Preprints and Publications

1. Polynomial Fourier Decay For Patterson-Sullivan Measures. (pdf).

2. Exponential Mixing Via Additive Combinatorics. Submitted. (pdf). (Slides). (Notes).

3. On the Space of Ergodic Measures for the Horocycle Flow on Moduli Spaces of Abelian Differentials.

   Joint with Jon Chaika and John Smillie. Annales Scientifiques de l'ENS, 2023. (pdf). (Slides).

4. Random Walks, Spectral Gaps, and Khintchine's Theorem on Fractals.

   Joint with Manuel Luethi. Inventiones, 2022. Journal. (pdf). (Slides).

5. Singular Vectors on Fractals and Projections of Self-similar Measures.

   Geom. & Funct. Analysis (GAFA), 2020. Journal. (pdf).

6. Bounded and Divergent Trajectories And Expanding Curves on Homogeneous Spaces.

   Trans. of the Amer. Math. Soc., 2020. Journal. (pdf). (Slides).

7. Exceptional Directions for the Teichmuller Geodesic Flow and Hausdorff Dimension.

   J. Eur. Math. Soc. (JEMS), 2020. Journal. (pdf). (Slides).

   Joint with: H. Al-Saqban, P. Apisa, A. Erchenko, S. Mirzadeh and C. Uyanik.

8. Geodesic Planes in Geometrically Finite Manifolds.

   Disc. & Cont. Dyn. Syst. Series A, 2019. Journal. (pdf). Erratum, appeared in DCDS.

9. Pointwise Equidistribution and Translates of Measures on Homogeneous Spaces.

   Erg. Theory & Dyn. Syst., 2018. Journal. (pdf). (Slides).

Expository

• Mixing, Resonances, and Spectral Gaps on Geometrically Finite Locally Symmetric Spaces. Preprint, 2022. (pdf).

• Extremality of Submanifolds of Systems of Linear Forms via Height Functions. Preprint, 2018. (pdf)