Welcome to Brundaban Sahu's Homepage

ବୃନ୍ଦାବନ ସାହୁ

Brundaban Sahu

Professor
School of Mathematical Sciences
National Institute of Science Education and Research

Ph.D., 2008, Harish-Chandra Research Institute
Thesis Advisor: Professor B. Ramakrishnan

M.Sc., 2001, Sambalpur University
B.Sc., 1999, Gangadhar Meher College

Contact Information:

School of Mathematical Sciences
NISER, Bhubaneswar
Via-Jatni, Khurdha
Odisha - 752 050, INDIA

Office: M213
Phone: +91 674 249 4098
Email: brundaban[DOT]sahu[AT]niser[DOT]ac[DOT]in
brundaban[DOT]sahu[AT]gmail[DOT]com

@ICTP, September 2014 (Thanks to Pavel Snurnitsyn for the picture)

Research Interests:

Number Theory, Modular Forms, Jacobi Forms, Representations of Numbers by Quadratic Forms

Curriculum Vitae:

sahu-curriculum.pdf

Publications and Preprints:

Shivansh Pandey and Brundaban Sahu, Nonvanishing of L-functions and Poincare series for Jacobi forms of matrix index

B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, On the number of representations of certain quadratic forms of sixteen variables II

Shivansh Pandey and Brundaban Sahu, Representation of a natural number as sum of odd number of squares and convolution sums of divisor functions

Abhash Kumar Jha, Shivansh Pandey and Brundaban Sahu, L-function associated to Jacobi forms of half-integral weight and a converse theorem,

Journal of Mathematical Analysis and Applications, 534 (2024), no. 1, paper number. 128041

B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, Explicit evaluation of triple convolution sums of the divisor functio

International Journal Number Theory, 20 (2024), 4, 1073-1098

B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, A simple extension of Ramanujan-Serre derivative map and some applications

The Ramanujan Journal, 61 (2023), 1379-1410

B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, Representations of squares by certain diagonal quadratic forms in odd number of variables

Rocky Mountain Journal of Mathematics, 53 (2023), no. 4, 1219-1244

Shivansh Pandey and Brundaban Sahu, Nonvanishing of kernel functions and Poincare series for Jacobi forms,

Journal of Mathematical Analysis and Applications, 515 (2022), no. 2, paper number. 126455

B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, On the number of representations of a natural number by certain quaternary quadratic forms,

Modular Forms and Related Topics in Number Theory, Springer Proceedings in Mathematics and Statistics, vol 340, pp: 173-198, 2020

Moni Kumari and Brundaban Sahu, Rankin-Cohen type operators for Hilbert-Jacobi forms,

Modular Forms and Related Topics in Number Theory, Springer Proceedings in Mathematics and Statistics, vol 340, pp: 143-156, 2020

Abhash Kumar Jha and Brundaban Sahu, Rankin-Cohen brackets on Jacobi forms of several variables and special values of certain Dirichlet series,

International Journal Number Theory (15), 2019, no-5, 925-933

B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, On the number of representations by certain quadratic forms in 8 variables,

Automorphic Forms and Related Topics, 215-224, Contemp. Math., Vol-732, American Mathematical Society, Providence, RI, 2019

Abhash Kumar Jha and Brundaban Sahu, Differential operators on Jacobi forms and special values of certain Dirichlet series,

Automorphic Forms and Related Topics, 91-99, Contemp. Math., Vol-732, American Mathematical Society, Providence, RI, 2019

Moni Kumari and Brundaban Sahu, Rankin-Cohen brackets on Hilbert modular forms and special values of certain Dirichlet series

Functiones et Approximatio Commentarii Mathematici, 58 (2018), 2, 257-268

B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, On the number of representations of certain quadratic forms and a formula for the Ramanujan Tau function,

Functiones et Approximatio Commentarii Mathematici, 58 (2018), 2, 233-244

B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, Representations of an integer by some quaternary and octonary quadratic forms,

In: Akbary, Amir, Gun, Sanoli (eds.) Geometry, Algebra, Number Theory and Their Information Technology Applications,

Springer Proceedings in Mathematics and Statistics, vol 251, pp: 383-409, 2018

B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, On the number of representations by certain octonary quadratic forms with coefficients 1, 2, 3, 4 and 6,

International Journal Number Theory, 14 (2018), 3, 751- 812

B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, On the representations of a positive integer by ceratin classes of quadratic forms in eight variables,

In: Andrews G., Garvan F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series,

Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham, pp 641-664, 2017

Abhash Kumar Jha and Brundaban Sahu, Rankin-Cohen brackets on Siegel modular forms and Special values of Certain Dirichlet series,

The Ramanujan Journal, 44 (2017), 1, 63-73

B. Ramakrishnan and Brundaban Sahu, Evaluation of convolution sums and some remarks on cusp forms of weight 4 and level 12,

Mathematical Journal of Okayama University, 59 (2017), 71-79

B. Ramakrishnan and Brundaban Sahu, On the number of representations of certain quadratic forms in 20 and 24 variables,

Functiones et Approximatio Commentarii Mathematici, 54 (2016), 2, 151-161

B. Ramakrishnan and Brundaban Sahu, Identities for the Ramanujan Tau function and certain convolution sum identities for the divisor functions,

Number Theory, RMS-Lecture Notes Series, No. 23, 2016, 63-75

Abhash Kumar Jha and Brundaban Sahu, Rankin-Cohen brackets on Jacobi Forms and the adjoint of some linear maps,

The Ramanujan Journal, 39 (2016), 3 , 533-544

R. Osburn, B. Sahu and A. Straub, Supercongruences for sporadic sequences,

Proceedings of the Edinburgh Mathematical Society (Series 2), 59 (2016), 2, 503-518

B. Ramakrishnan and Brundaban Sahu, On the number of representations of certain quadratic forms of sixteen variables,

International Journal of Number Theory, 10 (2014), 8, 1929-1937

R. Osburn and B. Sahu, A supercongruence for generalized Domb numbers,

Functiones et Approximatio Commentarii Mathematici, 48 (2013), 1, 29-36

B. Ramakrishnan and Brundaban Sahu, Evaluation of the convolution sums ∑_{l+15m=n} σ(l)σ(m) and ∑_{3l+5m=n}σ(l)σ(m) and an application,

International Journal Number Theory, 9 (2013), 3, 799-809

R. Osburn and B. Sahu, Supercongruences for Apéry-like numbers,

Advances in Applied Mathematics, 47 (2011), 631-638

R. Osburn and B. Sahu, Congruences via modular forms,

Proceedings of the American Mathematical Society, 139 (2011), 7, 2375-2381

B. Ramakrishnan and Brundaban Sahu, Rankin-Cohen Brackets and van der Pol-Type Identities for the Ramanujan's Tau Function,

arXiv:0711.3512v1

B. Ramakrishnan and Brundaban Sahu, Rankin's method and Jacobi forms of several variables,

Journal of the Australian Mathematical Society, 88 (2010), 1, 131-143

S. Gun, F. Luca, P. Rath, B. Sahu and R. Thangadurai, Distribution of Residues Modulo p,

Acta Arithmetica, 129 (2007), 325-333

B. Ramakrishnan and Brundaban Sahu, On the Fourier expansions of Jacobi forms of half integral weight,

International Journal of Mathematics and Mathematical Sciences, Vol 2006

S. Gun, B. Ramakrishnan, B. Sahu and R. Thangadurai, Distribution of quadratic non-residues which are not primitive roots,

Mathematica Bohemica, 130 (2005), 4, 387-396

Academic Visits/ Visiting Positions:

Visiting Faculty, IISER Berhampur (August-December, 2024)

BHU, Varanasi/ Harish-Chandra Research Institute (HRI), Prayagraj (February 10--15, 2020)

Harish-Chandra Research Institute (HRI), Prayagraj (January 1--6, 2020)

Indian Institute of Technology, Guwahati (November, 2019)

Visiting Faculty, IISER Berhampur (Januray-May, 2019)

Mahidol University International College, Bangkok (July, 2018)

University College Dublin (UCD). Dublin (June 5--10, 2017)

Harish-Chandra Research Institute (HRI), Allahabad (September 26- October 1, 2016)

Harish-Chandra Research Institute (HRI), Allahabad (June 29- July 9, 2015)

Harish-Chandra Research Institute (HRI), Allahabad (September 23- October 4, 2013)

Harish-Chandra Research Institute (HRI), Allahabad (December 9- 15, 2012)

Harish-Chandra Research Institute (HRI), Allahabad (July 9- 20, 2012)

Harish-Chandra Research Institute (HRI), Allahabad (December 12- 23, 2011)

University College Dublin (UCD), Dublin (July 9- 23, 2011)

Institut des Hautes Etudes Scientifiques (IHES), Paris (July 15- September 15, 2009)

Professional Positions:

Professor (July, 2022--), National Institute of Science Education and Research, Bhubaneswar

Associate Professor (July, 2017-June, 2022), National Institute of Science Education and Research, Bhubaneswar

Reader-F (July 2014-June, 2017), National Institute of Science Education and Research, Bhubaneswar

Assistant Professor (August 2010-June 2014), National Institute of Science Education and Research, Bhubaneswar

Postdoctoral Fellow (Science Foundation of Ireland), November 2008-October 2010, Advisor: Professor Robert Osburn, University College Dublin

Junior/ Senior Research Fellow (August 2002-October 2008), Harish-Chandra Reserach Institute, Allahabad

NBHM Junior Research Fellow (November 2001-July 2002), Indian Statistical Institute, Bangalore

Academic Administration:

Chairperson, SMS (July 2022--)

Member, Board of Studies - Mathematical Sciences, HBNI (2021--)

Member, Board of Studies - Mathematical Sciences, NIST Berhampur (2024--)

Member, PGCS SMS/ PGCI (2022-24)

Member, UGCS SMS/ UGCI (2022-24)

Chairman COVID Task Force, NISER (2021-22)

Member, PGCS SMS (2020-22)

Member COVID Task Force/ Quarantine Cordination Committee (2020-22)

Chief Warden, NISER (2018-20)

Member, UGCS SMS (2018-20)

Member, PGCS SMS (2016-18)

Member, PGCS SMS (2014-16)

Convenor PGCS-SMS (2013-14)

Member, Library Commitee, NISER (2012-20)

Member, UGCS SMS (2012-13)

Advising:

Mr. Abhash Kumar Jha, Ph.D. 2016 (Thesis: Adjoint of some linear maps constructed using Rankin-Cohen brackets and special values of certain Dirichlet series), Current Position: Assistant Professor, IIT BHU Varanasi (Previously NPDF at IISc Bengaluru, PDF at HRI, Prayagraj, Assistant Professor at BHU)

Ms. Moni Kumari, Ph.D. 2018 (Thesis: Rankin-Cohen type opearators and some properties of Fourier coefficients of modular forms), Current Position: Assistant Professor, IIT Jammu (Previously PDF at TIFR Mumbai/ Bar-Ilan University, Tel Aviv/ MPIM, Bonn, Assistant Professor, IIT Jodhpur)

Mr. Shivansh Pandey, Ph.D. 2024 (Thesis: Nonvanishing of L-functions and differential operators for Jacobi forms), Current Position: PDF at TIFR Mumbai

Ms. Sneha Chaubey, M. Sc. Thesis, 2012 (Title: The irrationality of zeta(3) and Apery numbers), Current Position: Assistant Professor, IIIT New Delhi, (Previously Ph.D Student at UIUC)

Mr. Ankush Goswami, M. Sc. Thesis, 2013 (Title: Some additive problems in number theory), Current Position: PDF University of Texas Rio Grande Valley (Previously Ph.D Student at U. Florida)

Mr. Priyaranjan Mallick (Project Fellow (2014-2017) under DST Project SR/FTP/MS-053/2012)

Mr. Sagar Srivastava, M. Sc. Thesis, 2016 (Title: Number of representations of integers by some special quadratic forms), Current Position: Graduate Student, TIFR Mumbai

Mr. Akash Jena, M.Sc. Thesis, 2017 (Title: The Kronecker-Weber Theorem and the Frobenius Density Theorem), Current Position: Graduate Student, Indiana University, Bloomington

Mr. Swaroop S. Hegde, M. Sc. Thesis 2020 (Title: Combinatorics and Representation Theory of Symmetric Groups), Current Position: Graduate Student, University of Georgia

Mr. Paresh Singh Arora, M.Sc. Thesis 2021 (Title: Rankin-Selberg method on modular forms and applications), Current Position: Graduate Student, Louisiana State University

Mr. Archisman Bhattacharjee, M.Sc. Thesis 2022 (Title: Quadratic forms and their universality), Current Position: Graduate Student, Louisiana State University

Mr. Ayanava Mandal, M.Sc. Thesis 2024 (Title: Homologocal algebra and computations in modular forms)

Ms. Raveena Ganash (Ph.D student, 2023--ongoing)

Mr. Arnab Mitra (Ph.D student, 2024--ongoing)

Mr. Ashim Mondal (Project Fellow (2023--) under SERB Project CRG/2022/000359)

Projects:

Core Research Grant (CRG/2022/000359)

Funding Organisation: SERB, Department of Science and Technology, Govt. of India.

Amount: Rs 19, 09, 600/-

Duration: 2023-2026 (3 Years)

MATRICS (MTR/2017/000228)

Funding Organisation: SERB, Department of Science and Technology, Govt. of India.

Amount: Rs 6, 60, 000/

Duration: 2018-2021 (3 Years)

Modular Forms and Supercongruences (SR/FTP/MS-053/2012)

Funding Organisation: Department of Science and Technology, Govt. of India.

Amount: Rs 12, 24, 000/

Duration: 2014-2017 (3 Years)

Courses

MA706: Groups and Rings, Spring 2025

M101: Mathematics I, Fall 2024

MTH 601: Algebra I (Graduate), Fall 2024 (IISER, Berhampur)

M402: Representations of Finite Groups, Spring 2024

MA601: Algebra I (Graduate), Fall 2023

M463: Finite Fields, Spring 2023

M305/MA703: Number Theory, Fall 2022

MA605: Topology I (Graduate), Spring 2022

M463: Finite Fields, Fall 2021

M308: Complex Analysis, Spring 2021

M403: Commutative Algebra, Fall 2020

M553: Classical Groups, Spring 2020

MA601: Algebra I (Graduate), Fall 2019

M101: Mathematics I, Summer 2019

MTH302: Rings and Modules, Spring 2019 (IISER, Berhampur)

M402: Representations of Finite Groups, Spring 2019

M463: Finite Fields, Fall 2018

M102: Mathematics II, Summer 2018

M402: Representations of Finite Groups, Spring 2018

M463: Finite Fields, Fall 2017

M205: Linear Algebra, Spring 2017

M101: Mathematics I, Fall 2016

M101: Mathematics I, Summer 2016

M458: Algebraic Number Theory, Spring 2016

M601: Algebra I (Graduate), Fall 2015

M560: Modular forms of one variable, Spring 2015

M302: Algebra III, Fall 2014

M307: Algebra IV, Spring 2014

M601: Algebra I (Graduate), Fall 2013

M307: Algebra IV, Spring 2013

M461: Commutative Algebra, Fall 2012

M601: Algebra I (Graduate), Fall 2012

M459: Algebraic Topology, Spring 2012

M601: Algebra I (Graduate), Fall 2011

M202: Algebra I, Fall 2011

ME601/ ME 801: Commutative Algebra, Spring 2011

M501: Topology, Fall 2010

MATH20160: Polynomial Ring and Group Theory, Spring 2009 (UCD)

Seminar:

NISER Mathematics Seminar

NISER Colloquium

Professional Member:

Ramanujan Mathematical Society

American Mathematical Society

Upcoming event(s):

International Conference on Analytic Number Theory (February 03-07, 2025), IISER Berhampur

National Conference on the Recent Developments in Mathematical Sciences (February 5-7, 2025), University of Hyderabad

33èmes Journées Arithmétiques (June 30-July 4, 2025), University of Luxembourg, Luxembourg

Organization of Recent Conferences/ Workshops:

Inter IISER-NISER Math Meet 2023 (September 29- October 1, 2023), NISER Bhubaneswar

Workshop on Number Theory (February 20-25, 2023), NISER Bhubaneswar

Lecture series on Transcendence on Commutative Algebraic Groups (December 9--15, 2019) by Professor M. Waldschmidt

Advanced Foundation School (AFS- III), (July 1--27, 2019), NISER, Bhubaneswar

Workshop on Number Theory (November 30--December 6, 2018), NISER, Bhubaneswar

School and Workshop on Modular Forms and Black Holes (January 5--14, 2017), NISER, Bhubaneswar

Discussion Meeting on Automorphic Forms (December 21-27, 2016), NISER, Bhubaneswar

Click here for some past events, with links to presentations.

Proceedings:

Springer Proceedings in Mathematics and Statistics - 340

Modular Forms and Related Topics in Number Theory

(Editors: B. Ramakrishnan, Bernhard Heim, Brundaban Sahu)

Link:

Click here for some usefull links.

Webpage of Avaneesh Krishna Sahu