Research Interests

• Homogeneous Dynamics

• Diophantine Approximation

• Geometry of Numbers

• Function Field Analogues

This often leads to the use of various tools, such as

• Combinatorics

• Automatic Sequences

• Fractal Geometry

• Ergodic Theory

• Number Theory

• Algebraic Groups

Papers and Preprints

0. PhD Thesis - Geometry of Numbers in Positive Characteristic 

1. On Covering Radii in Function Fields - Monatshefte fur Math 206, 705–734 (2025). Journal Arxiv Talk 

2. Counterexamples to Minkowski's Uniqueness Conjecture and Escape of Mass in Positive Characteristic - Combinatorics and Number Theory 13-3 (2024), 179--205. DOI 10.2140/cnt.2024.13.179 Arxiv Journal 

3. On the Maximum Size of Ultrametric Orthogonal Sets over Discrete Valued Fields (joint with Angelot Behajaina) - Designs, Codes, and Cryptography (2024). https://doi.org/10.1007/s10623-024-01480-0 Journal Talk 

4. Hausdorff Dimension  of the Set of Singular Vectors in Function Fields (joint with Taehyeong Kim) -  Advances in Mathematics, Volume 461, 2025, 110084, ISSN 0001-8708, https://doi.org/10.1016/j.aim.2024.110084  Arxiv  Talk 

5. Counting Problems for Orthogonal Sets and Sublattices in Function Fields (joint with Angelot Behajaina) - Arxiv  submitted

6. On the Minimal Denominator Problem in Function Fields - Arxiv  Talk Journal Journal of Number Theory, Volume 280, 2026, Pages 35-48, ISSN 0022-314X, https://doi.org/10.1016/j.jnt.2025.08.005.

7. Geometric Properties of Periodic Lattices in Function Fields - Arxiv Talk submitted

8. Escape of Mass of the Thue-Morse Sequence (joint with Erez Nesharim and Uri Shapira ) - Arxiv Talk submitted

Presentations

1. Geometry of Numbers and Diophantine Approximations in Function Fields 

2. Escape of Mass of Sequences 

3. The Minimal Denominator Problem in Function Fields 

4. Maximum Size of Ultrametric Orthogonal Sets over Discrete Valued Fields 

5. Covering Radii in Positive Characteristic

6. Well Rounded Lattices Intersect Every A Orbit 

7. Hausdorff Dimension of the Set of Singular Vectors in Function Fields

8. Words in Diophantine Approximations (this is the same as the escape of mass lecture, but in view of combinatorics on words and automatic sequences)

Note: Several of these slides have open problems at the end. If you are interested in discussing them with me, please feel free to send me an email.