My research centers on the study of curves and arcs on hyperbolic surfaces. 

Some of the questions I have been working on are related to geometric (dilogarithm) identities, the density of geodesics on hyperbolic surfaces, the self-intersection numbers of curves and arcs on surfaces, big mapping class groups, congruence subgroups of the modular group, and pseudomodular surfaces. 

10. Optimal special polygon for the congruence subgroup Γ0(p^n)
with Sang-hyun Kim, Mong Lung Lang, and Ser Peow Tan
in preparation

9. Graded Bridgeman identities on hyperbolic surfaces
with Ara Basmajian, Hugo Parlier, and Ser Peow Tan
in preparation

8. Some arithmetic aspects of ortho-integral surfaces
with Khanh Le
Submitted (arXiv)

7. Some remarks on subgroups of free-by-cyclic groups
with Hoang Thanh Nguyen
Vietnam Journal of Mathematics, 2025 (PDF | journal)

6. Self-intersection of arcs on a pair of pants
with Hanh Vo
Bulletin of the London Mathematical Society, 57 (2025), 2190 - 2209 (journal | arXiv)

5. Optimal special polygons for the congruence subgroups Γ0(p) and Γ0(pq)
with Sang-hyun Kim, Mong Lung Lang, and Ser Peow Tan
Journal of Geometric Analysis, Volume 35, 216 (2025) (PDF)

4. Ortho-integral surfaces
Advances in Mathematics, Volume 466, April 2025, 11016 (journal)

3. Geometric filling curves on punctured surfaces
Glasgow Mathematical Journal, Volume 65, Issue 2, May 2023, pp. 383 - 400 (arXiv | journal)

2. Measuring pants
with Hugo Parlier, and Ser Peow Tan
Transactions of the American Mathematical Society, 376 (2023), 5281 - 5306 (arXiv | journal)

1. Quantifying some properties of curves and arcs on hyperbolic surfaces
PhD Thesis, University of Luxembourg (2022) (https://orbilu.uni.lu/handle/10993/50710)

1. Ara Basmajian

2. Sang-hyun Kim (2)

3. Mong Lung Lang (2)  

4. Khanh Le     

5. Hoang Thanh Nguyen

6. Hugo Parlier (2)

7. Ser Peow Tan (4)

8. Hanh Vo