Address:
Dr. Shankey Kumar,
Visiting Assistant Professor
507, Department of Mathematics
Indian Institute of Technology Dharwad
Karnataka, India-580011
Doctor of Philosophy (Mathematics) IIT Indore (2016-2021).
Master of Science (Mathematics) IIT Delhi, 2015.
Bachelor of Education (Mathematics) D. A. V. College, Ch. Chara Singh University, Meerut, U.P., India, 2012
Research Experience:
(1) Postdoc, Indian Institute of Technology Madras (February 2023-February 2026)
(2) Postdoc, National Institute of Science Education and Research (NISER), Bhubaneswar, India (December 2021- February 2023)
Research Visit:
School of Mathematics and Statistics, Hunan Normal University, Changsha, China (April 06, 2025 - May 03, 2025)
Several Complex Variables and Functional Analysis
ORCID ID: 0000-0003-0388-3964 orcid.org/0000-0003-0388-3964
Scopus ID: 57219742898 https://www.scopus.com/authid/detail.uri?authorId=57219742898
Google Scholar: https://scholar.google.com/citations?user=ct__RKcAAAAJ&hl=en&oi=ao
Invited Talks:
Resource Person for the seminar on "Bohr Radius in Higher Dimensions" April 16, 2025, Department of Mathematics, Hengyang Normal University, Hengyang, China
Resource Person for the Seminar on "Properties of Real Numbers", March 04, 2025, Department of Mathematics, Mar Thoma College, Chungathara, Malappuram, Kerala, India
Conferences Attended:
The 31st ICFIDCAA-2025, August 20 - 24, 2025, School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang, Malaysia
The 11th International Conference on Mathematics and Computing (ICMC 2025), January 09-11, 2025, Department of Mathematics, IIT Bhilai, Raipur, India
The 39th Annual Conference of Ramanujan Mathematical Society, December 27-29, 2024, CHRIST (Deemed to be University), Kengeri Campus, Bangalore, India
International Conference on Special functions, Analytic functions, Metrics and quasiconformalitY (ICSAMY 2024), December 17 - 20, 2024, Department of Mathematics, IIT Indore, Indore, India
The 30th ICFIDCAA-2024, August 19 - 23, 2024, Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai, Japan, (Partially funded by ITS (SERB))
International Conference on Complex Analysis and Computational Fluid Dynamics, Feb 16 - 18, 2024, Department of Mathematics, KIIT Deemed to be University, Bhubaneswar, India
The 29th ICFIDCAA-2023, August 21 - 25, 2023, Department of Mathematics, Pondicherry University, Pondicherry, India
The 28th International Conference (Virtual) of Forum for Interdisciplinary Mathematics (Synergies in Computational, Mathematical, Statistical and Physical Sciences), November 23 - 27, 2020, Stella Maris College and Sri Sivasubramaniya Nadar College of Engineering, Chennai, Tamil Nadu, India
National Seminar on Complex Analysis and Operator Theory, March 28 - 30, 2019, University of Jammu, Jammu, India
Workshops and Internship Attended:
Harmonic Mappings, Partial Differential Equations, and Applications (HMPDEA 2025), January 07-09, 2025, Department of Mathematics, IIT Bhilai, Raipur, India
International Workshop on Geometric Function Theory, August 18 - 20, 2023, Department of Mathematics, IIT Madras, Chennai, India
International Workshop on Recent Advances in Operator Semigroups, December 18 - 21, 2017, Department of Mathematics, University of Delhi, Delhi, India
Quasiconformal Mappings and their Applications, December 11 - 16, 2017, Indian Institute of Technology Indore, Indore, India
IST on Advanced Linear Algebra, July 10 - 22, 2017, IIT Gandhinagar, Gujarat, India
MTTS Programme, May 29- June 24, 2017, Indian Institute of Technology Indore, Indore, India
Internship in ``Measure Theory", May 15 - July 15, 2014, Indian Institute of Technology Delhi, Delhi, India
Under Review
Shankey Kumar and S. Ponnusamy, On the Boundary Schwarz lemma and the rigidity theorem for certain mappings.
2026
Shankey Kumar and S. Ponnusamy, Bounds on mixed Bohr radii of vector-valued holomorphic functions on Banach spaces, Analysis and Mathematical Physics, 16(27), 1-25. https://doi.org/10.1007/s13324-026-01173-y
V. Arora, J. Chen, Shankey Kumar and Q. Li, Schwarz-Pick type lemma and Landau type theorem for alpha-harmonic mappings, Mediterranean Journal of Mathematics, 23(60), 1-21. https://doi.org/10.1007/s00009-026-03056-9
Shankey Kumar and S. Ponnusamy, Schwarz-pick estimates for pluriharmonic functions and their consequences, The Journal of Geometric Analysis, 36(90), 1-43. https://doi.org/10.1007/s12220-026-02327-x
2025
Shankey Kumar and R. Manna, Multi-dimensional Bohr radii of Banach space valued holomorphic functions, Bulletin des Sciences Mathematiques, 205, 1-28, Article No.-103688. https://doi.org/10.1016/j.bulsci.2025.103688
V. Arora, Shankey Kumar, and S. Ponnusamy, Asymptotic value of the multidimensional Bohr radius, Monatshefte fur Mathematik, 207(3), 365-384. https://doi.org/10.1007/s00605-025-02095-w
Shankey Kumar, Mapping properties of certain nonlinear integral operators involving Hornich operations, Bulletin of the Malaysian Mathematical Sciences Society, 48(43), 1-16. https://doi.org/10.1007/s40840-025-01824-6
Shankey Kumar, S. Ponnusamy, and G. B. Williams, The Bohr-type inequalities for holomorphic functions with lacunary series in complex Banach space, New York Journal of Mathematics, 31, 259-281. http://nyjm.albany.edu/j/2025/31-12.html
2023
Shankey Kumar and R. Manna, Revisit of multi-dimensional Bohr radius, Journal of Mathematical Analysis and Applications, 523(1), 1-15, Article No.-127023. https://doi.org/10.1016/j.jmaa.2023.127023
Shankey Kumar, On the multidimensional Bohr radius, Proceedings of the American Mathematical Society, 151, 2001-2009. https://doi.org/10.1090/proc/16280
Shankey Kumar, A generalization of the Bohr inequality and its applications, Complex Variables and Elliptic Equations, 68(6), 963-973. https://doi.org/10.1080/17476933.2022.2029853
2022
Shankey Kumar and S.K. Sahoo, A generalization of the Bohr-Rogosinski sum, Lobachevskii Journal of Mathematics, 43(8), 2176-2186. https://dx.doi.org/10.1134/S1995080222110166
2021
Shankey Kumar and S.K. Sahoo, Radius of convexity for integral operators involving Hornich operations, Journal of Mathematical Analysis and Applications, 502(2), 1-21, Article No.-125265. https://www.sciencedirect.com/science/article/pii/S0022247X21003449
Shankey Kumar and S.K. Sahoo, Bohr inequalities for certain integral operators, Mediterranean Journal of Mathematics, 18(268), 1-12. https://doi.org/10.1007/s00009-021-01891-6
2020
Shankey Kumar and S.K. Sahoo, Properties of $\beta$-Ces\`{a}ro operators on $\alpha$-Bloch space, Rocky Mountain Journal of Mathematics, 50(5), 1723-1743. https://doi.org/10.1216/rmj.2020.50.1723
Shankey Kumar and S.K. Sahoo, Preserving properties and pre-Schwarzian norms of nonlinear integral transforms, Acta Mathematica Hungarica, 162(1), 84-97. https://doi.org/10.1007/s10474-020-01027-4
Shankey Kumar and S. Ponnusamy, Survey on the Bohr radius in higher dimension, Proceedings of the Eleventh International Conference on Mathematics and Computing. ICMC 2025. Lecture Notes in Networks and Systems, vol 1420. Springer, Singapore (2026), 237--247. (Awarded the best paper) https://doi.org/10.1007/978-981-96-6941-7_19
Papers reviewed for Journals:
International Journal of Mathematics
Bulletin of the Malaysian Mathematical Sciences Society
Integral Transforms and Special Functions
Journal of Mathematical Inequalities
The Korean Journal of Mathematics
The Canadian Mathematical Bulletin
Complex Analysis and Operator Theory
MR Reviewer for MathSciNet