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I am a postdoc at the Mathematics department of the University of Utah.

My research interests lie in the areas of Homogeneous and Teichmuller Dynamics and applications thereof to Diophantine approximation, billiard dynamics and geometry of hyperbolic 3-manifolds.

I received my PhD from Ohio state in 2019. My advisor is Nimish Shah.

CV (PDF)»

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Preprints and Publications

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

  Joint with Jon Chaika and John Smillie. In preparation.

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

  Joint with Manuel Luethi (pdf). (Video lecture).

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

  GAFA, 2020 (pdf).

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

  Transactions of the American Mathematical Society, 2020 (pdf). Talk at Maryland, April. 2018 (slides)

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

  Joint with: H. Al-Saqban, P. Apisa, A. Erchenko, S. Mirzadeh and C. Uyanik. (Journal of the European Mathematical Society, to appear) (pdf). Talk at JMM, Jan. 2018 (slides)

• Geodesic Planes in Geometrically Finite Manifolds.

  Discrete & Cont. Dyn. Syst. Series A Vol 39, No 2. (pdf)

• Pointwise Equidistribution and Translates of Measures on Homogeneous Spaces.

  Ergodic Theory & Dynamical Systems Vol 40, Issue 2. (pdf). Talk at Penn. State workshop, Oct. 2017 (slides)

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Expository

• Extremality of Submanifolds of Systems of Linear Forms via Height Functions.

  Preprint, 2018 (pdf).

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Teaching

• In Summer 2017, I was a TA for the Analysis Qualifying Exam Prep. Class. Here is a link to solutions of old style quals (pdf)