Research Interests

My work generally spans the areas of fractal geometry, ergodic theory and analysis, although I am also interested in connections to probability and combinatorics.

In particular, my recent work is concerned with:

• Geometric properties of (random and deterministic) fractals of dynamical, arithmetic and combinatorial origin. In particular, geometrical aspects of dynamical rigidity and smoothness of self-similar measures.
• Combinatorial problems in fractal geometry (distance sets, direction sets, Kakeya-type sets, projection theorems, etc).
• Applications of fractal geometry in ergodic theory and analysis. 
• Self-affine sets and the subadditive thermodynamic formalism.