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

• Complex Analysis
• Surface Braid Groups
• Mapping Class Groups of Hyperbolic Surfaces
• Teichmüller Spaces (Complex Analytic Properties)
• Proper Holomorphic Mappings in Several Complex Variables
• Quadrature Domains in Higher Dimensions
• Green's Function on Planar Domains

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]

Teaching

• Algebraic Topology (Fall 2022, Current Offering at Kerala School of Mathematics)
• Differential Equations (Spring 2023 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 on Swayam Central )
• Linear Algebra (Fall 2020 on Swayam Central )
• Linear Algebra and Numerical Analysis (Spring 2016 & 2017 at IIT Madras)
• Riemann Surfaces (Fall 2018 at Chennai Mathematical Institute)

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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