Research
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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.
Preprints & Publications
2025
9. Optimal special polygon for the congruence subgroup Γ0(p^n) (Nhat Minh Doan, Sang-hyun Kim, Mong Lung Lang, Ser Peow Tan). In preparation
8. Graded Bridgeman dilogarithm identities on hyperbolic cone surfaces (Ara Basmajian, Nhat Minh Doan, Hugo Parlier, Ser Peow Tan). In preparation
7. Some arithmetic aspects of ortho-integral surfaces (Nhat Minh Doan, Khanh Le). Transactions of the American Mathematical Society, to appear (arXiv)
2024
6. Some remarks on subgroups of free-by-cyclic groups (Nhat Minh Doan, Hoang Thanh Nguyen). Vietnam Journal of Mathematics, 2025 (PDF | journal)
5. Self-intersection of arcs on a pair of pants (Nhat Minh Doan, Hanh Vo). Bulletin of the London Mathematical Society, 57 (2025), 2190 - 2209 (journal | arXiv)
2022
4. Optimal special polygons for the congruence subgroups Γ0(p) and Γ0(pq) (Nhat Minh Doan, Sang-hyun Kim, Mong Lung Lang, Ser Peow Tan). Journal of Geometric Analysis, Volume 35, 216 (2025) (PDF)
2021
3. Ortho-integral surfaces (Nhat Minh Doan). Advances in Mathematics, Volume 466, April 2025, 11016 (journal)
2020
2. Geometric filling curves on punctured surfaces (Nhat Minh Doan). Glasgow Mathematical Journal, Volume 65, Issue 2, May 2023, pp. 383 - 400 (arXiv | journal)
1. Measuring pants (Nhat Minh Doan, Hugo Parlier, Ser Peow Tan). Transactions of the American Mathematical Society, 376 (2023), 5281 - 5306 (arXiv | journal)
2022
Quantifying some properties of curves and arcs on hyperbolic surfaces. PhD Thesis, University of Luxembourg (2022) (https://orbilu.uni.lu/handle/10993/50710)
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© 2025 Nhat Minh Doan
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