Dr. Mahender Singh

Brief bio: I have been working as a regular faculty member in the Department of Mathematical Sciences of IISER Mohali since 2013. Prior to that, I was a postdoctoral fellow at the Institute of Mathematical Sciences Chennai from 2009 to 2012. I obtained my PhD from the Harish-Chandra Research Institute in 2009. My interests are broadly in topology and algebra. Algebraic topology can be described as the study of topological spaces by means of algebraic objects associated to them. I have been working on structural aspects of compact groups acting freely on manifolds, equivariant maps, free rank, index theory, and recently topological complexity. My interest in group theory has been in cohomology, automorphisms, (twisted)-conjugacy classes and other structural aspects of finite groups, generalized braid groups, Artin groups and Coxeter groups. Recently, I have also been thinking about mapping class groups of orientable surfaces. Knot theory is the study of embedded circles in the 3-space. I have been interested in various ramifications and extensions of classical knot theory. Specifically, I have been working on cohomological, computational and structural aspects of quandles and their more general avatars. These objects give strong invariants for knots and appear naturally in diverse areas of mathematics including group theory, solutions of the quantum Yang-Baxter equation, Hopf algebras and symmetric spaces, to name a few.