arpaninto

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.