka Koskela, Zoltán Balogh, and Stefan Wenger. I made my habilitation at the University of Bern in 2014 before becoming Assistant Professor at Montana State University. In 2017 I returned to Switzerland.

## Publications

- Quantitative quasisymmetric uniformization of compact surfaces, with Lukas Geyer. To appear in The Proceedings of the American Mathematical Society.
- Iterated function system quasiarcs, with Annina Iseli. Conformal Geometry and Dynamics (2017).
- Quasiconformal mappings that highly distort dimensions of many parallel lines, with Zoltán Balogh and Jeremy Tyson. Annales Academiæ Scientiarum Fennicæ Mathematica (2017).
- Frequency of Sobolev dimension distortion of horizontal subgroups of the Heisenberg group, with Zoltán Balogh and Jeremy Tyson. Annali della Scuola Normale Superiore di Pisa, Classe di Scienza (2017).
- Steiner's formula in the Heisenberg group, with Zoltán Balogh, Fausto Ferrari, Bruno Franchi, and Eugenio Vecchi. Nonlinear Analysis: Theory, Methods, and Applications (2015).
- Sharp differentiability results for the lower local Lipschitz constant and applications to non-embedding, with Thomas Zürcher. Journal of Geometric Analysis (2015).
- Weak contact equations for mappings into Heisenberg groups, with Zoltán Balogh and Piotr Hajłasz. Indiana University Mathematics Journal (2014).
- Dimension distortion by Sobolev mappings in foliated metric spaces, with Zoltán Balogh and Jeremy Tyson. Analysis and Geometry of metric spaces (2013).
- Quasisymmetric Koebe Uniformization with Sergei Merenkov. Revista Mathematicá Iberoamericana (2013).
- Modulus and Poincaré Inequalities in non-self-similar Sierpińnski carpets, with Jeremy Tyson and John Mackay. Geometric and Functional Analysis (2013).
- Analytic aspects of quasiconformal mappings of metric spaces, with Pekka Koskela. In Metric and Differential Geometry, the Jeff Cheeger Anniversary Volume (2012).
- Space filling with metric measure spaces, with Thomas Zürcher. Mathematische Zeitschrift (2012).
- Quasisymmetric structures on surfaces. Transactions of the American Mathematical Society (2010).
- Spaces of small metric cotype, with Ellen Veomett. Journal of Topology and Analysis (2010).
- Peano cubes with derivatives in a Lorentz space, with Thomas Zürcher. Illinois Journal of Mathematics (2009).
- Quasisymmetric parameterizations of two dimensional metric planes. Proceedings of the London Mathematical Society (2008).
- Exceptional sets for quasiconformal mappings in general metric spaces, with Pekka Koskela. International Mathematics Research Notices (2008). See the Errata.