About Me:
I, Gautam Kalita, have been serving as an Associate Professor of Mathematics in the Department of Science and Mathematics, Indian Institute of Information Technology Guwahati, since March 1, 2022. I joined Indian Institute of Information Technology Guwahati as an Assistant Professor of Mathematics on April 30, 2014. Prior to joining IIIT Guwahati, I have acquired the following education qualifications:
- Ph. D. in Mathematical Sciences from Tezpur University, Assam (January 2011-February 2014).
Title of Ph. D. Thesis: Certain families of algebraic curves and polynomials, and their connections to hypergeometric functions.
Thesis Advisor: Dr. Rupam Barman, Currently Professor of Mathematics, IIT Guwahati. - Master of Science (M. Sc.) in Mathematics from Tezpur University, Assam (2008-2010).
Title of M.Sc Dissertation: Permutation polynomials over finite fields.
Supervisor: Dr. Rupam Barman, Currently Professor of Mathematics, IIT Guwahati. - Bachelor of Science (B. Sc.) with Mathematics honours from Bajali College, Pathsala under Gauhati University, Assam (2005-2008).
- Higher Secondary (H.S) in Science stream from Bajali College, Pathsala under A.H.S.E.C, Assam (2003-2005).
- H.S.L.C (Matriculation) from Bajali H.S. School, Pathsala under S.E.B.A, Assam (-2003).
In addition, I have received the following fellowships/awards/recognations from different agengies:
- INSPIRE Fellowship from DST, Govt. of India to pursue Ph.D. for securing 1st class 1st position in M.Sc. in Mathematics.
Duration of the fellowship 2011-2016 (availed only one year).
- UGC-CSIR Junior Research Fellowship (JRF+LS) in Mathematical Sciences, June 2010.
- Graduate Aptitude Test in Engineering (GATE) 2010 in Mathematics.
- UGC-CSIR Junior Research Fellowship (JRF+LS) in Mathematical Sciences, December 2009.
- Undergraduate Rank Holder Scholarship from UGC, India for securing overall university 1st class 1st position in B.Sc. in Mathematics. Duration of the fellowship 2008-2010.
I have also hold the following administration positions:
- Associate Dean, Academic Affairs (Post-Gratuate), Indian Institute of Information Technology
Guwahati from 4th April, 2022 to till date.
- Head of the Department, Science and Mathematics, Indian Institute of Information Technology Guwahati from 11th October, 2017 to 3rd April, 2022.
Research:
The broad areas of my research are Number Theory, Algebra, and Cryptography.
In particular, I am interested in algebraic varieties, hypergeometric functions, p-adic analysis, supercongruences,
Apéry-like numbers, modular forms, supercharacter theory, exponential sums, and permutation polynomials.
Projects
- Transformations and special values of Gaussian hypergeometric series; and their connections to supercongruences, Funded by DST-SERB under Extra Mural Research Funding (Individual Centric), 2018-2021.
- Hypergeometric series and (super)congruences for Apery-like numbers, Funded by National Board of Higher Mathematics (NBHM), Department of Atomic Energy, 2018-2021.
- Apery-like numbers, hypergeometric functions, and related supercongruences, Funded by DST-SERB under Mathematical Research Impact Centric Support (MATRICS), 2019-2022.
Ph.D. Students
- Shaik Azharuddin: Joined on 14th August, 2021.
Proposed work: Multiple hypergeometric series, algebraic curves, and related mathematics.
Present Position: UGC Junior Research Fellow. - Fahim Sayed: Joined on 24th August, 2020.
Proposed Work: Supercharacter theory of finite groups, exponential sums, and related mathematics.
Present Position: CSIR Junior Research Fellow. - Arijit Jana: Joined on 17th July, 2017, Submitted on 26th May, 2021, Thesis Defended on 26 August, 2021.
Title of the thesis: Some conjectural supercongruences for truncated hypergeometric series.
Present Position: Post Doctoral Fellow, HRI, Prayagraj. - Arjun Singh Chetry: Joined in 14th January 2016, Submitted on 18th September, 2020, Thesis defended on 28th January, 2021.
Title of the thesis: Generalized Apery numbers, hypergeometric functions, and related supercongruences.
Present Position: Assistant Professor, Department of Mathematics, Digboi College, Assam.
Teaching:
I have taught the following courses at IIIT Guwahati:
- MA102 Mathematics II: Multivariable Calculus and Ordinary Differential Equations.
- MA205 Discrete Mathematics.
- CS401 Number Theory in Cryptography.
- MA203 Mathematics III: Probability and Stochastic Processes.
- MA204 Mathematics IV: Complex Analysis and Partial Differential Equation.
- MA305 Optimization Techniques.
Publications:
Journals
- F. Sayed and Gautam Kalita, On a supercharacter analog of of nilpotent group, Under review.
- Gautam Kalita, Twisted Kloosterman sums and Gaussian hypergeometric series, Under review.
- F. Sayed and Gautam Kalita, Moments of mixed Kloosterman sums, supercharacters, and elliptic curves, Under review.
- A. S. Chetry and Gautam Kalita, Lauricella hypregometric series F_B^(n) over finite fields, Under review.
- F. Sayed and Gautam Kalita, Moments of Kloosterman sums, supercharacters, and elliptic curves, Indian Journal of Pure and Applied Mathematics (SCI Expanded), Accepted for publication.
- A. Jana and Gautam Kalita, Supercongruences motivated by some generalized VanHamme congruences, Res. Number Theory (Scopus), Accepted for publication.
- F. Sayed and Gautam Kalita, Eighth power moment of Kloosterman sum, supercharcaters, and elliptic curves, The Ramanujan J. (SCI Expanded), https://doi.org/10.1007/s11139-021-00415- w (2021).
- A. S. Chetry and Gautam Kalita, Lauricella hypregometric series F_A^(n) over finite fields, The Ramanujan J. (SCI Expanded), Accepted for publication.
- A. Jana and Gautam Kalita, On some conjectural supercongruences on sums involving certain rising factorials, Results in Mathematics (SCI Expanded) 76, Article 155, pp. 10 (2021).
- Gautam Kalita and A. Jana, On some supercongruence conjectures for truncated hypergeometric series, Indian Journal of Pure and Applied Mathematics (SCI Expanded) 52, 168--192 (2021) (2021).
- Gautam Kalita and A. Jana, Certain character sums, Gaussian hypergeometric series, and their connections to algebraic curves, Finite Fields Appl. (SCI Expanded) 72 (2021), https://doi.org/10.1016/ j.ffa.2021.101832..
- A. S. Chetry, A. Jana, and Gautam Kalita, Proof of a supercongruence conjecture of Bing He, Res. Number Theory (Scopus) 7, Article 21, pp. 8 (2021).
- Gautam Kalita, Another proof of a supercongruence conjecture of Z.-W. Sun, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences (SCI Expanded) 91 (2), 283--287 (2021).
- A. Jana and Gautam Kalita, Proof of some conjectural supercongruences of Guo and Schlosser, The Ramanujan Journal (SCI Expanded) 54, 649--658 (2021).
- A. Jana and Gautam Kalita, Supercongruences for sums involving fourth power of some rising factorials, Proceedings: Mathematical Sciences (SCI Expanded) 130, Art. 59, 2020.
- A. S. Chetry and Gautam Kalita, On a general VanHamme-type supercongruence, Journal of the Ramanujan Mathematical Society (SCI Expanded) 35 (4), 1--9, 2020.
- A. Jana and Gautam Kalita, Supercongruences for sums involving rising factorial (1/l)_k^3, Integral Transforms and Special Functions (SCI Expanded) 30 (9), 683--692, 2019.
- Gautam Kalita and A. S. Chetry, On some supercongruences concerning truncated hypergeometric series, Proceedings of the American Mathematical Society (SCI Expanded) 147 (2), 533--546, 2019.
- A. S. Chetry and Gautam Kalita, More supercongruences for generalized Apéry number, Journal of Combinatorics and Number Theory 10 (3), 169--181, 2019.
- Gautam Kalita, Values of Gaussian hypergeometric series and their connections to algebraic curves, International Journal of Number Theory (SCI Expanded) 14 (1), 1--18, 2018.
- Gautam Kalita, Beukers-like supercongruences for generalized Apéry numbers, The Ramanujan Journal (SCI Expanded) 47 (3), 501--508, 2018.
- Gautam Kalita and A. S. Chetry, Congruences for generalized Apéry numbers and Gaussian hypergeometric series, Research in Number Theory (SCOPUS) 3:5, 2017.
- R. Barman and Gautam Kalita, Hyperelliptic curves over Fq and Gaussian hypergeometric series, Journal of the Ramanujan Mathematical Society (SCI Expanded) 30 (3), 331--348, 2015.
- R. Barman, Gautam Kalita, and N. Saikia, Hyperelliptic curves and values of Gaussian hypergeometric series, Archiv der Mathematik (Basel) (SCI Expanded) 102 (4), 345--355, 2014.
- R. Barman and Gautam Kalita, Hypergeometric functions over Fq and traces of Frobenius for elliptic curves, Proceedings of the American Mathematical Society (SCI Expanded) 141 (10), 3403--3410, 2013.
- R. Barman and Gautam Kalita, Elliptic Curves and Special Values of Gaussian hypergeometric series, Journal of Number Theory (SCI Expanded) 133 (9), 3099--3111, 2013.
- R. Barman and Gautam Kalita, On the polynomial equation x^d + ax + b = 0 and Gaussian hypergeometric series, International Journal of Number Theory (SCI Expanded) 9 (7), 1753--1763, 2013.
- R. Barman and Gautam Kalita, Certain values of Gaussian hypergeometric series and a family of algebraic curves, International Journal of Number Theory (SCI Expanded) 8 (4), 945--961, 2012.
- R. Barman and Gautam Kalita, Hypergeometric functions and a family of algebraic curves, The Ramanujan Journal (SCI Expanded) 28 (2), 175--185, 2012.
Conferences
- Certain transformation formulas for Gaussian hypergeometric series, Proceedings of 10th International Conference of IMBIC on Mathematical Sciences for
Advancement of Science and Technology, Institute for Mathematics, Bioinformatics, Information Technology and Computer Science, Kolkata 700091, West Bengal,
India, December 21--23, 2016.
Reviewing work
I have been serving as a Reviewer for
- Mathematical Reviews, published by the American Mathematical Society, since 2017.
- Zentralblatt MATH, published by the European Mathematical Society, the Heidelberg Academy of Sciences and Humanities, and FIZ Karlsruhe, since 2021.
I have been also serving as a Referee of research articles for the following journals:
- International Journal of Number Theory (World Scientific).
- Proceedings of the National Academy of Sciences, India Section A: Physical Sciences (Springer).
- Journal of Mathematical analysis and Applications (Elsevier).
- Journal of Symbolic Computation (Elsevier).
- Proceedings of the Americal Mathematical Society.
- Research in the Mathematical Sciences (Springer).
- Bullitin of the Australian Mathematical Society.
Last Updated On 31st May, 2022
Dr. Gautam Kalita
Associate Professor of Mathematics.
PhD (Tezpur University).
Email:
gautam.kalita@iiitg.ac.in