Dr. Shankey Kumar

Address:

Dr. Shankey Kumar, 

Visiting Assistant Professor

507, Department of Mathematics 

Indian Institute of Technology Dharwad

Karnataka, India-580011

Education:

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)

Research Publications and Citation Details:

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

Publications:

     Under Review

1. Shankey Kumar and S. Ponnusamy, On the Boundary Schwarz lemma and the rigidity theorem for certain mappings.

2026

2. 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

3. 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

4. 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

5. 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

6.  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

7. 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

8. 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

9. 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

10.  Shankey Kumar, On the multidimensional Bohr radius, Proceedings of the American Mathematical Society, 151, 2001-2009. https://doi.org/10.1090/proc/16280

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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