Birla Institute of Technology, Mesra
Faculty Image

Dr. Dinesh Kumar

Joined Institute on : 16-Aug-2021

  • Assistant Professor
  • Mathematics
  • Ph.D
Contact Address

Department of Mathematics, BIT Mesra Ranchi 835215

J1/22 B1, GF, MALVIYA NAGAR, NEW DELHI-110017

  • Phone Office - 9643502105
  • Phone Residence - 9999759280
  • Email - dineshkumar@bitmesra.ac.in
Work Experience

Teaching : 10 Years

Research : 16 Years

Individual: 6 Years
Professional Background

Ph.D(2016) University of Delhi. Title: Semigroups of Transcendental Entire Functions and their Dynamical Properties

M.Phil(2011) University of Delhi. Title: Fatou’s No Wandering Domain Conjecture: Sullivan’s Proof

Conference Organization/ Presentations (in the last five years)

 1. Gave a contributed talk entitled Semigroups of transcendental entire functions and their dynamics at the international workshop-cum-conference ``Complex Analysis: Geometric and Dynamical Aspects'' held at Centre of Excellence in Mathematical Sciences (CEMS), Almora from November 14-19, 2016.

2. Gave an invited talk entitled ``The dynamics of semigroups of transcendental entire functions'' in 83rd  Annual Conference of the Indian Mathematical Society-An International Meet-2017, held at Sri Venkateswara University, Tirupati from December 12-15, 2017.

3. Resource person in two days hands-on workshop in Mathematica/Excel/Tora organized by Department of Mathematics, Deen Dayal Upadhyaya College, University of Delhi from July 12-13, 2018.

4. Course Associate for Analysis (Measure and Integration) during December 17-29, 2018 at the Annual Foundation Schools for Mathematics (AFS-II, 2018) sponsored by the National Centre for Mathematics (NCM) and conducted at Central University of Rajasthan from December 3-29, 2018.

5. Gave an invited talk entitled ``Some aspects of semigroup of transcendental entire functions'' at the Mini Symposium in Mathematics held at Department of Mathematics, Deen Dayal Upadhyaya College, University of Delhi from February 22-23, 2019.

6. Resource person in three days Intensive Undergraduate Workshop-2019 conducted by Harishchandra Mathematics Society, Department of Mathematics, Deen Dayal Upadhyaya College, University of Delhi from March 22-24, 2019.

7. Gave an invited talk entitled ``Dynamics of Nearly Abelian Transcendental Semigroup'' at Research Seminar in Mathematical Sciences held at Department of Mathematics, Deen Dayal Upadhyaya College, University of Delhi on January 23, 2020.

8. Participated and presented a paper entitled ``Dynamics of nearly abelian transcendental semigroup'' in International Web-Conference on Complex Analysis and Differential Geometry: Revisiting(IWCADGR-2020) held at Sidho-Kanho-Birsha University, Purulia, West Bengal from June 29-30, 2020.

9. Participated in an online conference entitled: ``On geometric complexity of Julia sets- II'' held at the Institute of Mathematics of The Polish Academy of Sciences from August 24-27, 2020.

  1. Participated and presented a paper entitled ``Dynamics on Bungee set and Escaping set of a Transcendental entire function'' in the International Conference on Mathematics and Applications, ICMA 2024, held at Mata Sundari College for Women, University of Delhi, from January 10 - 12, 2024.

  2. Gave an invited talk entitled ``Some Results on Dynamics of Bungee Set and Escaping Set of a Transcendental Entire Function'' in the School of Basic Sciences, Indian Institute of Technology Bhubaneswar on 30.01.24.

  3. Participated in NCM Workshop on Quasiconformal Mappings and Holomorphic Dynamics held at Presidency University Kolkata from July 29--August 3, 2024.

  4. Gave an invited talk entitled ``Recurrence relations and its properties'' at Department of Mathematics, Deen Dayal Upadhyaya College, University of Delhi on August 27, 2024.

  5. Participated and presented a paper entitled ``Results on Dynamics of Bungee Set of Composite Entire Functions in the Eremenko-Lyubich Class'' in the International Conference on Recent Trends in Mathematics, ICRTM-2025, held at Hansraj College, University of Delhi, from February 07-08, 2025.

  6. Gave an invited talk entitled ``Dynamics of Transcendental Entire Functions’’ in the International Conference on Mathematics and Statistics in the Era of Data Science (ICMSDS- 2025), held at Central University of Jharkhand from March 18-20, 2025.

Participation in academic activities (outside India)

1. Participated in Advanced School and Workshop in Real and Complex Dynamics held at International Centre for Theoretical Physics (ICTP), Trieste, Italy from May 20-31, 2013.

2. Participated in the CIMPA-Nepal Research School on Aspects of Dynamical Systems held at Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal from November 3-16, 2014.

  1. Participated virtually in a conference entitled ``On geometric complexity of Julia sets-II,'' held at the Institute of Mathematics of The Polish Academy of Sciences from August 24--27, 2020.

    1. Participated virtually in a conference entitled ``On geometric complexity of Julia sets-III,'' held at the Mathematical Research and Conference Center of IMPAN in Bedlewo (Poland) from September 26 - October 1, 2021.
    1. Participated(online) in the conference ``On geometric complexity of Julia Sets V held in Bedlewo, Poland from July 21 - 26, 2024.
    1. Participated(online) in the conference ``On geometric complexity of Julia Sets VI held in Bedlewo, Poland from August 03 - 08, 2025.
Research Areas

Complex Dynamics(Complex Analysis), Iteration of transcendental entire functions.
Award and Honours

1. 2009 Qualified CSIR[NET] Junior Research Fellowship.

2. Awarded A. Narsinga Rao Memorial Prize for the year 2015 for the paper “On dynamics of semiconjugated entire functions" published in the JIMS Vol. 82 (1-2), pp. 53-59, 2015.

  1. Best paper presentation award for the paper ``Dynamics on Bungee set and Escaping set of a Transcendental entire function'' in the International Conference on Mathematics and Applications, ICMA 2024, held at Mata Sundari College for Women, University of Delhi, from January 10 - 12, 2024.
Publications
Publication Year 2025
  • Ramanpreet Kaur and Dinesh Kumar;Dynamics of nearly abelian transcendental semigroup .J Anal. ;33(2025) 2319-2333;1.1;2025
Publication Year 2024
  • Dinesh Kumar and Ramanpreet Kaur;Dynamics on Bungee set, Escaping set and Filled Julia set of composite Transcendental entire functions.Bull. Cal. Math. Soc. ;116(2024) 463-474;;2024
Publication Year 2023
  • Dinesh Kumar and Sanjay Kumar;A note on Schwazian derivatives and Normal families.Ganita;73(2023) 59-63;;2023
Publication Year 2021
  • Ramanpreet Kaur and Dinesh Kumar;Results on escaping set of an entire function and its composition   . Indian J. Pure Appl. Math.; 52(2021) 79-86;0.5;2021
  • Dinesh Kumar and Manisha Saini;The Growth of Solutions of Non-Homogeneous Linear Differential Equations.Kodai Math. J.;44(2021) 556-574;0.32;2021

1. On dynamics of composite entire functions and singularities, (with Sanjay Kumar), Bull. Cal. Math. Soc. Vol. 106, No. 1, pp. 65-72, 2014.

2. On dynamics of semiconjugated entire functions, J. Ind. Math. Soc. (N.S.) Vol. 82, No. 1-2, pp. 53-59, 2015.(Scopus)

3. The dynamics of semigroups of transcendental entire functions I, (with Sanjay Kumar), Indian J. Pure Appl. Math. Vol. 46, No. 1, pp. 11-24, 2015.(SCIE)

DOI: 10.1007/s13226-015-0104-0

4. On escaping sets of some families of entire functions and dynamics of composite entire functions, Math. Student Vol. 84, No. 1-2, pp. 87-94, 2015.

5. Dynamics of composite entire functions, (with Sanjay Kumar and Gopal Datt), J. Ind. Math. Soc. (N.S.) Vol. 83, No. 3-4, pp. 107-114, 2015. (Scopus)

6. The dynamics of semigroups of transcendental entire functions II, (with Sanjay Kumar), Indian J. Pure Appl. Math. Vol. 47, No. 3, pp. 409-423, 2016. (SCIE)

DOI: 10.1007/s13226-016-0173-8

7. Escaping set and Julia set of transcendental semigroups, (with Sanjay Kumar and K. K. Poon), Advances in Theoretical and Applied Mathematics Vol. 11, No. 4, pp. 423-436, 2016.

8. Semigroups of transcendental entire functions and their dynamics, (with Sanjay Kumar), Proc. Indian Acad. Sci. (Math. Sci.) Vol. 127, No. 2, pp. 349-360, 2017. (SCIE)

DOI: 10.1007/s12044-016-0298-z

9. Escaping set of $e^z-1,$ (with Sanjay Kumar), Thai J. Math. Vol. 15, No. 2, pp. 517-522, 2017. (Scopus)

10. On solutions of second order complex differential equations (with S. Kumar and M. Saini), Bull. Cal. Math. Soc. Vol. 111, No. 4, pp. 331-340, 2019.

11. Results on escaping set of an entire function and its composition (with R. Kaur)  Indian J. Pure Appl. Math. Vol. 52 pp. 79-86, 2021. (SCIE)

DOI: 10.1007/s13226-021-00121-9

12. The Growth of Solutions of Non-Homogeneous Linear Differential Equations (with M. Saini), Kodai Math. J. Vol. 44, No. 3, pp. 556-574, 2021. (SCIE)

DOI: 10.2996/kmj/kmj44306

  1. A note on Schwazian derivatives and Normal families (with S. Kumar), Ganita Vol. 73(1), pp. 59-63, 2023.
  2. Dynamics on Bungee set, Escaping set and Filled Julia set of composite Transcendental entire functions (with R. Kaur) Bull. Cal. Math. Soc. Vol. 116, No. 5, pp. 463-474, 2024.

  3. Dynamics of nearly abelian transcendental semigroup (with R. Kaur) J Anal. Vol. 33, pp. 2319-2333, 2025. (Scopus)

    DOI: 10.1007/s41478-025-00922-9
Member of Professional Bodies

Life member of Indian Mathematical Society
Current Sponsored Projects

  1. PI of the project entitled: ``A Study of Dynamics of Transcendental Entire Functions and Quasiregular Dynamics'', under the Seed Money Scheme of the Institute(2022-24) (completed).

  2. PI of the project entitled: ``Topological Investigation of the Escaping Set of a Transcendental Semigroup and Wandering domains in Quasiregular Dynamics'' under the SERB(TARE) scheme(2024-27) (8.25 Lakhs).
Text and Reference Books

Written One Unit for Postgraduate Programme(Mathematics) second semester of Uttarakhand Open University, Haldwani. Details of Unit is as follows: 

Programme Code: MSCMT-23

Programme: MSC Mathematics

Course Name: Measure Theory

Course Code: MAT-507

Unit Number and Unit Name: Unit-5 Measurable Functions
Member, Editorial Board

Reviewer of American Mathematical Society (Reviewer no: 117919)

Reviewer of Journal of the Indian Mathematical Society