Research
My principal 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.
My principal 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 of subgroups of diffeomorphism groups of surfaces.
I am also interested in quasimorphisms of subgroups of diffeomorphism groups 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.
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.
Publications and preprints:
Publications and preprints:
Center of Poisson and skein algebras associated to loops on surfaces, to appear in Indiana University Mathematics Journal.
Center of Poisson and skein algebras associated to loops on surfaces, to appear in Indiana University Mathematics Journal.
Lie bracket of undirected closed curves on a surface (with Moira Chas), Trans. Amer. Math. Soc., Vol. 375, No. 4 (2022), 2365–2386.
Lie bracket of undirected closed curves on a surface (with Moira Chas), Trans. Amer. Math. Soc., Vol. 375, No. 4 (2022), 2365–2386.
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.
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.
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.
Equal angles of intersecting geodesics for every hyperbolic metric, New York Journal of Mathematics, Volume 24 (2018) 167-181.
Unpublished articles:
Unpublished articles: