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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
Additional Information

Lie bracket of undirected closed curves on a surface (Moira Chas), to appear in Trans. Amer. Math. Soc..

On the entropy norm on the group of diffeomorphisms of closed oriented surface (with Michael Brandenbursky), Journal of Topology and Analysis, Vol. 12, No. 1 (2020) 105-111.

Elementary equivalence in Artin groups of finite type, (with T. V. H. Prathamesh & Rishi Vyas), International Journal of Algebra and Computation, Volume 28 (02), March 2018.

Equal angles of intersecting geodesics for every hyperbolic metric, New York Journal of Mathematics, Volume 24 (2018) 167-181.

Center of the Goldman Lie algebra, Algebraic & Geometric Topology 16 (2016) 2839–2849.