Dr. Hemant Kumar Singh

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I am currently a Professor in the  Department of Mathematics, University of Delhi. My academic journey began with a deep fascination for mathematical structures, leading me to pursue a bachelor's degree from VBS Purvanchal University, a master's in Mathematics from IIT Delhi, and a Ph.D. in Algebraic Topology from the University of Delhi. My research primarily focuses on topological transformation groups, equivariant topology, and applications of the Borsuk-Ulam theorem. Over the years, I have had the privilege of contributing to mathematical research through publications in reputed journals, and I am always excited to explore new challenges in this ever-evolving field.

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. Through my research, I aim to contribute to a deeper understanding of symmetry, topology, and their implications in mathematical sciences. If you share similar interests or wish to collaborate, feel free to connect.