About Me

My academic journey has led me to the fascinating field of Complex Analysis. At the Kerala School of Mathematics, I engage deeply with the intricate structures of surface braid groups and the broader mapping class groups of hyperbolic surfaces, often collaborating with Chitrabhanu Chaudhuri. I am also captivated by the complex analytic properties inherent in Teichmüller spaces.

My postdoctoral research was dedicated to proper holomorphic mappings in certain classes of domains within \( \mathbf{C}^n \). A notable joint project with Jaikrishnan, we studied these mappings in specific domains in Several Complex Variables (SCV). My doctoral studies, on the other hand, explored quadrature domains in higher dimensions and the intriguing properties of the Green's function on planar domains.

Research & Publications

Research Interests

My research lies at the intersection of complex analysis, low-dimensional topology, and the geometry of complex manifolds. I am interested in the structure and properties of surface braid groups and the mapping class groups of hyperbolic surfaces, including the study of their representations and connections with classical braid groups. I also investigate the complex-analytic and geometric aspects of Teichmüller spaces and their links with several complex variables. In earlier work, I have studied proper holomorphic mappings in several complex variables and their applications to understanding the geometry of domains, including quadrature domains in higher dimensions. I have also examined the analytical properties of the Green’s function on planar domains, contributing to potential theory and its connections to conformal geometry.

Selected Publications

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

Courses Taught

At Kerala School of Mathematics

• Analysis on Manifolds (Fall 2025, Fall 2024): Differentiable manifolds, integration theory, and applications to geometry and physics.
• Bridge Course in Algebra (July–August 2025): Foundational algebra topics for incoming Integrated MSc-PhD program students.
• Algebraic Topology II (Spring 2024): Cohomology theory, duality theorems, and advanced topics.
• Algebraic Topology I (Fall 2023): Homotopy, fundamental groups, and basic homology theory.
• Differential Equations (Spring 2023): Techniques for solving ordinary and partial differential equations with applications.
• Differential Geometry (Fall 2021 & Spring 2022): Geometry of curves and surfaces, curvature, and geodesics.
• Complex Analysis (Spring 2021): Functions of a complex variable, integration, series, and residue theory.
• Topology (Fall 2020): Topological spaces, continuity, compactness, and connectedness.

Online Courses via Swayam Central

• Complex Analysis (Spring 2020): Accessible introduction to complex function theory. View lectures.
• Linear Algebra (Fall 2020): Vector spaces, transformations, eigenvalues. View lectures.

At Chennai Mathematical Institute

• Riemann Surfaces (Fall 2018): Theory of one-dimensional complex manifolds for advanced mathematics and physics.

At Indian Institute of Technology Madras

• Linear Algebra and Numerical Analysis (Spring 2016 & 2017): Linear systems and numerical methods for scientific computing.

Experience & Education

Professional Experience

• Assistant Professor, Kerala School of Mathematics (Current)
• Postdoctoral Fellow, Chennai Mathematical Institute (2018–2019)
• Postdoctoral Fellow, IIT Madras (2016–2018)
• Research Associate, Indian Institute of Science, Bangalore (July 2015 – June 2016)

Education

• PhD in Mathematics, Indian Institute of Science, Bangalore
• ALGANT Masters, Università di Padova and Université Paris-Sud
• B.Math (Hons.), Indian Statistical Institute, Bangalore

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