I have done the following projects so far:
1) Topological Analysis of Contact and Pore Networks (June 2025 - May2026): I worked under the guidance of Prof. Vijay Natarajan on topological analysis of pore and contact networks in granular ensembles for my masters thesis. The main motivation was to explore what the fact that the particle space and the void space are complements of each other so one should be able to infer something about one from the other. In this direction, Alexander duality was applied to granular materials. We also explored relations between Betti numbers and average coordination number of the granular materials. The thesis can be found here.
2) Detecting multiplicative inverses in Clifford algebras (May 2024 - ): I am studying the multiplicative inverse problem in Clifford algebras under the guidance of Prof. Dmitry Shirokov. I am reading current research on the subject and then also independently think about the problem myself. I use Mathematica to carry out symbolic computation in Clifford algebras. Currently, I am on a break from this project due to personal reasons.
3) Special theory of Relativity, Lorentz group and its representations (January 2024 – July 2024): I did a theory project on Special Theory of Relativity and Representations of the Lorentz Group under supervision of Prof. Sunil Mukhi. I started by reading Special theory of relativity from Robert Resnick’s book ‘Introduction to Special Relativity’. Then I read about representations of SU(2) and SO(3) and then tried to lift them up to representations of SO(3,1) following the book ‘Group Theory in Physics’ by Wu-Ki Tung. I realised that I wanted to delve deeper into the theory from a mathematical point of view and so I read some Lie theory covering representations of semi-simple Lie algebras from Brian C. Hall’s book ‘Lie Groups, Lie Algebras, and Representations’.
Publications so far:
1) Sharma, H., Shirokov, D. On Commutative Analogues of Clifford Algebras and Their Decompositions. Adv. Appl. Clifford Algebras 36, 9 (2026). DOI, ArXiV.
2) Sharma, H., Shirokov, D. Determinant, Characteristic Polynomial, and Inverse in Commutative Analogues of Clifford Algebras. Adv. Appl. Clifford Algebras 35, 44 (2025). DOI , ArXiV.