Tuomas Sahlsten

I have been studying problems related to geometric measure theory, in particular, on the fractal dimensions and local distributions of measures in Euclidean spaces. Currently, I am interested of the applications of dynamical systems to number theoretic and geometric problems. Especially, I am quite fascinated by arithmetic dynamics and in particular beta-expansions of real numbers, and also by Furstenberg's CP-chains which have recently had some cool applications in fractal geometry.

Publications

1. On Fourier analytic properties of graphs
   with J. Fraser and T. Orponen
   Int. Math. Res. Not. IMRN (2013), to appear
2. Tangent measures of typical measures
   Real Analysis Exchange (2013), to appear
3. Dimension, entropy and the local distribution of measures
   with P. Shmerkin and V. Suomala
   J. London Math. Soc. (2013), to appear
4. Tangent measures of non-doubling measures
   with T. Orponen
   Math. Proc. Cambridge Philos. Soc. 152 (2012), 555-569
5. Radial projections of rectifiable sets
   with T. Orponen
   Ann. Acad. Sci. Fenn. Math. 36 (2011), 677-681

• Fine Structure of Measures
  PhD Thesis, University of Helsinki (2012)

Collaborators

Here are some people I have collaborated or I am currently collaborating with: Andrew Ferguson, Jonathan Fraser, Jasun Gong, Timo Jolivet, Thomas Jordan, Vadim Kulikov, Antti Käenmäki, Bing Li, Niko Marola, Sara Munday, Tuomas Orponen, Tony Samuel, Pablo Shmerkin, Ville Suomala and Jim Tseng. Check out their work as well!