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

  1. Quantitative quasisymmetric uniformization of compact surfaces, with Lukas Geyer. To appear in The Proceedings of the American Mathematical Society.
  2. Iterated function system quasiarcs, with Annina Iseli. Conformal Geometry and Dynamics (2017).
  3. Quasiconformal mappings that highly distort dimensions of many parallel lines, with Zoltán Balogh and Jeremy Tyson. Annales Academiæ Scientiarum Fennicæ Mathematica (2017).
  4. 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).
  5. Steiner's formula in the Heisenberg group, with Zoltán Balogh, Fausto Ferrari, Bruno Franchi, and Eugenio Vecchi. Nonlinear Analysis: Theory, Methods, and Applications (2015).
  6. Sharp differentiability results for the lower local Lipschitz constant and applications to non-embedding, with Thomas Zürcher. Journal of Geometric Analysis (2015).
  7. Weak contact equations for mappings into Heisenberg groups, with Zoltán Balogh and Piotr Hajłasz. Indiana University Mathematics Journal (2014).
  8. Dimension distortion by Sobolev mappings in foliated metric spaces, with Zoltán Balogh and Jeremy Tyson. Analysis and Geometry of metric spaces (2013).
  9. Quasisymmetric Koebe Uniformization with Sergei Merenkov. Revista Mathematicá Iberoamericana (2013).
  10. Modulus and Poincaré Inequalities in non-self-similar Sierpińnski carpets, with Jeremy Tyson and John Mackay. Geometric and Functional Analysis (2013).
  11. Analytic aspects of quasiconformal mappings of metric spaces, with Pekka Koskela. In Metric and Differential Geometry, the Jeff Cheeger Anniversary Volume (2012).
  12. Space filling with metric measure spaces, with Thomas Zürcher. Mathematische Zeitschrift (2012).
  13. Quasisymmetric structures on surfaces. Transactions of the American Mathematical Society (2010).
  14. Spaces of small metric cotype, with Ellen Veomett. Journal of Topology and Analysis (2010).
  15. Peano cubes with derivatives in a Lorentz space, with Thomas Zürcher. Illinois Journal of Mathematics (2009).
  16. Quasisymmetric parameterizations of two dimensional metric planes. Proceedings of the London Mathematical Society (2008).
  17. Exceptional sets for quasiconformal mappings in general metric spaces, with Pekka Koskela. International Mathematics Research Notices (2008). See the Errata.