School of Basic Sciences

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Department of
Mathematics
School of Basic Sciences

Prof. Tarakanta Nayak

Professor
  • Office: 341, SBS
  • +91 674-713-5166
  • tnayakATiitbbsDOTacDOTin
  • Department of Mathematics
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Research Interests:
Complex Dynamics; Fractals; Independence polynomials and Independent fractals of graphs
Education
Degree Discipline Year School
  Ph.D. Mathematics 2001-2006 Indian Institute of Technology Guwahati
  Post doc Mathematics 2008-2009 School of Mathematical Sciences, Tsinghua University, Beijing

Math-I, Math-II, Transform Calculus, Probability, Statistics & Stochastic Processes, Complex Analysis, Fractals, Advanced Complex Analysis, Complex Dynamics, Linear Algebra, Discrete Mathematics, Ordinary Differential Equations

PhD
Completed: 3 (Tarun Kumar Chakra, Subhasis Ghora and Soumen Pal)
Continuing: 3 (Pooja, Sukanta Das and Moumita Manna)
MSc projects for students of IIT Bhubaneswar
Completed: 19
Continuing: 2
BTech projects for students of IIT Bhubaneswar
Completed: 4
MSc and BTech projects for other students 
Completed: 8

Student Supervision

PhD: Soumen Pal and Sukanta Das (continuing)

Subhasis Ghora (Thesis submitted in 2022)

Tarun Kumar Chakra, 2018 (Thesis: Iteration of meromorphic functions with an omitted value)

Post Doc:  Dr Kedarnath Senapati , 2014-2016

MSc:

14. Dynamics of Reduced Independence polynomials,  2021-22

13. Line segments as independence fractals, Saikat Giri, 2019-20

12. Fixed points and their multipliers for a polynomial, Rajen Kumar, 2018-19.

11. Graphs whose independence fractals are line segments, Sanjoy Mondal, 2018-19

10. Quasiconformal mapping and No wandering theorem, Abhisek Pandey,  2018-19

9.  Fractal Transformation using Iterated Function System, Chavan Ratan,  2017-18

8. Quasiconformal mappings,  Garima Gupta, 2016-17

7. A study of roots of Independence polynomials, Vijay Kumar Meena, 2016-17

6. The Independence fractal of a graph, Kartik Pandey, 2016-17

5. Finding all roots of a polynomial by Newton’s Method, Soumen Pal, 2015-16

4. A study on palindromic polynomials,  Priti Prasanna Mondal, 2015-16

3. Polynomial root finding, Anudeep Nain, 2014-15

2. The Julia sets of relaxed Newton  method for polynomials with two roots, Satyabrata Jana, 2014-15

1. Dynamical behaviour of multiply connected Fatou components of transcendental entire functions, Jogender Singh, 2014-15.

Summer and Winter projects:

4. Roots of Chromatic Polynomials, winter project by Labhansh Gemini, NIT Hamirpur, 11-31 Dec 2018

3. The independence polynomial of a graph, summer project by Satyabrat Rath, NIT Rourkela, 2018

2. On Herman rings of transcendental meromorphic functions, summer project by Pranav Kumar Upadrasta, IIT Kharagpur (under SRF Programme – 2014,  jointly sponsored by IASc-Bangalore, INSA-New Delhi and NSAI-Allahabad).

1. When two fractals are the same, summer project by Prashant Kumar Ojha, NIT Rourkela during May 15 — July 15, 2011.

  • Ramanujan Prize for 2018 given by Ramanujan Institute for Advanced Study in Mathematics, University of Chennai
  • Member of INYAS (Indian National Young Academy of Science), 2018-2022
  • Junior Associate of International Centre for Theoretical Physics, Italy for the period 2012-2017
  1. Project title and duration: Topological investigation of teh Escaping set of a transcendental semigroup and wandering domains in quasiregular dynamics, 2024-2027, Funded by SERB, DST Govt of India (Ongoing)
  2. Project title and duration: DIVERSASIA – Embracing diversity in Asia through the adoption of Inclusive Open Practices, 2021-2024, Funded by Erasmus plus, Euros 97046 (Completed)
  3. Project title and duration:Independence polynomials of graphs and associated fractals, 2019-22. Mathematical Research Impact Centric Support (MTR/2018/000498 dated 12.03.2019), Funded by SERB, DST, Amount: Rupees 6.6 Lakhs. (Completed).
  4. Project title and duration:Omitted values in complex dynamics, 2014-17. Supported by the Department of Science & Technology, Govt. of India. Amount: Rupees 13.44 Lakhs (Completed).
  5.  Project title and duration: Julia sets of transcendental meromorphic functions, 21/07/2010 – 30/06/2012. Supported by  IIT Bhubaneswar. Amount: Rupees 5 Lakhs(Completed).
  6. Project title and duration: Topological aspects of transcendental  dynamics, 2009-2010. Supported by the China Postdoctoral Science Foundation (Grant no. 20090450420). Amount: RMB 30,000.(Completed).

Sponsored projects

  1. Project title and duration: Independence polynomials of graphs and associated fractals, 14 March 2019-13 March 2022. Supported by the Department of Science & Technology, Govt. of India. Amount: Rupees 6.6 Lakhs
  2.  Project title and duration:Omitted values in complex dynamics, 2014-17. Supported by the Department of Science & Technology, Govt. of India. Amount: Rupees 13.44 Lakhs.
  3.  Project title and duration: Julia sets of transcendental meromorphic functions, 21/07/2010 – 30/06/2012. Supported by  IIT Bhubaneswar. Amount: Rupees 5 Lakhs
  4. Project title and duration: Topological aspects of transcendental  dynamics, 2009-2010. Supported by the China Postdoctoral Science Foundation (Grant no. 20090450420). Amount: RMB 30,000.
  1. Tarakanta Nayak and Soumen Pal, The Julia sets of Chebyshev’s method with small degrees, Nonlinear Dynamics(2022)
  2. Subhasis Ghora and Tarakanta Nayak, On Fatou sets containing Baker omitted value, Accepted, Journal of Dynamics and Differential Equations(2021)
  3. Tarakanta Nayak and Soumen Pal, Quadratic and cubic Newton maps of rational functions, Proceedings-Mathematical Sciences(2022), https://doi.org/10.1007/s12044-022-00688-1
  4. Subhasis Ghora and Tarakanta Nayak, On periods of Herman rings and relevant poles, Indian J Pure Appl Math (2021). https://doi.org/10.1007/s13226-021-00112-w.
  5. Sasmita Barik, Tarakanta Nayak and Ankit Pradhan, Graphs whose independent fractals are line segments, Bulletin of the Malaysian Mathematical Sciences Society, 44(1), 55-78 (2020) https://doi.org/10.1007/s40840-020-00936-5
  6. Tarun Kumar Chakra and Tarakanta Nayak, Iteration of the translated tangent, Bulletin of the Malaysian Mathematical Sciences Society, 42 (2019), no. 5, 1993-2008.
  7. Tarun Kumar Chakra, Gorachand Chakraborty and Tarakanta Nayak, Herman rings with small periods and omitted values, Acta Mathematica Scientia, Series B, 38 (2018), no. 6, 1951-1965
  8. Tarun Kumar Chakra, Tarakanta Nayak and Kedarnath Senapati, Iteration of certain exponential-like meromorphic functions, Proceedings of Indian Academy of Sciences (Mathematical Sciences), 128 (2018), no. 5, Art. 64, 18 pp.
  9. Tarun Kumar Chakra, Gorachand Chakraborty and Tarakanta Nayak, Baker omitted value, Complex Variables and Elliptic Functions, 61 (2016), no. 10, 1353 – 1361.
  10. Tarakanta Nayak, Herman rings of meromorphic maps with an omitted value, Proceedings of the American Mathematical Society, 144 (2016), no. 2, 587 – 597.
  11. Tarakanta Nayak, On Fatou components and omitted values, Geometry, groups and dynamics, 349 – 358, Contemporary Mathematics, 639, American Mathematical Society, Providence, RI, 2015.
  12. Tarakanta Nayak and M. Guru Prem Prasad, Julia sets of Joukowski-exponential maps, {\it Complex Analysis and Operator Theory}, 8 (2014), no.5, 1061–1076.
  13. Tarakanta Nayak and Jian-Hua Zheng, Omitted values and dynamics of meromorphic functions, Journal of London Mathematical Society, (2) 83 (2011), no.1, 121–136.
  14. Tarakanta Nayak and M. Guru Prem Prasad, Iteration of certain meromorphic functions with unbounded singular values, Ergodic Theory and Dynamical Systems, 30 (2010), no.3, 877–891.
  15. Tarakanta Nayak and Zheng Jian Hua, Omitted values and dynamics of meromorphic functions, Abstracts, International Congress of Mathematicians, 19–27 August, 2010, 313
  16. M. Guru Prem Prasad and Tarakanta Nayak, Dynamics of $\lambda \tanh (e^z)$, Discrete and Continuous Dynamical Systems Series A, 19 (2007), no.1, 121–138.
  17. M. Guru Prem Prasad and Tarakanta Nayak, Dynamics of certain class of critically bounded entire transcendental functions, Journal of Mathematical Analysis and Applications, 329 (2007), no.2, 1446–1459.
  18. Tarakanta Nayak and M. Guru Prem Prasad, Bifurcation and chaotic burst in the dynamics of $\lambda e^{b z + c e^z}$, Journal of Combinatorics, Information and System Sciences, 28/29 (2003/2004), 211–226.
  19. Subhasis Ghora and Tarakanta Nayak, Rotation domains and Stable Baker omitted value, with Subhasis Ghora, Qualitative Theory of Dynamical Systems(2021), https://doi.org/10.1007/s12346-021-00527-0

Tarakanta Nayak, Polynomials through pictures, Resonance (September 2021) 2Rajen Kumar and Tarakanta Nayak, The Real Non-attractive Fixed Point Conjecture and Beyond, Mathematics Newsletter, 31 (Sept 2020), no. 2, 64-71. 3Exploding Julia sets in the dynamics of f ?(z) = ?J1(iz)/iz, Proceedings of The Third National Conference on Non-linear Systems and Dynamics, (NCNSD-2006), 171-174, Allied Publishers Pvt. Ltd.

  1. Baker omitted value, Invited talk in 34 th Annual Conference of the Ramanujan Mathematical Society, 1-3 August 2019, Pondicherry University, Punducherry, India
  2. Independence fractal of a graph, Invited talk in 83rd Annual Conference of Indian Mathematical Society, 12-15 Dec 2017, Sri Venkateswar University, Tirupati, Andhra Pradesh, India
  3. Completely invariant domains, Complex Analysis: Geometric and Dynamical Aspects, Non 14-19, 2016, Centre of Excellence in Mathematical Sciences, Almora, India
  4. Herman rings, Frontiers in Complex Dynamics, Dec 19 — 20, 2012, University of Barcelona, Spain
National Conference
  1. Complex Dynamics of some simple maps, National Workshop on Topological Dynamics Dec 10 — 12, 2015, National Institute of Technology, Karnataka, Surathkal, India

Associate Professor, 24 February 2020 onwards, IIT Bhubaneswar Assistant Professor, May 2010 — February 2020, IIT Bhubaneswar Postdoc, September 2008 — May 2010, Tsinghua University, China Report: Omitted values and conformal measures in complex dynamics Assistant Professor, December 2007 — August 2008, National Institute of Technology Rourkela Postdoc, 5 February 2007 — 1 December 2007 Harish-Chandra Research Institute, Allahabad, India

Professional Activities

  • Reviewer, Mathematical Reviews (Published by American Mathematical Society)
  • Regional Coordinator (Odisha), Madhava Mathematics Competition (since 2015)
  • Acted as supervisor for Joint Science Academies’ Summer Research Fellowship Programme
  • Member, Board of studies, Salipur Autonomous College, Salipur (2014-2016)
  • Zonal coordinator, Indian National Mathematical Olympiad for Utkal University zone
  • Member in the interview board for selection of Trained Graduate Teachers in Kendriya Vidyalaya Sangathan on 30 April, 2011
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