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    Dr. Sudhansu Sekhar Rout
    Dr. Sudhansu Sekhar Rout

    Assistant Professor (Grade I)

    Office Address:

    Department of Mathematics National Institute of Technology Calicut N.I.T. Campus P.O. 673601 Kozhikode, Kerala.

    Contact no:

    0495 228 5226

    Email ID:

    sudhansu@nitc.ac.in

    Home Address:

    Qtr No:D-24, Department of Mathematics National Institute of Technology Calicut N.I.T. Campus P.O. 673601 Kozhikode, Kerala.

  • Ph.D.: National Institute of Technology Rourkela

  • Post-Doc: Harish-Chandra Research Institute Prayagraj (Allahabad)

    • Educational Qualifications

    • Ph.D.: National Institute of Technology Rourkela

    • Post-Doc: Harish-Chandra Research Institute Prayagraj (Allahabad)

     

     

     

    		 
    Ph.D. students supervised
    		 
    2019-2024
    		 
    Pritam Kumar Bhoi, (Thesis defended on Dec 09, 2024)
Thesis title: Sums of S-units and perfect powers in recurrence sequences (Co-supervisor)
    		 
    Jan 2023-now
    		 
    Parvathi S Nair,
Thesis title: Algebraic approximations to S-units (tentative) (sole)
    		 
    July 2023-now
    		 
    Rudranarayan Padhy,
Thesis title: Integral points on dynamical systems (tentative) (sole)
    		 
    July 2023-now
    		 
    Darsana N.,
Thesis title: On zeros and S-units in recurrence sequences (tentative) (sole)
       
      
    M.Sc. students supervised
    		 
    2022-23
    		 
    Pradum Gupta (M210626MA),
Project title: Elliptic Functions and its Applications
    		 
    2023-24
    		 
    Dinesh Prasanth R (M220609MA), 
Project title: On Cyclotomic Polynomials
    2023-24

    Pragya Sahrawat (M220606MA),
    Project title: Automatic sequences and curves over finite field

    		 
    2023-25
    		 
    Sarita (M231028MA),
Mini Project: On simple continued fractions
Project Phase-I: Rational approximations to algebraic numbers 
Project Phase-II: Rational approximations to algebraic numbers-II
    		 
    2024-26
    		 
    Hitish Kumar Khuntia (M241223MA),
Mini Project: Unique factorization property in quadratic number fields
Project Phase-I: Nagell–Lutz theorem on torsion points of an elliptic curve

    • Awarded Open Arms travel grant to attend ICM 2018 by the Organizing Committee.

    • Awarded Prof. A.K. Agarwal prize by the Indian Mathematical Society.

    • Awarded HRI Post doctoral Fellowship, by Harish-Chandra Research Institute Allahabad.

    • Awarded NBHM Post doctoral Fellowship, by National Board for Higher Mathematics (Did not avail).

    • Qualified Junior Research Fellowship (JRF) and National Eligibility Test for Lectureship (NET) in Mathematics conducted by CSIR.

    • Qualified Graduate Aptitude Test in Engineering (GATE) in Mathematics.

    • National Merit Scholarship, Govt. of Odisha.

    I am currently working as an Assistant Professor (Grade-I) in the Department of Mathematics, National Institute of Technology Calicut, India. My broad area of research is Number Theory and my research interest includes:

    • Diophantine equations
    • S-units in recurrence sequences
    • Special values of zeta functions
    • Arithmetic of dynamical systems

     

    • The Institute of Mathematical Sciences Chennai, India (June 14, 2022 - June 24, 2022)

    • Harish-Chandra Research Institute, Allahabad, India (Dec 26, 2017 - Jan 05, 2018)

    • University of Sopron, Hungary (June 03-- June 11, 2017)

    • University of Debrecen, Hungary (May 08- June 02, 2017)

    • Indian Statistical Institute Delhi, India (Dec 19--30, 2016)

    • National Institute of Technology Rourkela, India (July 25--August 04, 2016)

    • Indian Statistical Institute Delhi, India (May 30--June 04, 2016)

    • Gave an invited talk in Departmental Seminar at NIT Calicut in January 2023 on Perfect Powers and S-units in Recurrence Sequences.

    • Gave an invited talk in Institute Seminar at KSoM in June 2022 on S-units in Recurrence Sequences.

    • Gave an invited talk in Lectures on Transcedence on commutative algebraic groups at NISER Bhubaneswar in December 2019 on intersection of orbits in dynamical systems.

    • Gave an invited talk in Workshop on Number Theory at NISER Bhubaneswar in December 2018 on Sums of $S$-units in recurrence sequences.

    • Gave a talk in the International Congress of Mathematicians, Rio de Janeiro, Brazil in August 2018, on Lucas non-Weiferich primes in arithmetic progression.

    • Gave a series of lectures in the Teacher's Enrichment Workshop(TEW) at IMA Bhubaneswar in June 2018 on Complex Analysis.

    • Gave a series of lectures in the Interactive Mathematics Training Camp for Undergraduate Students at IMA Bhubaneswar in May 2018 on Linear Algebra.

    • Gave two lectures in the National Workshop on LaTex at IMA Bhubaneswar in March 2018.

    • Gave an invited talk in the 83rd Annual Conference of the Indian mathematical society at SV University Tirupati in Dec 2017 on Lucas-Weiferich primes and $abc$ conjecture.

    • Gave a talk at University of Debrecen, Hungary in May 2017 on "Lucas-Weiferich primes and $abc$ conjecture'.

    • Gave a talk in the Number Theory Meet at Harish-Chandra Research Institute Allahabad in Sep. 2016 on Balancing non-Wieferich primes in arithmetic progression.

    • Gave a talk in the Number Theory Seminar at Harish-Chandra Research Institute Allahabad in March 2016 on On $ell$-th order gap balancing numbers.

    • Gave a talk at Veer Surendra Sai University of Technology, Burla in Jan 2016 on Perfect powers in balancing and Lucas-balancing numbers.

    • Gave a talk at National Institute of Technology Rourkela in Oct. 2015 on Balancing non-Wieferich primes in arithmetic progression.

      2022-2023(Monsoon)   2022-2023(Monsoon) 
    B.Tech (ME)
    		 
    MA2001D: Mathematics-III
    		 
    B.Tech.(CS-03)
    		 
    MA2003D: Mathematics-IV
    		 
    Ph.D.
    		 
    Advanced Topics in Mathematics-II
    		 
    M.Sc.(S2)
    		 
    MA6324: Abstract Algebra
      2023-2024(Monsoon)   2023-2024(Winter) 
    B.Tech.(CE-03)
    		 
    MA2001D: Mathematics-III
    		 
    B.Tech.(CE-01)
    		 
    MA2002D: Mathematics-IV
    		 
    B.Tech.(MT-01)
    		 
    MA2001D: Mathematics-III
    		 
    B.Tech.(EC-02)
    		 
    MA2002D: Mathematics-IV
      2024-2025(Monsoon)   2024-2025(Winter) 
    B.Tech.(CS-02)
    		 
    MA2002E: Mathematics-III
    		 
    B.Tech.(ME-01)
    		 
    MA2013E: Mathematics-IV
    		 
    M.Sc.(S3)
    		 
    MA7251E: Number Theory & Cryptography
    		 
    B.Tech.(ME-04)
    		 
    MA2013E: Mathematics-IV
    		 
    M.Sc.(S1)
    		 
    ZZ6003E: Research Methodology
    		 
    B.Tech.(CE-01)
    		 
    MA2013E: Mathematics-IV
      2025-2026(Monsoon)   2025-2026(Winter) 
    B.Tech.(EE 03-04)
    		 
    MA2001E: Mathematics-III
    		 
     B.Tech.(CE 03)
    		 
    MA2013E: Mathematics-IV
    		 
    ITEP (MATHS)
    		 
    ED3201: Linear Algebra
    		 
    B.Tech.(ME 01) 
    		 
    MA2013E: Mathematics-IV

     

    Area of Research 

    Number Theory 

    1. Gap balancing numbers, (with G. K. Panda), Fib. Quart. 51(3) (2013), 239–248. 
    2. Periodicity of balancing numbers, (with G K Panda), Acta. Math. Hungar.143(2) (2014), 274–286. 
    3. Balancing Dirichlet series and related L-functions, (with G K Panda),  Indian J. Pure Appl. Math 45(6) (2014), 943–952.
    4.  k-Gap balancing numbers, (with G K Panda),  Period. Math. Hungar. 70(1) (2015), 109–121. 
    5. Stability of balancing sequence modulo p,  (with G K Panda and R. K. Davala), Unif. Distrib. Theory 10(2) (2015), 75–89.
    6. Balancing non-Wieferich primes in arithmetic progression and abc conjecture, Proc. Japan Acad. Ser. A Math. Sci. 92(9) (2016), 112–116.
    7. Diophantine equations concerning balancing and Lucas balancing numbers, (with P.K. Dey), Arch. Math. (Basel) 108(1) (2017), 29–43.
    8. Linear combinations of prime powers in sums of terms of binary recurrence sequences,  Lith. Math. J. 57 (4) (2017), 1–15.
    9. Analytic continuation of multiple Fibonacci zeta functions, (with N. K.  Meher), Proc. Japan Acad. Ser. A Math. Sci. 94(6) (2018), 64–69. 
    10. ℓ-th order gap balancing numbers, (with R. Thangadurai), Integers 18 (2018), Paper No. A56.
    11. Analytic continuation of multiple Lucas zeta functions, (with N. K.  Meher), J. Math. Anal. Appl. 468(2018), 1115-1130.
    12. Sums of S-units in recurrence sequences, ( A. Bérczes, L. Hajdu, and I. Pink),  J. Number Theory 196(2019), 353-363.
    13. Lucas non-Weiferich primes in arithmetic progressions, Funct. Approx. Comment. Math. 60(2019), 167-175.
    14. Prime powers in sums of terms of binary recurrence sequences, ( E. Mazumdar), Monatsh Math. 189(4) (2019), 695-714..
    15. Sums of fifth powers being a perfect power: A special case, (P. Das and P. K. Dey) J. Ramanujan Math. Soc. 35(1) (2020), 23-33. 
    16. Perfect powers in alternating sum of consecutive cubes, (P. Das, P. K. Dey and B. Maji), Glas. Math. Ser. III 55(1) (2020), 37-53. 
    17. The dynamical Mordell - Lang problem for intersection of two orbits, J. Number Theory 207(2020), 122-137. 
    18. The Mordell-Weil bases for the elliptic curve y2 = x3 − m2x + m2, (with A. Juyal), Czechoslovak Math. J. 71(146) (2021) 1133-1147. 
    19. Multiple Lucas Dirichlet series associated to additive and Dirichlet characters, (with N. K.  Meher), Mediterr. J. Math. 18(6), 262 (2021).
    20. S-parts of sums of terms of linear recurrence sequences, (with N. K.  Meher), Acta Math. Hunga.  168(2) (2022), 553-571.
    21. The orbit intersection problem in positive characteristic, Acta Arith. 206(3) (2022), 277-290.
    22. Cullen Numbers in Sums of Terms of Recurrence Sequence, (with N. K.  Meher), Results Math 78 Article number: 102 (2023). 
    23. Sums of $S$-units in sum of terms of recurrence sequences, (with P.K. Bhoi, and G. K. Panda), Ramanujan J. 62 (2023), 457-468.
    24. On perfect powers that are sum of two balancing numbers, (with P.K. Bhoi, and G. K. Panda), Period. Math. Hungar., 88 (2024), 93-101.
    25. On the resolution of the Diophantine equation U_n + U_m = x^q, (with P.K. Bhoi, and G. K. Panda), Ramanujan J. 66, 36 (2025). 
    26. Sums of S-units in sum of terms of recurrence sequences-II, (with P.K. Bhoi), Funct. Approx. Comment. Math. 72(1) (2025), 103-116.
    27. Sum of terms of recurrence sequences in the solution sets of generalized Pell equations, (with P.K. Bhoi, and R. Padhy), Funct. Approx. Comment. Math. 74(1) (2026), 63–72.
    28. Uniform bounds on S-integral preperiodic points for Chebyshev polynomials, (with R. Padhy) J. Korean Math. Soc. 62 (6) (2025), 1383-1396. 
    29. Zeros and S-units in sums of terms of recurrence sequences in function fields, (with Darsana N.), submitted for publication, (2024).
    30. Sums of terms of recurrence sequences and S-units in the solution sets of norm form equations, (with Darsana N), Bull. Aust. Math. Soc., accepted, (2026).
    31. Sums of S-units in X-coordinates of Pell equations, (with Parvathi S Nair), to appear in Period. Math. Hungar. (2026).
    32. Primitive prime divisors in the forward orbit of a polynomial, (with Shanta Laishram and Prabhakar Yadav), submitted for publication, (2025).
    33. Algebraic approximations to linear combinations of S-units (with Parvathi S Nair and Veekesh Kumar ), submitted for publication, (2025).
    34. Uniform bounds on S-integral points in backward orbits, (with R. Padhy), submitted for publication, (2025).
    35. On the number of irreducible representations of so(5) (with S. Nayak and N K Meher), submitted for publication, (2025).
    36. Diophantine equations for polynomial recursive sequences, (with Darsana N), submitted for publication, (2025).
    37. Simultaneous rational approximations to linear combinations of S-units, (with Parvathi S Nair), submitted for publication (2026).
    38. Prime ideal divisors of parametric recurrence sequences, (with Darsana N), submitted for publication, (2026).
    39. The quotient problem for linear recurrence sequences, (with Parvathi S Nair), submitted for publication (2026).
    40. Quantitative bounds on integrality for post-critically finite maps, (with R. Padhy), submitted for publication, (2026).

     

    1. National workshop on Mathematical aspects of Computer Science (March 14-15, 2009), Sambalpur University, Odisha, India.

    2. AFS -II (June 08- July 04, 2009) Bhaskaracharya Prastishthana, Pune, India.

    3. Discussion meeting on Geometry and Analysis (Jan 20- Feb 02, 2010) HRI Allahabad, India.

    4. Symposium in Number Theory (May 31- June 03, 2011), Bhaskaracharya Prastishthana, Pune, India.

    5. Winter School in Number Theory (December 20-24, 2011), IISER Kolkata, India.

    6. Workshop on Bloch-Kato conjectures (July 17-21, 2012) IISER Pune, India.

    7. The Pan Asian Number Theory Conference (July 23 -27, 2012) IISER Pune, India.

    8. Conference in Number Theory (December 12-14, 2012) Jadavpur University, Kolkatta, India.

    9. The annual conference of The Odisha Mathematical Society (December 29-30, 2012) Sambalpur University, Odisha, India.

    10. AIS on Analytic Number Theory (June 10- 29, 2013) KIIT University, Odisha, India.

    11. CIMPA Research School in Fourier analysis of groups in Combinatorics (Nov 18-30, 2013) NEHU, Shillong, India.

    12. AIS on Diophantine equations (June 16-July 04, 2014) Himachal Pradesh University, Shimla, India.

    13. Triveni Number Theory Meet (March 04-08, 2016 ) HRI Allahabad, India.

    14. Number Theory Meet (Sep 06-07, 2016) HRI Allahabad, India.

    15. International Conference of The Indian Mathematical Consortium in cooperation with American Mathematical Society (Dec 14-17, 2016) Banaras Hindu University, Varanasi, India.

    16. School and Workshop on Modular forms and Black holes (Jan 05- 14, 2017) NISER Bhubaneswar, Odisha, India.

    17. International Conference on Class Groups of Number Fields and Related Topics (Sep 04 - 07, 2017) HRI Allahabad, India.

    18. 83rd Annual Conference of The Indian Mathematical Society- An International meet (Dec 12-15, 2017), SV University, Tirupati, India.

    19. GIAN course on Transcendental numbers and special values of Dirichlet series ( Dec 16- 21, 2017) IIT Ropar, India.

    20. Number Theory: Arithmetic, Diophantine, and Transcendence (Dec 22-25, 2017), IIT Ropar, India.

    21. International Congress of Mathematicians (Aug 01-09, 2018), Rio de Janeiro, Brazil. 

    22. Workshop on Number Theory (Nov 30- Dec 06, 2018), NISER Bhubaneswar, Odisha, India.

    23. Lectures on Transcedence on commutative algebraic groups (Dec 09-15, 2019), NISER Bhubaneswar, Odisha, India.

    24. 48th Orissa Mathematical Society Conference (April 10-11, 2021), IMA Bhubaneswar, Odisha, India.

    25. International Conference on Class Groups of Number Fields and Related Topics-2022 (November 21-24, 2022), KSoM, Kozhikode, India.

    26. Workshop on Arithmetic of Dynamical Systems (May 15-20, 2023) KSoM, Kozhikode, India.

    27. International Conference on Diophantine Equations, Polynomials and Related Areas, (Nov 26-30, 2024), ISI Delhi, India.

    28. International Conference on Transcendence, Arithmetic and Diophantine Explorations (TRADE), (Jan 03-05, 2025), KSoM, Kozhikode, India.

    1. Project Title :  A study on the zero multiplicity and S-units in recurrence sequences (File No. CRG/2022/000268)
      Fund Approved: Rs. 21,12,264 INR
      Funding Agency: Core Research Grant, SERB, DST, Govt. of India. 
      Duration: January 2023 - January 2026.

        2.  Project Title :  Integral Points on Dynamical Systems
             Fund Approved: Rs. 10,16,900 INR
             Funding Agency: National Board for Higher Mathematics, DAE, Govt. of India. 
             Duration: January 2023 - January 2025

     

     

    1. Life Member of Indian Mathematical Society (L/2023/107).
    2. Life Member of Odisha Mathematical Society (LMOMS/823/2022).
    3. Life Member of Ramanujan Mathematical Society (1921).

    • Workshop on Elliptic Curve and Cryptography, December 15-19, 2025, (Organized with Dr. Chiranjit Ray) funded by ANRF.

    • International Conference on Lie Algebra and Number Theory (ICLANT - 2024), June 10-14, 2024, (Organized with Dr. Saudamini Nayak and Dr. Chiranjit Ray) funded by NBHM, SERB, CDC-IMU, KSCSTE.

    • Teacher’s Enrichment Workshop on Probability and Number Theory, Jan 29-Feb 03, 2024, (Organized with Dr. M. Subramani, IIITDM Kancheepuram) funded by NCM .

    • Workshop on Number Theory & Some Applications, December 04-05, 2023, funded by SERB.

    • Expert talk by Prof. Shanta Laishram, ISI Delhi "Binary Recurrence Sequences and its Arithmetic" on January 24, 2023.

    • Expert talk by Prof. Kalyan Chakraborty Director, KSCSTE-Kerala School of Mathematics, "A couple of gems from Ramanujan's Garden" on December 22, 2022.

    • Expert talk by Prof. Michel Waldschmidt, Emeritus Professor, Sorbonne Universit'e, Institut Math'ematique de Jussie, France "On Markoff equation x2+y2+z2 = 3xyz" on November 23, 2022.

    Address:

    National Institute of Technology Calicut,
    NIT Campus P.O 673 601,
    Kozhikode, India.

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