Preprints:

• Graded Bridgeman dilogarithm identities on hyperbolic surfaces, Ara Basmajian, Nhat Minh Doan, Hugo Parlier, Ser Peow Tan. https://arxiv.org/abs/2601.03876 

• Optimal Farey sequence for the Congruence subgroup \Gamma_0(2^n),  Nhat Minh Doan, Sang-hyun Kim, Mong Lung Lang, Ser Peow Tan https://arxiv.org/abs/2601.01324 

• Carrier graphs for representations of the rank two free group into isometries of hyperbolic three space , Ser Peow Tan, Binbin Xu. https://arxiv.org/abs/1807.07277 

Publications

• 53. Equidistribution of partial coverings defined from closed geodesics, Asbjørn Christian Nordentoft, Ser Peow Tan. Adv. Math 495 (2026) arxiv.org/abs/2502.08472 

• 52. Optimal independent generating system for the congruence subgroups Γ_0(p), Nhat Minh Doan, Sang-hyun Kim, Mong Lung Lang, Ser Peow Tan. Journal of Geometric Analysis 35, Article 216 (2025) https://arxiv.org/abs/2209.13937

• 51. Prime orthogeodesics, concave cores and families of identities on hyperbolic surfaces, Ara Basmajian, Hugo Parlier and Ser Peow Tan. Adv. Math. 460 (2025). https://arxiv.org/abs/2006.04872

• 50. Measuring pants, Nhat Minh Doan, Hugo Parlier, Ser Peow Tan. Trans. AMS., Volume 376, Number 8, August 2023, Pages 5281–5306 (https://arxiv.org/abs/2002.02738). 

• 49. Caroline Series and hyperbolic geometry, John Parker, Ser Peow Tan. Notices of the AMS, 70, No 3(2023) 380-389.

• 48. Dilogarithm identities after Bridgeman, Pradthana Jaipong, Mong Lung Lang, Ser Peow Tan and Ming Hong Tee. Math. Proc. Cambridge Philos. Soc., 174, 1-23, (2023).

• 47. Hyperbolic jigsaws and families of pseudomodular groups II,  Beicheng Lou, Ser Peow Tan, and Anh Duc Vo.  IMRN, 2022 (21), 16524-16568 (2022).

• 46. Weakly positive and directed Anosov representations , Sungwoon Kim, Ser Peow Tan and Tengren Zhang.  Adv. Math. 408 (2022).

• 45. Shapes of hyperbolic triangles and once-punctured torus groups, Sang-hyun Kim, Thomas Koberda, Jaejeong Lee, Ken'ichi Ohshika, Ser Peow Tan, with an appendix by Xinghua Gao. Math. Z., 299,  2103–2130 (2021).  

• 44. Kim, Youngju ;  Tan, Ser Peow . Ideal right-angled pentagons in hyperbolic 4-space.J. Korean Math. Soc.  56  (2019),  no. 4, 1131--1158.  http://koreascience.or.kr/article/JAKO201918266171748.page 

• 43. Goldman, William ;  McShane, Greg ;  Stantchev, George ;  Tan, Ser Peow . Automorphisms of two-generator free groups and spaces of isometric actions on the hyperbolic plane. Mem. Amer. Math. Soc.  259  (2019),  no. 1249, vii+78 pp. ISBN: 978-1-4704-3614-8; 978-1-4704-5253-7. https://arxiv.org/abs/1509.03790 

• 42. Lou, Beicheng ;  Tan, Ser Peow ;  Vo, Anh Duc . Hyperbolic jigsaws and families of pseudomodular groups, I. Geom. Topol.  22  (2018),  no. 4, 2339--2366. https://arxiv.org/abs/1611.02922 

• 41.  Labourie, François ;  Tan, Ser Peow . The probabilistic nature of McShane's identity: planar tree coding of simple loops. Geom. Dedicata  192  (2018), 245--266.  https://arxiv.org/abs/1707.07441               

• 40.  Hu, Hengnan ;  Tan, Ser Peow ;  Zhang, Ying . Polynomial automorphisms of C^n preserving the Markoff-Hurwitz polynomial.  Geom. Dedicata  192  (2018), 207--243.     https://arxiv.org/abs/1501.06955    

• 39.  Series, Caroline ;  Tan, Ser Peow ;  Yamashita, Yasushi . The diagonal slice of Schottky space. Algebr. Geom. Topol.  17  (2017),  no. 4, 2239--2282. https://arxiv.org/abs/1409.6863 

• 38.  Bridgeman, Martin ;  Tan, Ser Peow . Identities on hyperbolic manifolds. Handbook of Teichmüller theory. Vol. V, 19--53, IRMA Lect. Math. Theor. Phys., 26, Eur. Math. Soc., Zürich,  2016.        https://arxiv.org/abs/1309.3578                  

• 37.  Maloni, Sara ;  Palesi, Frédéric ;  Tan, Ser Peow . On the character variety of the four-holed sphere.Groups Geom. Dyn.  9  (2015),  no. 3, 737--782.  https://arxiv.org/abs/1304.5770          

• 36.  Hu, Hengnan ;  Tan, Ser Peow ;  Zhang, Ying . A new identity for SL(2,C)-characters of the once punctured torus group.  Math. Res. Lett.  22  (2015),  no. 2, 485--499.   https://arxiv.org/abs/1402.3904          

• 35.  Luo, Feng ;  Tan, Ser Peow . A dilogarithm identity on moduli spaces of curves. J. Differential Geom.  97  (2014),  no. 2, 255--274.   https://projecteuclid.org/euclid.jdg/1405447806                      

• 34.  Hu, Hengnan ;  Tan, Ser Peow . New identities for small hyperbolic surfaces. Bull. Lond. Math. Soc.  46  (2014),  no. 5, 1021--1031.    https://arxiv.org/abs/1402.1573           

• 33.   Kim, Inkang ;  Kim, Joonhyung ;  Tan, Ser Peow . McShane's identity in rank one symmetric spaces. Math. Proc. Cambridge Philos. Soc.  157  (2014),  no. 1, 113--137.  https://arxiv.org/abs/1203.5901         

• 32.  Bridgeman, Martin ;  Tan, Ser Peow . Moments of the boundary hitting function for the geodesic flow on a hyperbolic manifold. Geom. Topol.  18  (2014),  no. 1, 491--520.  https://arxiv.org/abs/1302.0527          

• 31.  Tan, Ser Peow ;  Wong, Yan Loi ;  Zhang, Ying . Delambre-Gauss formulas for augmented, right-angled hexagons in hyperbolic 4-space. Adv. Math.  230  (2012),  no. 3, 927--956. https://arxiv.org/abs/1105.2697 

• 30.  Tan, Ser Peow ;  Wong, Yan Loi ;  Zhang, Ying . McShane's identity for classical Schottky groups. Pacific J. Math.  237  (2008),  no. 1, 183--200. https://arxiv.org/abs/math/0411628 

• 29. Tan, Ser Peow ;  Wong, Yan Loi ;  Zhang, Ying . End invariants for SL(2,C) characters of the one-holed torus. Amer. J. Math.  130  (2008),  no. 2, 385--412.   https://arxiv.org/abs/math/0511621

• 28. Tan, Ser Peow ;  Wong, Yan Loi ;  Zhang, Ying . Generalized Markoff maps and McShane's identity.Adv. Math.  217  (2008),  no. 2, 761--813.      https://arxiv.org/abs/math/0502464    

• 27.  Lang, Mong Lung ;  Tan, Ser Peow . A simple proof of the Markoff conjecture for prime powers Geom. Dedicata  129  (2007), 15--22. https://arxiv.org/abs/math/0508443                 

• 26.  Ng, Shawn Pheng Keong ;  Tan, Ser Peow . The complement of the Bowditch space in the SL(2,C) character variety. Osaka J. Math.  44  (2007),  no. 2, 247--254.  https://arxiv.org/abs/math/0603418                 

• 25. Kojima, Sadayoshi ;  Mizushima, Shigeru ;  Tan, Ser Peow . Circle packings on surfaces with projective structures: a survey. Spaces of Kleinian groups,  337--353, London Math. Soc. Lecture Note Ser., 329, Cambridge Univ. Press, Cambridge,  2006.  https://www.cambridge.org/core/books/spaces-of-kleinian-groups/circle-packings-on-surfaces-with-projective-structures-a-survey/46E58934104F303A9046C3866DBA2FBF                    

• 24.  Tan, Ser Peow ;  Wong, Yan Loi ;  Zhang, Ying . Necessary and sufficient conditions for McShane's identity and variations. Geom. Dedicata  119  (2006), 199--217. https://arxiv.org/abs/math/0411184                      

• 23.  Kojima, Sadayoshi ;  Mizushima, Shigeru ;  Tan, Ser Peow . Circle packings on surfaces with projective structures and uniformization. Pacific J. Math.  225  (2006),  no. 2, 287--300. https://arxiv.org/abs/math/0308147          

• 22.  Tan, Ser Peow ;  Wong, Yan Loi ;  Zhang, Ying . Generalizations of McShane's identity to hyperbolic cone-surfaces. J. Differential Geom.  72  (2006),  no. 1, 73--112.  https://arxiv.org/abs/math/0404226            

• 21.  Tan, Ser Peow ;  Wong, Yan Loi ;  Zhang, Ying . The SL(2,C) character variety of a one-holed torus. Electron. Res. Announc. Amer. Math. Soc.  11  (2005), 103--110.  https://arxiv.org/abs/math/0509033                    

• 20. Kojima, Sadayoshi ;  Mizushima, Shigeru ;  Tan, Ser Peow . Circle packings on surfaces with projective structures. J. Differential Geom.  63  (2003),  no. 3, 349--397. https://arxiv.org/abs/math/0111214 

• 19.  Lang, Mong-Lung ;  Lim, Chong-Hai ;  Tan, Ser-Peow . Principal congruence subgroups of the Hecke groups. J. Number Theory  85  (2000),  no. 2, 220--230.    https://www.sciencedirect.com/science/article/pii/S0022314X00925423                     

• 18.  Lang, Mong-Lung ;  Tan, Ser-Peow . Normalizers of the congruence subgroups of the Hecke group G5. II.  Proc. Amer. Math. Soc.  128  (2000),  no. 8, 2271--2280.  https://www.ams.org/journals/proc/2000-128-08/S0002-9939-00-05677-X/S0002-9939-00-05677-X.pdf 

• 17.  Lang, Mong-Lung ;  Tan, Ser-Peow . Normalizers of the congruence subgroups of the Hecke group G5. Proc. Amer. Math. Soc.  127  (1999),  no. 11, 3131--3140.   https://www.ams.org/journals/proc/1999-127-11/S0002-9939-99-05154-0/S0002-9939-99-05154-0.pdf

• 16. Tan, Eng-Chye ;  Tan, Ser-Peow . Quadratic Diophantine equations and two generator Möbius groups. J. Austral. Math. Soc. Ser. A  61  (1996),  no. 3, 360--368. https://www.cambridge.org/core/journals/journal-of-the-australian-mathematical-society/article/quadratic-diophantine-equations-and-two-generator-mobius-groups/07A480CCDAEBCD5A9F16199E2B244FF1

• 15. Tan, Ser Peow . Self-intersections of curves on surfaces. Geom. Dedicata  62  (1996),  no. 2, 209--225.   https://link.springer.com/article/10.1007/BF00147812                

• 14. Tan, Ser Peow . Quasi-Fuchsian structures on hyperbolic 3-manifolds admitting a decomposition into ideal tetrahedra. Arch. Math. (Basel)  66  (1996),  no. 3, 243--249.        

• 13.  Lang, Mong-Lung ;  Lim, Chong-Hai ;  Tan, Ser Peow . Independent generators for congruence subgroups of Hecke groups.  Math. Z.  220  (1995),  no. 4, 569--594. https://link.springer.com/article/10.1007/BF02572632         

• 12.  Tan, Ser Peow . Singular pleated surfaces and CP1-structures. Glasgow Math. J.  37  (1995),  no. 2, 179--190. 

• 11.  Lang, Mong-Lung ;  Lim, Chong-Hai ;  Tan, Ser Peow . An algorithm for determining if a subgroup of the modular group is congruence.  J. London Math. Soc. (2)  51  (1995),  no. 3, 491--502.   https://academic.oup.com/jlms/article-abstract/51/3/491/800729?redirectedFrom=fulltext                  

• 10. Tan, Ser Peow . Branched CP1-structures on surfaces with prescribed real holonomy. Math. Ann.  300  (1994),  no. 4, 649--667.  https://link.springer.com/article/10.1007/BF01450507                

• 9. Tan, Ser Peow . Conformally flat 3-manifolds and Euclidean polyhedra. Comm. Anal. Geom.  2  (1994),  no. 3, 415--429. https://www.intlpress.com/site/pub/files/_fulltext/journals/cag/1994/0002/0003/CAG-1994-0002-0003-a002.pdf 

• 8. Chan, Shih-Ping ;  Lang, Mong-Lung ;  Lim, Chong-Hai ;  Tan, Ser Peow . The invariants of the congruence subgroups G0(P) of the Hecke group G5.  Illinois J. Math.  38  (1994),  no. 4, 636--652.

• 7.  Tan, Ser Peow . Complex Fenchel-Nielsen coordinates for quasi-Fuchsian structures.  Internat. J. Math.  5  (1994),  no. 2, 239--251.

• 6.  Chan, Shih-Ping ;  Lang, Mong-Lung ;  Lim, Chong-Hai ;  Tan, Ser Peow . Some invariants of Γ0(N). Linear and Multilinear Algebra  35  (1993),  no. 1, 79--81.

• 5. Lang, Mong-Lung ;  Lim, Chong-Hai ;  Tan, Ser Peow . Subgroups of the Hecke groups with small index. Linear and Multilinear Algebra  35  (1993),  no. 1, 75--77.

• 4.  Chan, Shih-Ping ;  Lang, Mong-Lung ;  Lim, Chong-Hai ;  Tan, Ser Peow . Special polygons for subgroups of the modular group and applications. Internat. J. Math.  4  (1993),  no. 1, 11--34.

• 3.  Tan, Ser Peow . Deformations of flat conformal structures on a hyperbolic 3-manifold.  J. Differential Geom.  37  (1993),  no. 1, 161--176. https://projecteuclid.org/euclid.jdg/1214453426 

• 2.  Kamishima, Yoshinobu ;  Tan, Ser P.  Deformation spaces on geometric structures. Aspects of low-dimensional manifolds, 263--299, Adv. Stud. Pure Math., 20, Kinokuniya, Tokyo,  1992.    https://projecteuclid.org/euclid.aspm/1529259973               

• 1. Tan, Ser Peow . Representations of surface groups into PSL(2,R) and geometric structures. Thesis (Ph.D.)–University of California, Los Angeles. ProQuest LLC, Ann Arbor, MI,  1988. 105 pp.