Hello, I'm Pranav Haridas

Assistant Professor at Kerala School of Mathematics

RESEARCH TEACHING

I am currently an Assistant Professor at Kerala School of Mathematics, specializing in Complex Analysis. My research focuses on surface braid groups, mapping class groups of hyperbolic surfaces, and Teichmüller spaces.

Contact

Kerala School of Mathematics,

Kunnamangalam,

Kozhikode - 673571,

India

Email: pranav at ksom dot res dot in

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 \( \mathbf{C}^n\). 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 interesting properties of the Green's function on planar domains.

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 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. Online lectures available here)
  • Linear Algebra (Fall 2020 in the online portal Swayam Central. Online lectures available here)
  • 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

Post-doctoral Experience

I was a Research Associate at Indian Institute of Science, Bangalore from July 2015 to June 2016. Thereafter, I was a post-doctoral fellow at Indian Institute of Technology Madras from July 2016 to June 2018 and Chennai Mathematical Institute from July 2018 to February 2019.