I still do not have well defined research interests but I like Lie groups, Clifford algebras, applied topology and data analysis. I think I like application to real world over pure mathematics. Please take a look at my projects here.
Currently, I am working with Prof. Vijay Natarajan on topological analysis of pore and contact networks in granular ensembles for my masters thesis. I will explore the use of topological descriptors to characterize structural and kinetic properties of the granular ensemble. Topological descriptors developed based on persistence homology and Morse theory — persistent diagrams, Reeb graph, extremum graph — will be studied. The project objectives include structural characterization and empirical study via computational experiments.
I am also working with Prof. Dmitry Shirokov on multiplicative inverse problem in Clifford algebras i.e., do to detect multiplicative inverses in Clifford algebras. Right now, we are exploring some analogues of Clifford algebras hoping that they would help us understand multiplicative inverse problem in Clifford algebras.