Dr. Ramesh Venkadachalam Palani

Dr. Ramesh Venkadachalam Palani

Name: Dr. Ramesh Venkadachalam Palani
Designation: Assistant Professor
Phone: 04366-277230
Email: rameshmat@cutn.ac.in


Biographic Sketch:
I have guided seven PhD students to completion (six students of CUTN as a guide and one student of IIT Madras as a co-guide) and currently guiding two PhD scholars. Have guided an M.Phil. Scholar. I have mentored fifty-three master project students, many of whom have taken academia and industry jobs. I am currently guiding three master's students. I have mentored fifteen summer interns from outside CUTN and with financial support from three National Science Academies. I have institutionalised two initiatives, namely, nurture for college students and mathematics teachers of India and Talent Search in Sciences(TSS) for government school students in Thiruvarur. Through ""nurture"", I have mentored 370 students and 35 teachers from outside the Central University of Tamil Nadu in the last eight years, and through TSS, we have mentored more900 government school students. In the last eight years, more than ten master's students and one PhD scholar got placed in the industry, with salaries ranging from four lakhs to eighteen lakhs per annum. Many master's students are pursuing PhD.

Research Highlights :

Dr. Ramesh is interested in number theory, algorithms, and computing. Currently his research is in two directions, one around Gauss’s primitive root conjecture and second on designing scalable algorithms for shock capturing. He is also working on constructing a necessary and sufficient condition for 2 being a primitive root of Sophie Germain primes and a few generalisation of Sophie Germain primes. Further he is working on connecting the various partitions of primes with 2 as primitive root of 2p + 1. On estimating this, the idea is to generalize it to more general primes and work on connecting the primitive root and the number of orbits of the permutation (p!).

Recent Publications :

Ramesh V.P., Makeshwari M, (2023).
Is a Sophie Germain Prime a Primitive Root of Safe Prime? Mathematical Association of America: Mathematics Magazine

Ramesh V.P., Makeshwari M, Saswati Sinha (2023).
Connecting primitive roots and permutations, Indian National Science Academy: Indian Journal of Pure and Applied Mathematic, https://doi.org/10.1007/s13226-023-00384-4

Ramesh V. P., Gowtham R, Saswati Sinha (2023).
A note on the sum of cubic residues with even and odd index, Indian National Science Academy: - Indian Journal of Pure and Applied Mathematics, https://doi.org/10.1007/s13226-023-00370-w

Ramesh V.P., Makeshwari M, (2023).
A note on generalized Sophie Germain primes: In the direction of Legendre’s extended Sophie Germain primes, Resonance - Indian Academy of Sciences, 923-928,

Ramesh V.P., Makeshwari M, (2022).
A Primitive Root p of 2p+1 is a Sophie Germain Prime, The American Mathematical Monthly, 129(6), p. 538, 2022 https://doi.org/10.1080/00029890.2022.2059961

Ramesh V. P., Gowtham R, Saswati Sinha (2022).
A Note on Cubic Residues Modulo n, Indian National Science Academy: - Indian Journal of Pure and Applied Mathematics, 54, 6265, doi: https://doi.org/10.1007/s13226-022-00230-z (2022)

Ramesh V.P., Makeshwari M, (2022).
Least primitive root of any safe prime is prime, The American Mathematical Monthly, 129(10), 971 https://doi.org/10.1080/00029890.2022.2115816

Gajendra Babu, Prithvi M, Kapil K. Sharma & Ramesh V.P. (2022)
A Robust Numerical Algorithm on Harmonic Mesh for Parabolic Singularly Perturbed Convection-Diffusion Problems with Time Delay,  Numerical Algorithms, Numerical Algorithms, 91, 615634

Ramesh V.P., Janakiraman S., Prithvi M. & Narayani G. (2022).
A new a priori estimation for singularly perturbed problems with discontinuous data, Indian Journal of Pure and Applied Mathematics, 53, pages813825 (

Ramesh V.P., Kapil K. Sharma, Priyanga B., Narayani G. (2021).
A uniformly convergent upwind scheme on harmonic mesh for singularly perturbed turning point problems, International Journal for Computational Methods in Engineering Science and Mechanics, 376-385

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