Research: Geometric Measure Theory, Harmonic Analysis, Dynamical Systems

Selected Publications:

1. The dimension spectrum of graph directed Markov systems (with D. Leykekhman and M. Urbanski)  Selecta Math. to appear.
2. Intrinsic graphs and vertical beta numbers in the Heisenberg group. (with T. Orponen and K. Fassler) Amer. J. Math. to appear.
3. Conformal Graph Directed Markov Systems on Carnot groups. (with J. T. Tyson and M. Urbanski) Mem. Amer. Math. Soc. to appear.
4. Square functions and uniform rectifiability. (with J. Garnett, T. Le and X. Tolsa)
   Trans. Math. Amer. Soc. 368 (2016), no. 8, 6063–6102.
5. Removable sets for Lipschitz harmonic functions on Carnot groups. (with V. Magnani and J. T. Tyson) Calc. Var. PDE.  no. 3-4 (2015) 755–780.
6. Singular integrals on self-similar sets and removability for Lipschitz harmonic functions in Heisenberg groups. (with P. Mattila) J. Reine Angew. Math. 691 (2014), 29–60.