Rajesh Dey, PhD

About Me

I received my doctorate from IISER Bhopal in 2025 under the guidance of Prof. Kashyap Rajeevsarathy. My research focuses on Mapping Class Groups of surfaces, with particular interest in Liftable Mapping Class Groups arising from finite-sheeted simple regular branched covers. I am currently serving as a Visiting Faculty at Ashoka University. 

Research Interests

My research focuses on Mapping Class Groups of surfaces, with particular interest in Liftable Mapping Class Groups arising from finite-sheeted regular branched covers. This direction originates from the Birman–Hilden theory, which asks when mapping classes lift under a cover, and how to describe the algebraic structure (generators, presentations) of the corresponding liftable subgroups.

While liftability under finite abelian covers has been widely studied, such an analysis is yet to be undertaken for non-abelian finite simple covers. Addressing this gap, my doctoral research characterized the liftability of periodic mapping classes under alternating covers in a weaker sense, combining Birman–Hilden theory with a classification of certain subgroups of mapping class group. My current research explores liftability of infinite-order mapping classes under alternating covers, with future plans to extend this program to covers induced by other families of simple subgroups in the mapping class group, such as groups of Lie type and their derived subgroups.

Preprints

• Liftability of periodic mapping classes under alternating covers, joint work with Prof. Kashyap Rajeevsarathy and Dr. Apeksha Sanghi, arXiv link: arXiv:2509.02114.

• Alternating and symmetric actions on surfaces,  joint work with Dr. Kashyap Rajeevsarathy, arXiv link: arXiv:2310.06550.