IIT Indore
Research:

Specialization: Complex Analysis

Research Interest: Geometric Function Theory

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

  • to extend theory of hyperbolic-type geometry associated with quasiconformal mappings and domains having geometric characterizations;
  • 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 study analytic and geometric properties of partial sums, arc length, area, and radius problems for univalent functions;
  • to visualize mapping properties of basic hypergeometric 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. thesis entitled "Geometric Properties of the Cassinian Metric" defended on May 26, 2017.
  • Vibhuti Arora: Ongoing
  • Arstu: Ongoing
  • Shankey Kumar: Ongoing

Post-Doctoral Fellow(s):

  • 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: Ongoing
  • 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: Ongoing

Research Projects/Grants:

  • Research Project Title: Geometry of hyperbolic type metrics and their applications in analytic function theory (funded by NBHM, DAE; Duration: 2016 - 2019).

Teaching:

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

swadesh[at]iiti.ac.in
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