K. Senthil Kumar

Designation

Reader-F

Joining Date

04/01/2017

Expiry of Tenure

27/06/2049

Research Area

Number Theory

Education

Ph.D., 2014, Harish-Chandra Research Institute, Allahabad
M.phil., 2008, Annamalai University, Tamil nadu.
M.Sc., 2006, Annamalai University, Tamil nadu.
B. Sc., 2004, Poombuhar college (Bharathidasan University), Tamil nadu.

Professional Experiences:

Reader-F (Since July 2020), NISER, Bhubaneswar, India.
Assistant Professor (January 2017-June 2020), NISER, Bhubaneswar, India.
Visiting Fellow (July 2016-January 2017), Chennai Mathematical Institute, Chennai, India.
Postdoctoral Fellow (2014-2016), The Institute of Mathematical Sciences, Chennai, India

Research Interest

Transcendental number theory, Modular forms and Multiple zeta values

Awards

NBHM Ph. D., Fellowship, 2010.
CSIR-Junior Research Fellowship, 2008.
GATE Fellowship, 2008.

Publications

(With Gorekh Prasad Sena) On the number of algebraic points on the graph of the Weierstrass sigma functions, to appear in Bulletin of the Australian Mathematical Society.
Linear dependence of quasi-periods over the rationals, Comptes Rendus. Mathématique, Tome 359 (2021) no. 4, pp. 409-414.
(With Nabin Meher and R. Thangadurai) On a theorem of Mahler, Proc. Amer. Math. Soc. 145 (2017), no. 11, 4607-4615.
Order Structure and topological properties of the set of multiple zeta
values, Int. Math. Res. Not. IMRN. 5 (2016) 1541–1562.
(With Neeraj Kumar) Note on vanishing power sums of roots of unity,
Math. Student 84 (2015), no. 3–4, 69–73.
Fields of Mahler U -numbers and Schanuel’s Conjecture, J. Number
Theory 154 (2015), 82–100.
(With R. Thangadurai and M. Waldschmidt) Liouville numbers, Liouville
sets and Liouville fields, Proc. Amer. Math. Soc. 143 (2015), no. 8, 3215–3229.
(With R. Thangadurai and M. Waldschmidt) Liouville numbers and Schanuel’s conjecture, Arch. Math. (Basel) 102 (2014), no. 1, 59–70.

Preprints

Algebraic independence of values of Weierstrass zeta and elliptic functions (submitted).
Algebraic independence of values of Weierstrass zeta and elliptic functions (II). With an appendix by Robert Tubbs (submitted).
(With Gorekh Prasad Sena) Lehmer's Problem and Reciprocal Numbers.
(With Gorekh Prasad Sena) Lehmer's problem and splitting of rational primes in number fields (submitted).

Teaching

M207: Number Theory (July--Dec, 2017)
M602: Algebra-II (Jan--June, 2018)
M207: Number Theory (July--Dec, 2018)
M458: Algebraic Number Theory (Jan--June, 2019)
M207: Number Theory (July--Dec, 2019)
M402: Representations of Finite Groups (Jan--June, 2020)
M101: Mathematics-I (Dec 2020--Mar 2021)
M402: Representations of Finite Groups (Apr--July, 2021)
M302: Rings and Modules (Aug -- Dec, 2021)
M458: Algebraic Number Theory: (Jan-June, 2022)
M602: Algebra II (ongoing)

Responsibility

Chairperson, PGCI, NISER (Dec 2018-Mar 2021)
Convener, PGCS, SMS (September 2018-December 2020)
Member, PGCS, SMS (December 2020-Nov 2022)

Project/Thesis Guidance

Mr. Gorekh Prasad Sena (PhD Thesis, Ongoing)
Mr. Rajesh Kumar Palei, Some Topics in Number Theory (M.Sc., Thesis, 2021)
Mr. Rajesh Kumar Palei, On abc conjecture (M.Sc., Reading project, 2020)
Ms. S. Archana, Transformation groups, (PhD Reading Course, July-Dec, 2019)
Mr. Rajesh Kumar Palei, Prime number Theorem (M.Sc., Reading Project, July-Dec 2019)
Mr. Abhinav Thakur, On Class Number of Number Fields and Mahler Measure (M.Sc., Thesis, 2019)
Mr. Gorekh Prasad Sena, Elliptic functions (PhD Reading course, Jan-June 2018)
Mr. Shekh Mohammed Zahid, IMA Bhubaneswar, Transcendental numbers (Summer project, May-July, 2017)

Academic Presentations

Elliptic functions and algebraic independence, NCM Workshop, HRI, Prayagraj, 24 Nov- 3 Dec, 2022.
Linear dependence of quasi-periods over the rationals, RMS Pre-Conference Symposium, 36th Annual Ramanujan Mathematical Society Conference, Aug 4, 2021.
Algebraic Independence of the values of Weierstrass phi, zeta and sigma functions, KSOM, Jan 23-26, 2020.
Shuffle product, iterated integrals and Multiple zeta values, KSOM, Jan 18-22,2020.
Delivered a series of lectures on Galois Theory, AFS III, NISER, July 01-27, 2019.
Delivered a series of lectures on Galois theory, Summer outreach Program in Mathematics, (17-29 June 2019), NISER, Bhubaneswar.
On Transcendental numbers, Central university of Tamil Nadu, Thiruvarur, Dec 16-17, 2018.
Algebraic Independence of the values of Weierstrass functions, KSOM, Dec 10-14, 2018.
Representations of Finite groups, REFRESHER COURSE for College Teachers working in Kerala State, KSOM, Sep 06-09, 2018.
Delivered a series of lectures on graduate Algebra, Summer outreach Program in Mathematics, (18-30 June 2018), NISER, Bhubaneswar.
Delivered a series of lectures on Number Theory during the one month Training Program in Mathematics (May 21-June 16, 2018), NISER, Bhubaneswar.
Delivered a series of lectures on Complex Analysis during the one month Training Program in Mathematics (May 22-June 17, 2017), NISER, Bhubaneswar.
Tutor for the course Curves and surfaces, Summer outreach Program in Mathematics, (June 19-July 01, 2017), NISER, Bhubaneswar.
Impossibility of angle trisection by ruler and compass, NISER, 17th March 2017.
Elliptic functions and Elliptic integrals, Discussion meeting on Automorphic forms, NISER, Dec 21-27, 2016.
Duality principle of multiple zeta values, Two days Number Theory Meet @ HRI, September 06-07, 2016. Harish-Chandra Research Institute.
Prime decomposition in number fields, AIS Analytic Theory of Algebraic Numbers school at KIIT University, Bhubaneswar, Odisha, 13th June to 2nd July, 2016.
Modular forms: an introduction, AIS Analytic Number Theory School at KIIT University, Bhubaneswar, Odisha, June 01-20, 2015.
Order structure of multiple zeta values, Conference celebrating 65th birthday of Professor R. Balasubramanian, Dec 14-18, 2015, IMSc, Chennai, India.
Complex integration, Summer School in Mathematics, May 25-29, 2015 , IMSc, Chennai, India.
On Schanuel’s conjecture, International conference on automorphic forms and applications, February 13-14, 2015, Kerala School of Mathematics,
Kozhikode, India.
On algebraic sets, Discussion meeting – II on Algebraic curves, Feb 19 - March 5, 2014, Harish-Chandra Research Institute, Allahabad, India
Mahaler's classification of complex numbers, June 2013, Harish-Chandra Research Insitute, Allahabad, India.
Local global principle for quadratic forms and Hilbert’s symbol, AIS Number Theory: The circle method, June 25-July 14, 2012, The Institute of Mathematical Sciences, Chennai.
Universal Quadratic Forms and the Fifteen Theorem, June 2012, Harish-Chandra Research Institute, Allahabad, India.
Adam's theorem about Liouville numbers, Aug 2011, Harish-Chandra Research Institute, Allahabad, India.

Academic Visits

Kerala School of Mathematics, January 18--25, 2020.
Harish-Chandra Research Institute, October 15--18, 2019.
Centro Internazionale per la Ricerca Matematica, Trento, Italy, Sep 16-21,2019.
Harish-Chandra Research Institute, October 08--10, 2018.
Indian Statistical Institute Delhi, October 05--07, 2018.
Kerala School of Mathematics, September 06--09,2018.
Centre International de Rencontres Mathematiques-France, May 21--25, 2018.
Harish-Chandra Research Institute, January 12--21, 2018.
Harish-Chandra Research Institute, September 06--10, 2017.
NISER (Bhubaneswar), December 16-27, 2016.
Harish-Chandra Reseasrch Institute, August--September, 2016.
The Institute of Mathematical Sciences, October 2012--January 2013.
The Institute of Mathematical Sciences, December 2010--January 2011.
Visiting Student Summer Programme (VSSP), Harish-Chandra Research Institute, May--July 2010.

Conferences/Schools/Workshops Attended:

NCMW- Elliptic Curves, Elliptic Functions and Transcendence, HRI, Prayagraj, 24 Nov- 3 Dec, 2022.
International Conference in Number Theory and Workshop on Multiple zeta values, KSOM, Jan 18-26, 2020.
School (and Workshop) on Diophantine Geometry and Special Varieties, CIRM, Trento, Italy, Sep 16-21,2019.
Conference on Algebra and Number Theory, Central university of Tamil Nadu, Thiruvarur, Dec 16-17, 2018.
Conference on Number Theory, KSOM, Dec 10--14, 2018.
Conference: Diophantine Geometry, May 21--25, 2018, CIRM, Luminy, Marseille, France.
School and workshop on modular forms and black holes, January 05--14, 2017, NISER, Bhubaneswar, India.
Discussion meeting on automorphic forms, December 21--27, 2016, NISER, Bhubaneswar, India.
Two days Number Theory Meet @ HRI, September 06--07, 2016, Harish-Chandra Research Institute, Allahabad, India.
Leuca2016, Conference celebrating Michel Waldschmidt’s 70th birthday, June 13--17, 2016, Marina di San Gregorio, Patu` (Lecce), Italy.
AIS Analytic Theory of Algebraic Numbers school at KIIT University, Bhubaneswar, Odisha, 13th June to 2nd July, 2016.
Indo-French Program for Mathematics, The Institute of Mathematical Sciences, January 11--24, 2016, Chennai, India.
AIS Analytic Number Theory School at KIIT University, Bhubaneswar, Odisha, June 01-- 20, 2015.
Conference celebrating 65th birthday of Professor R. Balasubramanian, December 14--18, 2015, Institute of Mathematical Sciences, Chennai, India.
International conference on automorphic forms and applications, February 13--14, 2015 at Kerala School of Mathematics, Kozhikode, India.
Workshop on Jacobi forms and Modular forms of half-integral weight, February 02--12, 2015 at Kerala School of Mathematics, Kozhikode, India.
Discussion meeting – II on Algebraic curves, February 19 -- March 5, 2014 at Harish-Chandra Research Institute, Allahabad, India.
CMI – IMSC Joint conference on analytic theory of automorphic forms, Dec 09--13, 2013 at The Institute of Mathematical Sciences, Chennai, India.
CIMPA – ICTP Research school on algebraic curves over finite fields and applications, July 22 --August 02, 2013 at Manila, Philippines.
CMI – IMSc Lecture series in number theory, a course given by Prof. J. Oesterle on multiple zeta values, October 5, 2012 -- January 07, 2013 at The Institute of Mathematical Sciences, Chennai, India.
AIS Number theory: The circle method, June 25 --14 July 2012 at The Institute of Mathematical Sciences, Chennai, India.
Workshop on theory of prime numbers and related areas, May 06 -- 10, 2012 at Kerala School of Mathematics, Kozhikode, India.
International meeting on number theory celebrating the 60th birthday of Prof. R. Balasubramanian, December 15 -- 20, 2011 at Harish-Chandra Research Institute, Allahabad, India.
AFS-II, Panjab University, Chandigarh. June 02 -- 29, 2011.

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K. Senthil Kumar

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