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Dr. Arpan Kabiraj
Assistant Professor
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Integrated PhD (MS+PhD) in Mathematics (2011-2016)  : Indian Institute of Science, Bangalore, India

B.Sc.  in Mathematics (2006-2009)  : Jadavpur University, Kolkata, India



Assistant Professor (December 2019-May 2020) : IIT Bhubaneswar, India

INSPIRE Faculty (September 2016 - March 2020) : Chennai Mathematical Institute (CMI), Chennai, India

 Postdoctoral fellow (October  2017 - September 2018) : Ben-Gurion University, Israel


My principle areas of research are topological, combinatorial and geometric group theory. I am primarily interested in the study of geometric, combinatorial, computational and algebraic aspects of geometric objects namely curves on hyperbolic surfaces arising naturally in the study of low-dimensional topology and Riemann surface theory. In this context I am interested in certain problems related to the length function on Teichmüller space and various combinatorial objects associated to the Teichmüller space.

I am also interested in quasimorphisms on groups associated to geometry and topology of surfaces.

Apart from geometry, I am interested in logic, in particular first order theory of groups which occurs naturally while studying geometric objects, e.g. Braids groups, Mapping class groups etc.


IIT Bhubaneswar:

1) Instructor of the course “Mathematics-II”, January-May, 2020.

2) Instructor of the course “Algebraic Topology”, January-May, 2020


Chennai Mathematical Institute:

1) Instructor of the course “Riemannian Geometry” (REGO), August-November,2017.

2) Instructor of the course “Geometric Group Theory” (GGTH), August-November, 2019.



1) Teaching Assistant for MA 231 Topology, August-December, 2011.

2) Teaching Assistant for UM 101 Analysis and Linear Algebra I, August-December, 2012.

3) Teaching Assistant for MA 221 Real Analysis, August-December 2013.

4) Teaching Assistant for MA 232 Introduction to Algebraic Topology, August-December 2014.

5) Teaching Assistant for UM 101 Analysis and Linear Algebra I, August-December, 2015.

Research Area
Low-dimensional Topology

Recent Publications

Moira Chas and Arpan Kabiraj
Trans. Amer. Math. Soc. 375 (4) 2365–2386 (2022)
Michael Brandenbursky and Arpan Kabiraj
Journal of Topology and Analysis 12 (1) 105-111 (2020)
Arpan Kabiraj
New York Journal of Mathematics 24 167-181 (2018)
Arpan Kabiraj, T. V. H. Prathamesh and Rishi Vyas
International Journal of Algebra and Computation 28 (2) 331-344 (2018)
Arpan Kabiraj
Algebraic & Geometric Topology 16 2839–2849 (2016)