Research: Geometric Measure Theory, Harmonic Analysis, Dynamical Systems

Selected Publications:

1. The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups (with S. Li and R. Young)
   J. Reine Angew. Math. 784 (2022), 251–274
2. Conformal Graph Directed Markov Systems on Carnot groups. (with J. T. Tyson and M. Urbanski)
   Mem. Amer. Math. Soc. 266 (2020), no. 1291, viii+155 pp.
3. On uniform measures in the Heisenberg group. (with V. Magnani and J. T. Tyson)
   Adv. Math. 363 (2020), 106980.
4. The dimension spectrum of graph directed Markov systems (with D. Leykekhman and M. Urbanski)
   Selecta Math. 25 (2019)
5. Intrinsic graphs and vertical beta numbers in the Heisenberg group. (with T. Orponen and K. Fassler)
   Amer. J. Math. vol. 141 no. 4, (2019), p. 1087-1147.
6. Square functions and uniform rectifiability. (with J. Garnett, T. Le and X. Tolsa)
   Trans. Math. Amer. Soc. 368 (2016), no. 8, 6063–6102.