HEMVATI NANDAN BAHUGUNA GARHWAL CENTRAL UNIVERSITY
(Alias Dr. Abhay Pandit, Email: abhaykumar288@gmail.com, Mob: 9599219237)
Research interests: Operator Theory, Functional Analysis, Linear Dynamical Systems, Topological Dynamics, Operator Semigroups, Dynamics of Matrices in $R^n$, Convex Analysis and Applications of Linear Dynamics in Differential Equations
Prerequisite to work in my area: Linear Algebra, Real Analysis & Complex Analysis
Researchgate Google Scholar MathSciNet Orcid ID Scopus ID Web of Sciences ID
[1] Abhay Kumar, and Sachi Srivastava, Supercyclic $C_0$-semigroups, stability and somewhere dense orbits, Journal Mathematical Analysis and Applications, 476, (2), (2019), 539-548, Link
[2] Abhay Kumar, and Sachi Srivastava, Supercyclicity Criteria for $C_0$-Semigroups, Advances in Operator Theory, 5, (2), (2020), 1646-1666. Link
[3] Abhay Kumar, Hypercyclicity and Supercyclicity of Unbounded Operators, Advances in Operator Theory, 7, (45), (2022), 1-20. Link
[4] Abhay Kumar, Supercyclic Composition C_0-Semigroups, the Journal of Analysis, 31, (2023), 1175–1190. Link
[5] Abhay Kumar, Convex-cyclicity and K-transitivity of Semigroups of Operators on Finite and Infinite Dimensional Spaces, The Journal of the Indian Mathematical Society, 91(1-2), (2024), 83–94. Link
[1] Abhay Kumar, Supercyclicity and stability for solution semigroups for some PDEs in certain weighted Banach spaces, Yearly Academic Journal, Vol. 16, (2017), 24-28 (Proceedings of the National Seminar on Recent Development in Mathematics organized by the Department of Mathematics, Kalindi College, University of Delhi, Delhi during January 12-13, 2017). Link
[2] Abhay Kumar, Spectrum and the Godefroy and Shapiro Criterion for Hypercyclicity, (Proceedings of the International Conference held at Department of Mathematics, Magadh University Bodh-Gaya during September 18-19, 2018), Published in the book (Recent Advances in Mathematics and Scientific Computing, P-225-231, 2022. Link
[1] Abhay Kumar, Generation of Supercyclic $C_0$-Semigroups
I welcome inquiries from prospective master's students and PhD students in my area of expertise.
• Graduation in Mathematics Honours from Patna College, Patna University with 77.62%.
• Master in Mathematics from the University of Delhi South Campus (Associated college Tirumala Tirupathi Devsthanam's Sri Venkateshwara College) with 70.75%.
• Cleared UGC-JRF with AIR 88 in the year 2012.
• M.Phil. in Mathematics on the title "Some Fuzzy Matrix Games" (Linear Programming Problems, Applied Mathematics) from the University of Delhi, under the supervision of Prof. R.R. Saxena, DDU College, University of Delhi with 84.20%.
• Ph.D. in Mathematics on the title “Supercyclicity of $C_0$-Semigroups” (Operator Theory & Functional Analysis) from the University of Delhi under the supervision of Prof. Sachi Srivastava, Deptt. of Mathematics, University of Delhi, South Campus.
Research Paper Presentation:
• Presented a paper entitled “Supercyclicity and stability for solution semigroups to some PDEs in certain weighted Banach spaces” in the National Seminar on Recent Developments in Mathematics held at Department of Mathematics, Kalindi College, University of Delhi during January 12-13, 2017.
• Presented a paper entitled “Spectrum and the angle criterion for supercyclic semigroups of operators” in the International Conference on Mathematics and Applications held at Department of Mathematics, Ramjas college during April 26-28,2017.
• Presented a paper entitled “Supercyclic $C_0$-semigroups and somewhere dense orbits” in the Research scholar seminar & annual conference of the society of Mathematical Sciences held at Department of Mathematics, University of Delhi during May 01-02, 2017.
• Presented a poster entitled “Supercyclicity of $C_0$-Semigroups” in the international workshop on recent advances in Operator Semigroups held at Department of Mathematics, University of Delhi during December 18-21, 2017.
• Presented a paper entitled “Spectrum and the Godefroy and Shapiro Criterion for Hypercyclicity” in the UGC Sponsored International Conference held at Department of Mathematics, Magadh University Bodh-Gaya during September 18-19, 2018.
• Presented a research paper entitled “Supercyclicity Criteria for the Tensor Product of $C_0$-Semigroups” in the National Conference on the Ancient Mathematics & its Emerging Areas held at Department of Mathematics, Faculty of Engineering, Tirthankar Mahaveer University, Moradabad on 18 November 2022.
• Presented a research paper entitled “Co-Semigroups from Hille-Yosida time to now” in the International Conference on Connecting Ancient Indian Wisdom in Modern Contexts held at Pandit Lalit Mohan Sharma Campus Rishikesh, Uttarakhand, India, on June 11-12, 2024.
• Participated in the Internet seminar on Evolution Equation 2013/14: Positive Operator Semigroups and its Applications.
• Participated in the International conference “The Legacy of Srinivasan Ramanujan” held during December 17th-22nd at Department
of Mathematics, University of Delhi, 2012.
• Participated in the workshop on information literacy and competency organized by University of Delhi Library System held on 17th January, 2013.
• Participated in the National Seminar for Research Scholars held during September20th-21st at Department of Mathematics, University of Delhi, 2013.
• Participated in the workshop on information literacy and competency organized by University of Delhi Library System held on 4th December 2014.
• Participated in the workshop on Indian Women and Mathematics held at Department of Mathematics, University of Delhi, during April 2-4, 2015.
• Organized the workshop on LaTeX and HTML at Department of Mathematics, Janki Devi Memorial College, University of Delhi, during 7-8 October 2016.
• Participated in the workshop on MS Excel for compiling attendance and internal assessment organized by Department of Mathematics, Janki Devi Memorial College, University of Delhi, on 27 October 2016.
• Volunteered in the “33rd Annual Conference of the Ramanujan Mathematical Society” held at Department of Mathematics, University of Delhi during June 1-3, 2018.
• Participated in the International Meet on Analysis at Department of Mathematics, University of Delhi, during on November 24, 2018.
• Participated as a member of advisory committee in the International Conference held at Department of Mathematics, Magadh University, Bodh-Gaya during September 18-19, 2018.
• Participated in the 79th Orientation Programme, held from 17/07/2018 to 13/08/2018, has obtained Grade A at UGC HRDC Patna University.
• Participated in the 7th Refreshor Course in Mathematical Sciences, held from 29/12/2020 to 11/01/2021, has obtained Grade A+ at UGC HRDC Deen Dayal Upadhyay Gorakhpur University.
• Participated And Successfully Completed Ten Days Faculty Development Program on HTML Organized by Department of Physics, M. V. College, Buxar in Association With IIT Bombay Through Spoken Tutorial, Remote Training Program During COVID 19 Outbreak from 15th May to 24th May 2020.
• Successfully completed TWELVE DAY FACULTY DEVELOPMENT PROGRAMME (22nd May to 02nd June, 2020) on SCILAB (Scientific Laboratories) organized by IQAC, A.N. College, Patna in association with Indian Institute of Technology, Bombay through Spoken Tutorials, Remote Learning (An Initiative of National Mission on Education through ICT, MHRD. Govt. of India).
• Complete One week (Online) Faculty Development Programme on ‘Mathematical Analysis and its Applications’(26th July – 31st July 2021) organised by Vivekananda College, University of Delhi in collaboration with Mahatma Hansraj Faculty Development Centre Hansraj College, University of Delhi.
• Participated in faculty development programme(FDP) on Python 3 organized by the University Department of Mathematics, TMBU, Bhagalpur from 8-14th June, 2020.
• Participated and successfully completed One Week Faculty Development Program on GeoGebra organized by Department of Mathematics, R. K. College in association with Spoken Tutorial Software Training Project developed by Indian Institute of Technology - Bombay, an initiative of National Mission on Education Through ICT, MHRD, Govt. of India from 6th to 12th May, 2020.
• Completed successfully Two-week “Faculty Development Program (FDP)” on HTML and ExpEYES software organized by
Department of physics of S.V.P. College, Bhabhua, Bihar in association with IIT – Bombay through Spoken Tutorial, remote training during
COVID – 19 outbreak (An initiative of National Mission on Education through ICT, MHRD, Govt. of India) from 14th May to 27th May, 2020.
• Successfully completed ONE WEEK FACULTY DEVELOPMENT PROGRAMME (11th May to 17th May, 2020) on LaTeX & Xfig organized by IQAC, A.N. College, Patna in association with Indian Institute of Technology, Bombay through Spoken Tutorials, Remote Learning (An Initiative of National Mission on Education through ICT, MHRD. Govt. of India).
• Participated in Online workshop on NEP-2020 (Promotion of Indian Knowledge Systems) organized by UGC-HRDC, Osmania University, Hyderabad, Telangana from 13.12.2022 to 15.12.2022.
• Completed the NEP 2020 Orientation & Sensitization Programme under Malaviya Mission Teacher Training Programme (MM-TTP) of University Grants Commission (UGC) Organized by Malaviya Mission Teacher Training Centre, HNB Garhwal University from 18th to 30th December 2023.
• Completed the Refresher Course in Mathematical Sciences (Mathematics/ Statistics / Operational Research/ Computer Sciences) conducted from 18th September 2024 – 1st October 2024, (CPDHE), UGC - Malaviya Mission Teacher Training Centre (MMTTC),University of Delhi.
• Delivered a Keynote / Invited / Contributory talk entitled "Co-Semigroups from Hille-Yosida time to now" in the International Conference on "Connecting Ancient Indian Wisdom in Modern Contexts" organised by Sri Dev Suman Uttarakhand University, Badshahithaul, Tehri Garhwal, Uttarkhand, India held on June 11-12, 2024
[1] Former Assistant Professor at Janki Devi Memorial College, University of Delhi (2016-17, Adhoc);
[2] Assistant Professor at S.D. College (Sheodeni College), Kaler, Magadh University, Bodh-Gaya (2017-2022);
[3] Assistant Professor at HNB Garhwal Central University, Srinagar, Uttarakhand (2022-onwards)
Research Visits:
[1] Harish Chandra Research Institute, Allahabad, December 2018
[2] Harish Chandra Research Institute, Allahabad, December 2019
[3] IIT Roorkee, Roorkee, December 2021
[4] IIT Roorkee, Roorkee, June 2022
Personal Details:-
Email:- abhaykumar288@gmail.com Mob.-9599219237
