IIT Indore

Specialization: Complex Analysis

Research Interests: Geometric Function Theory (Univalent functions, Harmonic mappings, Hyperbolic-type metrics, Special functions)

We work on problems in the theory of univalent functions, special functions, quasiconformal mappings, and hyperbolic-type geometries. In particular, we aim

  • to extend the theory of hyperbolic-type geometries associated with quasiconformal mappings and domains having geometric characterizations;
  • to analyse geometrical and topological aspects of hyperbolic-type metric balls;
  • to investigate properties of conformal mappings associated with metrics bilipschitz equivalent to the hyperbolic metric;
  • to find necessary and sufficient conditions for certain analytic functions in terms of coefficient estimates, pre-Schwarzian and Schwarzian derivatives;
  • to obtain certain necessary and sufficient conditions for harmonic univalent mappings using shear construction;
  • to study analytic and geometric properties of partial sums, arc length, area, and radius problems for univalent functions;
  • to know spectral, boundedness, and compactness of complex integral operators;
  • to visualize mapping properties of (basic) hypergeometric functions and other related special functions using techniques from geometric function theory.

Ph.D. Scholars:

  • Navneet Lal Sharma: Ph.D. Degree awarded in 2016.
  • Sarita Agrawal: Ph.D. Degree awarded in 2016.
  • Manas Ranjan Mohapatra: Ph.D. Degree awarded in 2017.
  • Vibhuti Arora: Ph.D. Degree awarded in 2020.
  • Arstu: Ph.D. Degree awarded in 2021.
  • Shankey Kumar: Ph.D. degree awarded in 2021.
  • Sheetal Sanjay Wankhede: Ongoing
  • Pritam Naskar: Ongoing (jointly with Dr. Bibekananda Maji)
  • Ritwick Maity: Ongoing

Post-Doctoral Fellow(s):

  • Dr. Sudhananda Maharana: Institute Post-Doctoral Fellow: May 16, 2018 - May 15, 2019.
  • Dr. Nijjwal Karak: National Post-Doctoral Fellow supported by Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India, New Delhi: September 6, 2016 - September 5, 2018.
  • Dr. Sanjeev Singh: National Post-Doctoral Fellow supported by Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India, New Delhi: June 23, 2017 - September 29, 2017

Research Projects/Grants:

  • The Hurwitz metric and univalent functions (funded by Mathematical Research Impact Centric Support (MATRICS), Science and Engineering Research Board (SERB) Duration: February 19, 2020 - February 18, 2023).
  • Geometry of hyperbolic type metrics and their applications in analytic function theory (funded by NBHM, DAE; Duration: October 14, 2016 - October 13, 2019).


  • MA 610 Complex Analysis: 2024 Spring (Sole), 2023 Spring (Sole), 2020 Spring (Sole), 2017 Spring (Sole), 2016 Spring (Sole);
  • MA 603 Topology I: 2023 Autumn (Sole Instructor), 2022 Autumn (Sole), 2021 Autumn (Sole), 2020 Autumn (Sole), 2017 Autumn (Sole);
  • MA 714 Advanced Complex Analysis: 2023 Autumn (Sole Instructor), 2021 Autumn (Sole), 2017 Spring (Sole);
  • MA 707 Special Functions: 2022 Autumn (Instructor), 2019 Autumn (Sole), 2018 Spring (Sole), 2016 Spring (Sole);
  • MA 204 Numerical Methods: 2022 Spring (Instructor), 2013 Spring (Instructor), 2011 Spring (Instructor);
  • MA 105 Calculus: 2020 Autumn (Instructor), 2016 Autumn (Instructor);
  • MA 631 Functional Analysis: 2018 Autumn (Sole Instructor);
  • MA 203 Complex Analysis and Differential Equations-II: 2016 Summer (Instructor), 2015 Autumn (Instructor), 2014 Autumn (Instructor);
  • MA 673 Fundamentals of Discrete Mathematics 2015 Autumn (Instructor);
  • MA 797 Ph.D. Seminar Course: 2015 Autumn (Sole Instructor);
  • MA 798 Ph.D. Seminar Course: 2014 Spring (Sole Instructor);
  • MA 711 Analysis: 2013 Autumn (Sole Instructor);
  • MA 103 Mathematics I (Calculus): 2012 Summer (Instructor);
  • MA 702 Conformal Mappings: 2012 Spring (Sole Instructor), 2011 Spring (Sole Instructor);
  • MA 201 Mathematics-III (Complex Analysis and Differential Equations-II): 2011 Autumn (Instructor);
  • MA 703 Topics in Analysis: 2011 Autumn (Instructor);
  • MA 104 Mathematics-II (Linear Algebra and Differential Equations-I): 2011 Summer (Instructor).
Faculty Profile
Dr. Swadesh Kumar Sahoo



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