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.

IISc:

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.