Research:
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).
Teaching:
- 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).
