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A premier engineering college in the state, located at Kochi

COLLEGE CODE : MUT

Affiliated to APJ Abdul Kalam Technological University
Approved by AICTE

[email protected] | 0484-2883300/0484-2732100/111

Relentless passion for excellence...

(Promoted by The Muthoot Group)

NameDr. Vinod Kumar P B
DesignationResearch Professor
SpecializationTopology
E-Mail ID [email protected]
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Dr. Vinod Kumar P B

Educational Qualification:

  • Ph.D., Cochin University of Science and Technology, 2002
  • M.Phil., Cochin University of Science and Technology, 1997
  • M.Sc., Cochin University of Science and Technology, 1996
  • B.Sc., Mahatma Gandhi University, 1994

Areas of research interest:

  • Topology
  • Topological Dynamics
  • Topological Data Analysis
  • Chaos Theory
  • Fractal Geometry
  • Complex Dynamics
  • Linear Dynamics
  • Information Theory
  • Signal processing
  • Quantum Computing

Research Publications (since 2020)

Jose C, Jeeva; Sojan, Salviyas; Gregory, Geo Mathe; Krishnan, A Arjun; Joseph, Christom Kumar P B, Vinod; Mathews, Jithin; Jacob, Rinku; G, Sreekumar; George, Joel; Topological Methods for Flight Trajectory Analysis and Planned Path Optimization, IEEE Transactions on Intelligent Transport Systems (accepted for publication).

 

Jeeva Jose C, Vinod Kumar P B; On the space of generalized persistent diagrams, Springer Proceedings in Mathematics and Statistics (accepted for publication).

 

Cinderella T J, Vinod Kumar P B; Space of homeomorphisms on compact manifolds, Springer Proceedings in Mathematics and Statistics (accepted for publication).

 

Jauda P P, Vinod Kumar P B; Dynamics of a family of maps with constant mass centre, Springer Proceedings in Mathematics and Statistics (accepted for publication).

 

Amalraj P, P B Vinod Kumar, Stability and almost sensitivity of induced maps, Communications on Applied Nonlinear Analysis, 32, 2, 2025, 52-59.

 

Amalraj, P, Vinodkumar P. B; Existence of a homeomorphism from the space of continuous functions to the space of compact Subsets of a topological space; The Scientific Temper, 15(3), 2024, 2470-2472.

 

Amalraj P, Vinod Kumar P B; Some Properties of The Cantor Set in the Hyperspace K(X); Nanotechnology Perceptions; 20, S8, 2024, 1267-1274.

 

Cinderella T J, Vinod Kumar P B; Countable dense homogeneity property of connected compact manifolds, Gulf Journal of Mathematics, 17, 2, 2024, 208-215

 

Selvy R.; Vinod Kumar P. B.; Chaotic fuzzy iterated function systems, Journal of Intelligent and Fuzzy Systems, 46, 4, 2024, 9261-9270.

 

Sreeja, K. U.; Vinodkumar, P. B.; Ramkumar, P. B. Independence Polynomial and Z counting polynomial of Fibonacci tree, Advances and Applications in Mathematical Sciences, 21, 3, 2022, 1569 – 1577.

 

Sreeja, K. U.; Vinodkumar, P. B.; Ramkumar, P. B. Independence Polynomial of the Sierpinski gasket graph and the tower of Hanoi graph. Journal of Math. Comput. Sci. 11 (6) 2021, 7072-7081.

 

Sreeja, K. U.; Vinodkumar, P. B.; Ramkumar, P. B. Characterization of quadratic independence polynomial of path graph, cycle graph and wheel graph. Malaya journal of Mathematik, 9, 1, 2021, 1029-1034.

 

Sreeja, K. U.; Vinodkumar, P. B.; Ramkumar, P. B. Julia Sets of some graphs using independence polynomial, : Springer Proceedings in Mathematics and Statistics, 2021, 193-202.

 

Sanil Jose.; Vinod Kumar P. B., Julia Sets in Topological Spaces: Springer Proceedings in Mathematics and Statistics, 2021, 187-192.

 

Sreeja, K. U.; Vinodkumar, P. B.; Ramkumar, P. B. Characterization of quadratic independence polynomial of path graph, cycle graph and wheel graph. Malaya J. Mat. , 2021, no. 1, 1029–1034. 05C31 (05C69).

 

P Amalraj.; Vinod Kumar P. B., The nth iterated of a map with dense orbit, Springer Proceedings in Mathematics and Statistics, 2021, 177-180.

 

Jose S, Vinod Kumar P B, Julia sets in Topological spaces, Springer Proceedings in Mathematics and Statistics, 2021, 187-192 MR4764328.

 

Vinod Kumar P. B. Mandelbrot Set and Fermat’s Last Theorem. Modern Perspectives in Theoretical Physics, 2021, 109-116.

 

Sreeja, K. U.; Vinodkumar, P. B.; Ramkumar, P. B. A graph polynomial for independent sets of Fibonacci trees. Int. J. Math. Comput. Sci. 15, 2020, no. 4, 1129–1133.

 

Sanooj, B.; Vinodkumar, P. B. Li-Yorke chaotic eigen set of the backward shift operator on ℓ2(N). Concr. Oper. 7, 2020, no. 1, 180–182. 47B37, 37B05 .

 

Employment History:

  • Lecturer (contract), Cochin University of Science and Technology (1/6/2000 to 30/10/2001).
  • Lecturer, Rajagiri School of Engineering and Technology (3/9/2001 – 31/12/2001)
  • Senior Lecturer, Rajagiri School of Engineering and Technology (1/1/2002 – 30/5/2004)
  • Assistant Professor, Rajagiri School of Engineering and Technology (1/6/2004 – 30/5/2007)
  • Associate Professor, Rajagiri School of Engineering and Technology (1/6/2007 – 30/5/2010)
  • Professor, Rajagiri School of Engineering and Technology (1/7/2010 – 30/6/2024)
  • Senior Professor, Rajagiri School of Engineering and Technology (1/7/2024 – 30/9/2024)
  • Research Professor, Muthoot Institute of Technology and Science, from 11/11/2024 onwards.

Professional Membership

Member of American Mathematical Society

Member of London Mathematical Society

Member of Institute of Mathematics and Applications

Senior Member of Institute of Electrical and Electronics Engineers

Member of International Society of Difference Equations

Member of Society for Industrial and Applied Mathematics

Member of International Association of Engineers

Member of Indian Mathematical Society

Member of Ramanujan Mathematical Society

General Secretary of Kerala Mathematical Association.

Member of Association for Mathematical Research

 

Major Conferences organized:

  • International conference on Mathematics for Data Science and Dynamics, February 2024 – https://www.rajagiritech.ac.in/ICMDD2024/
  • International conference on Mathematics of Intelligent Computing and Data Science, September 2022, https://www.rajagiritech.ac.in/Home/icmicds2022/
  • International conference on Number theory and Discrete Mathematics, 2020 – to mark hundredth year of passing away of Srinivasa Ramanujan – https://www.rajagiritech.ac.in/icntdm/
  • International workshop and conference on Topology and Applications, December 2018 – https://www.rajagiritech.ac.in/extra/iwcta/
  • 79th Annual conference of Indian Mathematical Society, 2017 – https://www.rajagiritech.ac.in/home/Conf/79Maths.asp
  • 8th Conference on Technology and Innovation in Math Education, 2017 – https://www.rajagiritech.ac.in/extra/time2017/
  • International conference and workshop on Fractals and Wavelets, 2013 – https://www.rajagiritech.ac.in/extra/icfw/
  • Annual Conference of Kerala Mathematical Association, 2005
  • National workshop on Graph Theory, 2003
  • National seminar on Chaos and Fractals, 2002

 

Ph.D. students supervised/co supervised:

  1. Vincent N.S – Some properties of turbulent functions in topological spaces – (2018) – Christ University.
  2. Sreeja K U – Relations between independence polynomial of some graphs and its associated Julia set – awarded (2023) – A P J Abdul Kalam Technological University.
  3. Radhika Das – An Analysis of Diophantine problems with their integral solutions and enticing number patters – awarded (2024) – Bharathidasan University.
  4. Bindhu V A – Number Theory – Bharathidasan University (thesis submitted)

Ph.D. students (ongoing):

  1. Amalraj Pankajakshan Pillai – On chaotic functions in hyperspaces – (2017-2024) – A P J Abdul Kalam Technological University (Synopsis to be submitted)
  2. Selvy R – On Contractive Iterated Function Systems – (2019-2024)- A P J Abdul Kalam Technological University (Synopsis submitted) – CSIR fellowship
  3. Sanooj B – On hypercyclic operators in Hilbert spaces – ongoing (2017 – )
  4. Suja N Thomas – Some properties of set of periodic points and set of periods of continuous functions in topological spaces – ongoing (2017 – )
  5. Sanil Jose – On Julia sets in Topological Spaces – ongoing (2017 – )
  6. Cinderella T. J. – Some problems on the space of homeomorphisms – ongoing (2020 – ) UGC fellowship
  7. Jauda P. P. – Some properties of topological conjugacy – ongoing (2020 – ) UGC fellowship
  8. Jeeva Jose – Topological Data Analysis – ongoing (2021 – ) CSIR fellowship

Undergraduate Projects Supervised:

  1. Optimization of flight trajectories of aircrafts using topological data analysis: (with Salviyas Sojan, Christom Joseph, Geo Mathew Gregory, Arjun Krishnan.
  2. Early Alzheimer’s detection using the Topological Data Analysis and Machine Learning: (with Ann Mary K, Akila Gunaseelan, Hridya Ann George, Somina John).
  3. Detection and prediction of brain tumours using Topological data analysis: (with Fathima Roya Saifudeen, Aiswarya Menon, Elsamaria Sachin, Aleena Anna Suresh).
  4. Detection and prediction of lung cancer using Topological data analysis: (with Aneesh P B, Rahul S, Riya Roy, A Harikrishnan).

Interns Mentored:

  1. Meenu M S; Maharajas college, Ernakulam; Separation Axioms – 15 May 2023 to 15 June 2023.
  2. Murshitha E H; St. Paul’s College, Kalamassery; Energy of a vertex – 17 May 2023 to 17 June 2023.
  3. Anjali Udayan; St. Paul’s College, Kalamassery; Fractals – 17 May 2023 to 17 June 2023.
  4. Deny Mol Benny; Cochin University of Science and Technology; Domination Polynomial of a graph – 20 May 2023 to 20 June 2023.
  5. Arjun K S; S H College Thevara; Smallness in Topology – 27 March 2023 to 27 April 2023.
  6. Ronal Thomas; St. Stephens College; Data Analysis – 23 May 2023 to 23 August 2023.
  7. Devika S, St. Paul’s College, Kalamassery: SVD of Brain tumour: 1 June 2024 to 30 June 2024.
  8. Adithya Anil, St. Paul’s College, Kalamassery: Analysis of brain tumour: 1 June 2024 to 30 June 2024.

Professional activities:

  • Delivered invited talk at National University of Australia, November

2014

  • Delivered invited talk at National University of Singapore, October 2008.
  • Delivered invited talk at Massachusetts Institute of Technology, USA on 23rd February 2007.
  • Delivered invited talk at Michigan State University, USA on 22nd February 2007.
  • Delivered invited talk at Western Michigan University, USA on 21st February 2007.
  • Attended International Congress of Mathematicians in 2002 at Beijing, China
  • Delivered an invited lecture at the satellite Conference on International Congress of Mathematicians (ICM) 2002 on Bifurcation and Chaos held at Beijing Normal University, Kunming, Yunnan, People’s Republic of China during August 13 – 17, 2002.
  • Delivered a lecture at a conference on New Directions in Dynamical Systems 2002 to be held at Kyoto University, Japan during August 5 – 15, 2002
  • Delivered thematic lectures at the annual conference of Ramanujan Mathematical Society in 2003.
  • Delivered invited talks at various seminars/conferences/workshops in India.
  • Delivered invited lectures on behalf of Kerala Mathematical Association at various colleges in Kerala.
  • Resource person for UGC/AICTE refresher courses.
  • Attended quality improvement and examination reforms workshops organized by UGC/AICTE/NAAC.
  • Resource person for UGC/AICTE/NAAC sponsored Quality improvement programmes at various institutions.
  • Member of Ph.D. admission committee for Mathematics of A P J Abdul Kalam Technological University, Kerala.
  • Member of Curriculum committee for Mathematics of A P J Abdul Kalam Technological University, Kerala.
  • Member of selection committee for faculty recruitment/Ph.D. scholars of various institutions.
  • Member of Board of Studies in Mathematics of various institutions.
  • Chairman of Doctoral committee of several Ph.D. scholars of A P J Abdul Kalam Technological university.
  • D. thesis examiner of various institutions.
  • Question setter/examiner for examinations to Ph.D. programme of various universities.

Courses taught:

  •           100008/MA600A Topological Data Analysis
  •           100008/MA500A Topology
  •           MAM101 Topology – 1
  •           MAM203 Topology – II
  •           06DM8012 Topological data analysis
  •           06DM8002 Introduction to Dynamical systems 1
  •           06DM8004 Introduction to Dynamical systems 2
  •           06DM8002 Research Methodology
  •           06DC8001 Research and Publication Ethics
  •           06DM8008 One dimensional complex dynamics
  •           06DM8007 Basics of periodic point theory
  •           06DM8006 Basics of hypercyclic linear operators
  •           06DM8005 Basics of chaotic functions on hyperspace
  •           201102/MA100A Mathematical Foundation for Computer Science
  •           100908/MA100A Linear Algebra and Calculus
  •           06EE6011 Advanced Mathematics
  •           06SP6011 Linear Algebra
  •           06CS6013 Mathematical Foundations for Computer Science
  •           06SP6242 Wavelets: Theory and Applications
  •           MA101 Calculus
  •           IGN304 Coding Theory and Cryptography
  •           IGN205 Linear Algebra and Applications
  •           ME010804L06 Advance Operations Research
  •           EN010101 Engineering Mathematics 1
  •           EC010702 Information Theory and Coding
  •           EN010301A Engineering Mathematics II
  •           EN010401A Engineering Mathematics III
  •           EN010501A Engineering Mathematics IV
  •           EN010301B Engineering Mathematics

 

Centre of Excellence established:

Established “Centre for Topology and Applications” in 2018 to promote research in the areas of Topology and its related areas with funding from DST-NBHM.

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