About Me

I am an Assistant Professor at the Kerala School of Mathematics. My research is deeply rooted in Complex Analysis, especially in understanding foundational mathematical structures and their interconnections. I aim to contribute meaningfully to theoretical mathematics while also engaging collaboratively with scholars across disciplines.

My philosophy blends rigorous theory with collaboration. Many of my publications are joint works reflecting diverse expertise, advancing complex ideas in meaningful and innovative ways.

Core Research Interests

Surface Braid Groups and Mapping Class Groups

I study surface braid groups and the mapping class group of hyperbolic surfaces — algebraic structures capturing how points can move around on surfaces. These have profound implications in topology, geometry, knot theory, and even cryptography.
In collaboration with Chitrabhanu Chaudhuri, I focus on the structure and dynamics of these groups on hyperbolic surfaces, where negative curvature introduces rich mathematical behavior.

Complex Analytic Properties of Teichmüller Spaces

I also explore the Teichmüller spaces, which parameterize complex structures on surfaces. These are central to modern geometry and have ties to string theory, moduli spaces, and deformation theory.

My work involves applying advanced techniques in complex analysis to study the geometry, holomorphic functions, and boundary behavior of these spaces.

Postdoctoral & Doctoral Research

Proper Holomorphic Mappings in Several Complex Variables

During my postdoctoral work, I focused on proper holomorphic mappings in \( \mathbb{C}^n \), analyzing how complex functions behave between domains with intricate topologies. In joint work with Jaikrishnan Janardhanan, we investigated these mappings in quasi-balanced domains, contributing to SCV and complex geometry.

Quadrature Domains & Green’s Functions

My doctoral research focused on quadrature domains in higher dimensions and properties of the Green’s function in planar domains. These tools are central to potential theory, harmonic analysis, and mathematical physics.

This work contributes to our understanding of biholomorphic mappings, Laplace’s equation, and the geometric structure of complex domains.

Selected Publications

  1. Proper holomorphic mappings of quasi-balanced domains in \( \mathbb{C}^3 \)
    Complex Analysis and its Synergies, 9, 7 (2023) (with Jaikrishnan Janardhanan). Read the paper
  2. A note on the smoothness of the Minkowski function
    Complex Variables and Elliptic Equations, 66 (2021) (with Jaikrishnan Janardhanan). Read the paper
  3. A 1-point poly-quadrature domain not biholomorphic to a complete circular domain
    Analysis and Mathematical Physics, 9 (2019) (with Jaikrishnan Janardhanan). Read the paper
  4. Comments on the Green’s function of a planar domain
    Analysis and Mathematical Physics, 8 (2018) (with Diganta Borah and Kaushal Verma). Read the paper
  5. Quadrature domains in \( \mathbb{C}^n \)
    Computational Methods and Function Theory, 15 (2015) (with Kaushal Verma). Read the paper