Faculty Details | Department Of Mathematics

Research

My area of specialization is Number Theory.

My research interests include

Arithmetic of Elliptic Curves,
Cyclotomic Fields,
Iwasawa Theory,
Euler Systems,
Formal Groups,
P-adic Measures,
Galois Cohomology,
Permutation Polynomials,
Hilbert Polynomials,
Class Number

Education

PhD:

Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 2001
Thesis Title: Iwasawa Theory of Lubin-Tate Division Towers and p-Adic L-Functions
Supervisor: John Coates, FRS, Sadleirian Professor of Mathematics, DPMMS, Cambridge

Certificate for Advanced Study in Mathematics (Mathematical Tripos, Part III) at Trinity College, University of Cambridge, 1997 (distinction).
The Mathematical Tripos, Trinity College, University of Cambridge, 1996, (wrangler).
B.Sc. (Hons.) Mathematics, St. Stephen's College, University of Delhi, 1994 (90.2%).
Higher Secondary (XII), Cotton College, Guwahati, 1991 (PCM 93%).
High School (X), Govt. Higher Secondary School, Golaghat, Assam, 1989, (86.2%).

Experience

Associate Dean, Academic Affairs, IIT Guwahati, 2014-17
Vice Chairman, JEE Cell, IIT Guwahati, 2013-14
Preparatory Coordinator, IIT Guwahati, 2012-13
DPPC Secretary, Department of Mathematics, IIT Guwahati, 2011-12

Courses

I am teaching MA 542 this semester (Jan-April, 2015).

The other courses that I have taught so far at IIT Guwahati are:

Algebra and Number Theory (MA727: PhD course)
Linear algebra and Functional Analysis (MA 731: PhD course)
Real and Complex Analysis (MA 741: PhD course)
Galois Theory (MA 622: MSc elective)
Algebraic Number Theory (MA509: MSc elective)
Linear Algebra (MA522: MSc))
Modern Algebra (MA521: MSc)
Differential Equations (MA542: MSc)
Modern Algebra (MA222: BTech)
Mathematics II (MA102: BTech core course)
Mathematics I (MA101: BTech core course)

Awards

Sir William Hodge Fellowship, awarded jointly by Engineering and Physical Research Council (EPSRC), UK and Institut des Hautes Etudes Scientifiques (IHES), France, 200-2002.
Senior Rouseball Scholarship, awarded by Trinity College, Cambridge on the basis of postgraduate research work, 2000-2001.
Smith and Knight Prize in the annual mathematics essay competition for second year Ph.D. students at the University of Cambridge, 1999.
Research Scholar of Trinity College, the highest category of scholarships of the college open to students, awarded for excellence in Mathematical Tripos - Part III examination, 1997-2000.
Overseas Research Scholarship, awarded by the Govt. of UK, 1997-2000.
Internal Graduate Studentship, Trinity College, Cambridge, 1997-2000.
Senior Scholar of Trinity College, awarded for excellence in Tripos results, 1995-97.
Ramanujan Scholarship, awarded annually to one student from India to pursue higher studies in mathematics at the University of Cambridge, 1994-96.
Honorary Scholar of Cambridge Commonwealth Trust, 1994-1996.
State Merit Scholarship to study mathematics at the University of Delhi, 1991-1994.
Ramesh Goel Memorial Prize for the best student of mathematics at St. Stephen's College, 1994.

Journal Publications

22. Shamik Das and Anupam Saikia, "On θ-congruent numbers over real number fields.", Bulletin of Australian Mathematical Society , vol.103 ,pp.218-229, [2021]

21. Anupam Saikia, "On the Iwasawa μ-invariants of supersingular elliptic curves", Acta Aritmetica , vol.194 (2) ,pp.179-186, [2020]

20. Shamik Das and Anupam Saikia, "Families of non-congruent numbers with arbitrarily many pairs of prime factors", Integers , vol.20 [2020]

19. Shamik Das, Debopam Chakraborty and Anupam Saikia, "On the period of the continued fraction of $\sqrt{pq}$.", Acta Aritmetica , vol.196 (3) ,pp.291-302, [2020]

18. Rajesh P. Singh, Bhaba K. Sarma and Anupam Saikia, "A public key crystosystem using a group of permutation polynomials", Tatra Mt. Math. Publ. , vol.77 ,pp.139-162, [2020]

17. Debopam Chakraborty and Anupam Saikia, "On a conjecture of Mordell", Rocky Mountain J. Mathematics , vol.49 (8) ,pp.2545-2556, [2019]

16. Naba Kanta Sarma, Anupam Saikia., "Torsion of elliptic curves over imaginary quadratic fields of class number 1", Rocky Mountain J. Math , vol.48 (8) ,pp.2689-2703, [2018]

15. Anupam Saikia and Kumari Saloni, "Bounding Hilbert coefficients of parameter ideals", Journal of Algebra , vol.67 (142) ,pp.328-344, [2018]

14. Anupam Saikia and Dishari Chaudhuri, "On the derived length of units in group algebra", Czechoslovak Math. J , vol.67 (142) ,pp.855-865, [2017]

13. Debopam Chakraborty and Anupam Saikia, "An explicit construction for unramified quadratic extensions of biquadratic fields.", Acta Arithmetica , vol.178 (2) ,pp.153-161, [2017]

12. Debopam Chakraborty and Anupam Saikia, " Congruence relations for the fundamental unit of a pure cubic field and its class number", Journal of Number theory , vol.166 ,pp.76-84, [2016]

11. Debopam Chakraborty, Saikia Anupam. .. ():-., "On relative class number and continued fractions.", Bull. Korean Math. Soc. , vol.52 (5) ,pp.1559-1568, [2015]

10. Chaudhuri Dishari, Anupam Saikia., "On group algebras with unit groups of derived length at most four", Publ. Math. Debrecen , vol.86 (1-2) ,pp.39-48, [2015]

9. Debopam Chakraborty, Saikia Anupam., "Another look at real quadratic fields of relative class number 1", Acta Arithmetica , vol.163 (4) ,pp.371-377, [2014]

8. Rupam barman and Anupam Saikia, "Iwasawa λ-invariants of p-adic measures on Znp and their Γ-transforms.", Journal of Number Theory , vol.132 (10) ,pp.2258-2266, [2012]

7. A.Saikia, B.K. Sarma, R.P. Singh, "Poly Dragon: An Efficient Multivariate Public Key Cryptosystem", Journal of Mathematical Cryptology. , vol.4 ,pp.349-364, [2011]

6. Rupam Barman and Anupam Saikia, "Iwasawa λ-invariants and Γ-transforms of p-adic measures on Zⁿ_p", International Journal of Number Theory , vol.8 ,pp.1819-1829, [2010]

5. Anupam Saikia and Rupam Barman, "Coefficients of a p-adic measure on Znp and Iwasawa λ-invariant of its Γ-transform.", Asian-Eur. J. Math. , vol.3 (4) ,pp.545-554, [2010]

4. Rupam Barman and Anuoam Saikia, "A note on Iwasawa μ-invariants of elliptic curves", Bull. Braz. Math. Soc. (N.S.) , vol.41 (3) ,pp.399-407, [2010]

3. Rupam barman and Anupam Saikia, "Iwasawa λ-invariants and Γ-transforms", J. Ramanujan Math. Soc. , vol.24 (2) ,pp.199-209, [2009]

2. A.Saikia., "Selmer Groups of Elliptic Curves with Complex Multiplication.", Canadian Journal of Mathematics. , vol.56 (1) ,pp.194-204, [2004]

1. A.Saikia., "A Simple Proof of a Lemma of Coleman.", Mathematical Proceedings of the Cambridge Philosophical Society. , vol.130 (part 2) ,pp.209-220, [2001]

Conference Publications

3. Anupam Saikia., "Explicit Reciprocity Law of Bloch-Kato and Exponential Maps.", The Bloch-Kato Conjecture for the Riemann Zeta Function, London Mathematical Society Lecture Note Series, Cambridge University Press. ,pp.65-96, [2015]

2. A. Saikia., "Ribet`s Construction of a Suitable Cusp Eigenform.", Workshop on Iwasawa Theory of Totally Real Fields, IIT Guwahati. [2008]

1. A. Saikia., "On units generated by Euler systems.", International Conference on Number Theory, Harish-Chandra Research Institute, Allahabad. [2006]

PostDoc Fellow

Current

Currently no current student.

Completed

1	Dr. Jaitra Chattopadhyay (NBHM PDF)
2	Dr. Mohit Mishra (NBHM PDF)

Research Scholars

Current

1	H Laxmi
2	Ansh Agrawal

Completed

1	Shamik Das
2	Rupam Barman
3	Dishari Chaudhuri
4	Debopam Chakraborty
5	Kumari Saloni
6	Naba Kanta Sarma
7	Rajesh Pratap Singh

1. Selmer Groups of Elliptic Curves and Their Applications Funding Agency : MATRICS, SERB Principal Investigator: Anupam Saikia Co-investigator: Duration/Starting Year: 2021 Status: Ongoing
2. Web Course: Number Theory Funding Agency : The Ministry of Human Resource Development, Govt. of India Principal Investigator: Anupam Saikia Co-investigator: Duration/Starting Year: 2009 Status: Completed

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