Designation

Reader-F

Joining Date

Expiry of Tenure

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

- On the values of Weierstrass zeta and sigma functions. With an appendix by David Masser, to appear in
**Acta Arithmetica**. - (With Gorekh Prasad Sena) Lehmer's problem and splitting of rational primes in number fields,
**Acta Math. Hungar.**, 169 (2) (2023), 349–358 - (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
**,**84 (2015), no. 3–4, 69–73.

Math. Student - Fields of Mahler U -numbers and Schanuel’s Conjecture
**, J. Number**154 (2015), 82–100.

Theory - (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. With an appendix by Robert Tubbs.
- (With Gorekh Prasad Sena) Lehmer's Problem and Reciprocal Numbers.

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 (Aug--Dec, 2022)
- M308 and MA709: Complex Analysis (Jan--May, 2023)
- M458 and MA857: Algebraic Number Theory (Teaching)

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, 2023)
- 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

**Gelfond-Schneider theorem**, KSOM, August 07--12, 2023.- E
**lliptic 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

- Harish-Chandra Research Institute, June 20--July 14, 2023.
- 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 Research 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:**

- Conference on Number Theory, KSOM, August 07--12, 2023.
- 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 the 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 the 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.

Sponsored Projects

SERB MATRICS GRANT, Department of Science and Technology, Govt. of India; Duration: 2022-2024.