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. Degree awarded in 2017.
- Vibhuti Arora: Thesis submitted in March 2020.
- Arstu: Ongoing
- Shankey Kumar: 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).
Teaching:
- MA 610 Complex Analysis: 2020 Spring Semester (Sole Instructor), 2017 Spring Semester (Sole Instructor),
2016 Spring Semester (Sole Instructor);
- MA 707 Special Functions: 2016, 2018 Spring Semester (Sole Instructor); 2019 Autumn Semester (Sole Instructor);
- MA 631 Functional Analysis: 2018 Autumn Semester (Sole Instructor);
- MA 603 Topology I: 2017 Autumn Semester (Sole Instructor);
- MA 714 Advanced Complex Analysis: 2017 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 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).
