Ser Peow Tan


Professor, Dept of Mathematics, NUS






Current interests (mathematical)

·        Geometric structures on manifolds

·        Circle packings on projective surfaces

·        Identities on hyperbolic manifolds

·        Dynamics of group actions



Curriculum Vitae

A copy of my recent CV can be downloaded here:  CV (pdf file).



Conferences and Workshops

§  Co-chair, with Bill Goldman and Caroline Series, Program on Geometry, Topology and Dynamics of Character Varieties at the Institute for Mathematical Sciences, NUS in the summer of 2010.

§  Member of the Scientific Committee, “Aspects of hyperbolicity in Geometry, Topology and Dynamics", Jul 2011, Warwick, UK.

§  Member of organizing committee (with Bill Goldman and Anna Wienhard) "Workshop on Moduli Spaces of Representations", Feb 6-10, 2012, part of the trimester on Geometry and analysis of surface groups representations at the Institute Henri Poincare, Paris, France.

§  Organizer, the Inaugural Singapore Summer Lectures in Geometry in the summer of 2012.

§  Member of the organizing committee of the topology session, Asian Mathematical Conference 2013, Jun/Jul 2013, Busan, Korea.

§  Member of the organizing committee for Teichmüller Theory and Low-Dimensional Topology, January 11 - 15, 2016 at Tsinghua Sanya International Mathematics Forum, Sanya, China.

§  Co-chair, with Graeme Wilkin,   Program on Geometry, Topology and Dynamics of Moduli Spaces at the Institute for Mathematical Sciences (IMS) in Singapore from August 1-19, 2016.

§  Co-chair, with Jean-Marc Schlenker of Mini-Workhop “Geometric structures and representation varieties”, May 3-5, 2017, National University of Singapore. link:

§  Member of the organizing committee for the workshop “Representation varieties and geometric structures in low dimensions ”, University of Warwick, 2-6 July 2018.


Recent Papers and Preprints


§  Martin Bridgeman, and Ser Peow Tan, Moments of the boundary hitting function for the geodesic flow on a hyperbolic manifold,  Geometry and Topology, 18 (2014), 491--520. arXiv:1302.0527


§  Feng Luo, and Ser Peow Tan, A dilogarithm identity on moduli spaces of curves, Journal of Differential Geometry, 97, no. 2 (2014): 255-274,  arXiv:1102.2133.


§  Sara Maloni, Frederic Palesi, and Ser Peow Tan, On the character variety of the four-holed sphere, Groups Geometry and Dynamics, 9, no. 3 (2015): 737-782. (Switzerland), eprint arXiv:1304.5770.


§  Inkang Kim, Joonhyung Kim, and Ser Peow Tan, McShane's Identity in Rank One Symmetric Spaces, Math. Proceedings of the Cambridge Philosophical Society, 157 (2014), 113--137. eprint arXiv:1203.5901.


§  Martin Bridgeman, and Ser Peow Tan, Identities on hyperbolic manifolds, Handbook on Teichmueller Theory Vol 5 (2016) 19—53, eprint arXiv:1309.3578.


§  Hengnan Hu, and Ser Peow Tan, New identities for small hyperbolic surfaces, Bulletin of the London Mathematical Society, 46, no. 5 (2014): 1021-1031. eprint arXiv:1402.1573.


§  Hengnan Hu,  Ser Peow Tan, and Ying Zhang, A new identity for SL(2,C)-characters of the once punctured torus group, Mathematical Research Letters, 22, no. 2 (2015): 485-499, eprint arXiv:1402.3904.


§  W Goldman, G McShane, G Stantchev, S P Tan. Automorphisms of two-generator free groups and spaces of isometric actions on the hyperbolic plane, to appear, Memoirs of the AMS, eprint arXiv:1509.03790.


§  C. Series, S P Tan, Y Yamashita, The diagonal slice of Schottky space, to appear, Algebraic and Geometric Topology, eprint .


§  H Hu, S P Tan* and Y Zhang, 'Polynomial automorphisms of C^n preserving the Markoff-Hurwitz polynomial', (submitted) eprint


§  Beicheng Lou, Ser Peow Tan, Anh Duc Vo, “Hyperbolic jigsaws and families of pseudomodular groups I”, (submitted) eprint arXiv:1611.02922



List of Selected Publications ( click  here for full list of publications)

1.     Yoshinobu Kamishima and Ser Peow Tan, Deformation spaces on geometric structures, Advanced Studies in Pure Mathematics. 20, pp 263-299, 1992.

2.     Ser Peow Tan, Deformations of flat conformal structures on a hyperbolic 3-manifold, J. Differential Geom. 37, pp 161-176, 1993.

3.     Ser Peow Tan, Complex Fenchel-Nielsen Coordinates for Quasi-Fuchsian Structures, International Journal of Mathematics, 5-2, pp 239-251, 1994.

4.     Ser Peow Tan, Branched $CP^1$-structures on surfaces with prescribed real holonomy, Mathematische Annalen, 300, pp 649-667, 1994.

5.     Mong Lung Lang, Chong-Hai Lim and Ser Peow Tan, Independent generators for Congruence subgroups of the Hecke Groups, Mathematische Zeitschrift, 220, pp 569-594, 1995.

6.     Mong Lung Lang, Chong-Hai Lim and Ser Peow Tan, Principal congruence subgroups of the Hecke groups. J. Number Theory 85 (2000), no. 2, 220--230.

7.     Sadayoshi Kojima, Shigeru Mizushima and Ser Peow Tan, Circle packings on surfaces with projective structures. J. Differential Geom.  63 (2003), no. 3, 349—397.

8.     Ser Peow Tan, Yan Loi Wong and Ying Zhang, Generalizations of McShane's identity to hyperbolic cone-surfaces, J. Differential Geom.  72 (2006), no. 1, 73--112.

9.     Ser Peow Tan, Yan Loi Wong and Ying Zhang, Generalized Markoff maps and McShane's identity. Adv. Math.  217  (2008),  no. 2, 761--813.

10. Ser Peow Tan, Yan Loi Wong and Ying Zhang, End invariants for ${\rm SL}(2,\mathbf C)$ characters of the one-holed torus.  Amer. J. Math.  130  (2008),  no. 2, 385--412.


Collaborators (Past and Present)



PhD Thesis of my students

 Ying Zhang

(Professor, Soochow University, PRC)

My first student Ying Zhang successfully defended his PhD thesis in July 2004. The title is "Hyperbolic cone-surfaces, generalized Markoff maps, Schottky groups and McShane's Identity". You can download the pdf file here.

Hengnan Hu

My second student Hengnan Hu successfully defended his thesis in Nov 2013. The title is “Identities on hyperbolic surfaces, group actions and the Markoff-Hurwitz equations”. You can download the pdf file here.



Gallery of Images




Tan Ser Peow
Department of Mathematics
National University of Singapore
Block S17, 10 Lower Kent Ridge Road

Singapore 119076
Republic of Singapore

mattansp  (at) nus (dot) edu (dot) sg

(65) 6516-6160 (office)
(65) 6779-5452 (fax)

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Tan Ser Peow <mattansp (at) nus (dot) edu (dot) sg>







Last Modified: 2 August 2012.