My work revolves around understanding the intricate relationships between topological spaces and group actions. Specifically, I study the cohomological structure of orbit spaces, free actions of compact Lie groups, and the existence of equivariant maps. I have explored parametrized versions of the Borsuk-Ulam theorem, cohomology of transformation groups, and various applications in algebraic topology. I am exploring the structural properties of finite topological spaces and how they relate to concepts in persistent homology.Â