Rami Luisto

Research

My mathematical research interests are largely in the field of quasiconformal geometry, metric geometry, quantitative topology and in regularity of Sobolev and BV mappings.

In the field of quasiconformal and metric geometry my spesific research questions are focused on branched covers, quasiregular mappings and mappings of finite distortion between Euclidean domains. In particular, I am interested in the so called branch set of a mapping, along with the interplay of the structure of the branch set and the local & global behaviour of the mapping. I'm also interested in the structure of BLD-mappings between (sub)Riemannian manifolds and more general path-metric spaces.

In machine learning and AI I am currently focused on studying topics related to computer vision and NLP, especially as they relate to intelligent document processing.

Illustration of a unique path-lifting result from a paper joint with E. Prywes.

To keep up with the current advances both in my field and the surrounding fields I use arxivist. I warmly recommend a daily dosage.

Publications

  1. On proper branched coverings and a question of Vuorinen (Joint with Aapo Kauranen and Ville Tengvall). Bulletin of the London Mathematical Society volume 54, Issue 1, pages 145-160 (2022). [arxiv:1904.12645]
  2. A Non-Euclidean Story or: How to Persist When Your Geometry Doesn’t. Journal of Humanistic Mathematics, Volume 12 Issue 1 (January 2022), pages 506-556. [arxiv:2003.13758]
  3. On BLD-mappings with small distortion (Joint with Aapo Kauranen and Ville Tengvall). Complex Analysis and its Synergies (2021) 7:5. [arxiv:1909.08860]
  4. Open and Discrete Maps with Piecewise Linear Branch Set Images are Piecewise Linear Maps (Joint with Eden Prywes). Journal of the London Mathematical Society volume 103, Issue 3, pages 1186-1207 (2021). [arxiv:1809.10874]
  5. Weak regularity of the inverse under minimal assumptions (Joint with Stanislav Hencl and Aapo Kauranen). Archive for Rational Mechanics and Analysis volume 238, pages 185-213 (2020). [arxiv:1804.03449]
  6. Mappings of finite distortion: compactness of the branch set (Joint with Aapo Kauranen and Ville Tengvall). Journal d'Analyse Mathematique (2021). [arxiv:1709.08724]
  7. A Newman property for BLD-mappings. Conform. Geom. Dyn. 23 (2019), 135-146. [arXiv:1709.08438]
  8. Stoïlow's theorem revisited (Joint with Pekka Pankka.) Expositiones Mathematicae 38 (2020), no. 3, 303-318. [arxiv:1701.05726]
  9. A characterization theorem for BLD-mappings between metric spaces, The Journal of Geometric Analysis (2017) 27:2081. [arXiv:1509.01832]
  10. Note on local-to-global properties of BLD-mappings, Proceedings of the AMS 144 (2016), no.2, 599-607. [arXiv:1406.0320]
  11. Rigidity of extremal quasiregularly elliptic manifolds (Joint with Pekka Pankka). Groups, Geometry & Dynamics 10 (2016), no. 2, 723-732. [arXiv:1307.7940]

Theses