I am currently an Assistant Professor at Kerala School of Mathematics.

Research

My research interests broadly lie in Complex Analysis. Currently, I am studying surface braid groups and, more generally, the mapping class group of hyperbolic surfaces with Chitrabhanu Chaudhuri. I am also exploring the complex analytic properties of Teichmüller spaces.

During my postdoctoral stint, I explored proper holomorphic mappings of a certain class of domains in \( \textbf{C}^n\). In a joint project with Jaikrishnan, we studied proper holomorphic mappings in certain special class of domains in several complex variables (SCV).

During my doctoral studies, I studied quadrature domains in higher dimensions and their properties and certain intersting properties of the Green's function on planar domains.

Publications

1. Proper holomorphic mappings of quasi-balanced domains in \( \textbf{C}^3 \), 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 \( \textbf{C}^n \), Computational Methods and Function Theory 15, 2015 (with Kaushal Verma). [Link]

Teaching

Courses

• Differential Equations (Spring 2023 at Kerala School of Mathematics)
• Algebraic Topology (Fall 2022 at Kerala School of Mathematics)
• Differential Geometry (Fall 2021 and Spring 2022 at Kerala School of Mathematics)
• Complex Analysis (Spring 2021 at Kerala School of Mathematics)
• Topology (Fall 2020 at Kerala School of Mathematics)
• Complex Analysis (Spring 2020 in the online portal Swayam Central. Please click here for the online lectures)
• Linear Algebra (Fall 2020 in the online portal Swayam Central. Please click here for the online lectures)
• Linear Algebra and Numerical Analysis (Spring 2016 and Spring 2017 at Indian Institute of Technology Madras)
• Riemann Surfaces (Fall 2018 at Chennai Mathematical Institute)

In this semester I am offering a course on Algebraic Topology at Kerala School of Mathematics.

Education

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