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.  

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. 

CV

Publications and preprints:   

1. Lifting criteria of closed curves to some finite covers of odd degree (with Deblina Das) https://arxiv.org/abs/2411.00481

2. Simple lift of non-simple closed curves (with Deblina Das),  https://arxiv.org/abs/2404.07627.  

3. Explicit Lie bracket of closed geodesics on a hyperbolic surface with applications (with Moira Chas), https://arxiv.org/abs/2308.02006

4. Center of Poisson and skein algebras associated to loops on surfaces, Indiana Univ. Math. J.72(2023), no.6, 2455–2472. 

5. Lie bracket of undirected closed curves on a surface (with Moira Chas), Trans. Amer. Math. Soc., Vol. 375, No. 4 (2022), 2365–2386.

6. 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.

7. 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.

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

9. Goldman bracket and length equivalent curves, preprint.

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

PhD Thesis

Goldman bracket : center, geometric intersection number & length equivalent curves.

Unpublished articles:

1)  A characterisation of filling curves.