📧 pranav@ksom.res.in
đź“ž 0495 2809006
Office: F5
Dr. Pranav Haridas is an Assistant Professor at the Kerala School of Mathematics whose research bridges complex analysis and geometric group theory. His work in several complex variables focuses on holomorphic mappings between domains, the behavior of intrinsic metrics such as the Kobayashi and Teichmüller metrics, and geometric features of domains like the Minkowski function and Bers embeddings. These analytic questions are often tackled using tools such as Hörmander's $L^2$ estimates and insights from domain geometry.
In parallel, he studies surface braid groups, mapping class groups, and their liftability properties, including the Birman–Hilden theory. His research investigates how topological structures of surfaces interact with algebraic invariants and quantum representations, contributing to a deeper understanding of moduli spaces and holomorphic equivalences. This unified approach allows him to draw connections between surface homeomorphisms, complex manifolds, and fundamental group actions.
đź”— Personal Homepage
- Proper holomorphic mappings of quasi-balanced domains in $\mathbb{C}^3$ (with J. Janardhanan), Complex Anal. Synerg., 2023.
- A note on the smoothness of the Minkowski function (with J. Janardhanan), Complex Var. Elliptic Equ., 2021.
- A 1-point poly-quadrature domain of order 1 not biholomorphic to a complete circular domain (with J. Janardhanan), Anal. Math. Phys., 2019.
- Comments on the Green's function of a planar domain (with D. Borah and K. Verma), Anal. Math. Phys., 2018.
- Quadrature domains in $\mathbb{C}^n$ (with K. Verma), Comput. Methods Funct. Theory, 2015.