abhash.mat | Indian Institute of Technology (BHU)

Dr. Abhash Kumar Jha

Assistant Professor

Department of Mathematical Sciences

Phone No(s): 8895229266

Email: abhash.mat@iitbhu.ac.in

Area of Interest: Number theory and automorphic forms, elliptic and Siegel modular forms, Jacobi forms

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Current position:
Assistant Professor, Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi: June 09, 2020 - present.

Previous positions:
Assistant Professor, Department of Mathematics, BHU, Varanasi, Jan 16 - June 08, 2020.
Post-doctoral fellow, Harish-Chandra Research Institute, Allahabad, May 2019 - Jan 15, 2020.
SERB-NPDF, IISc., Bangalore, (Postdoc Mentor: Prof. Soumya Das), May 2017 - April 2019.

Education:
Ph.D., NISER, Bhubaneswar (Thesis Advisor: Prof. Brundaban Sahu).
M.Sc., BHU, Varanasi.
B.Sc., U. P. College, Varanasi.

Taylor expansions of Hilbert-Jacobi forms (with Mohd. Shahvez Alam), submitted.
Construction of Hilbert-Jacobi cusp forms using Rankin-Cohen type operators (with Mohd. Shahvez Alam), submitted.
An asymptotic expansion of the constant term of certain automorphic function (with Babita, B. Maji and M. Pal), submitted.
An asymptotic expansion for a Lambert series associated to Siegel cusp forms of degree n (with Babita, B. Maji and M. Pal), submitted.
Fourier coefficients of Jacobi Poincare series and applications (with Animesh Sarkar), J. Math. Anal. Appl., accepted for publication.
An asymptotic expansion for a Lambert series associated to Siegel cusp forms (with Babita, A. Juyal, and B. Maji), Ramanujan Journal, 64(2024) no. 4, 1199-1212.
L- function associated to Jacobi forms of half-integral weight and a converse theorem (with S. Pandey and B. Sahu) J. Math. Anal. Appl., 534 (2024), no. 1, 128041.
Rankin-Cohen bracket of Jacobi forms and Jacobi Poincare series (with S. Pandey), Acta Arithmetica, 212 (2024), 115-132.
Asymptotics and sign patterns for coefficients in expansions of Habiro elements (with A. Goswami, B. Kim and R. Osburn), Mathematische Zeitschrift, 304 (2023), no. 4, paper no. 57.
Non-vanishing of Hermitian and Hermitian-Jacobi Poincare series (with P. Anamby), submitted.
Estimates for the shifted convolution sum involving Fourier coefficients of cusp forms of half-integral weight (with L. Vaishya), Funct. Approx. comment. Math. 68 (2023), no. 1, 7-18.
Some identities for the partition function (with A. Goswami and A. K. Singh), J. Math. Anal. Appl., 508(2022), no. 1, 125864.
Congruences for some partition functions (with A. Goswami), J. Ramanujan Math. Soc. 37, no.3 (2022) 241–256.
Estimates of shifted convolution sums involving Fourier coefficients of Hecke-Maass eigenforms (with L. Vaishya), Int. J. Number Theory, 17 (2021), no. 7, 1631-1643.
Determining Siegel modular forms of half-integral weight by their fundamental Fourier coefficients, Acta Arithmetica, 195 (2020), no. 3, 269-279.
Analytic properties of twisted real-analytic Hermitian Klingen type Eisenstein series and applications (with S. Das), Abh. Math. Semin. Univ. Hambg., 89 (2019), no. 2, 105-116.
Differential operators on Jacobi forms and special values of certain Dirichlet series (with B. Sahu), Automorphic forms and related topics, 91-99, Contemp. Math., 732, Amer. Math. Soc., Providence, RI, 2019.
On simultaneous non-vanishing of twisted L-function associated to newforms on Γ_0(N) (with A. Juyal and M. K. Pandey), Journal of the Ramanujan Mathematical Society, 34 (2019), no. 2, 245-252.
Rankin-Cohen brackets on Jacobi forms of several variables and special values of certain Dirichlet series (with B. Sahu), Int. J. Number Theory, 15 (2019), no. 5, 925-933.
Construction of cusp forms using Rankin-Cohen brackets (with A. Kumar), Analytic number theory, modular forms and q-hypergeometric series, 329-341, Springer Proc. Math. Stat., 221, Springer, Cham, 2017.
Rankin-Cohen brackets on Siegel modular forms and special values of certain Dirichlet series (with B. Sahu), Ramanujan Journal, 44 (2017), no. 1, 63 - 73.
Rankin-Cohen brackets on Jacobi forms and the adjoint of some linear maps (with B. Sahu), Ramanujan Journal, 39 (2016), no. 3, 533-544.

MA514: Analytic Number Theory (Odd Semester 2024-2025).
MA551 Mathematics (Odd Semester 2024-2025).
MA 111: Algebra (Even semester 2023-2024).
MA 515: Abstract Algebra (Even semester 2023-2024).
MA 311: Linear Algebra (Odd semester 2023-2024)
MA 111: Algebra (Even semester 2022-2023).
MA 515: Abstract Algebra (Even semester 2022-2023).
MA 311: Linear Algebra (Odd semester 2022-2023).
MA 416: Complex Analysis (Even semester 2021-2022).
CSE 504: Mathematics for Computer Science (Even semester 2021-2022).
MA 101: Engineering Mathematics - I (Odd semester 2021-2022).
CSO 204: Discrete Mathematics (Odd semester 2021-2022).
MA 102: Engineering Mathematics - II (Even semester 2020-2021).
MA 101: Engineering Mathematics - I (Odd semester 2020-2021).
CSO 204: Discrete Mathematics (Odd semester 2020-2021).
Number Theory (Even semester 2019-2020).
Multivariable Calculus (Even semester 2019-2020).

Seminars & Talks:

Differential Operators Acting on Jacobi Forms and Jacobi Poincare Series, 36th Automorphic Forms Workshop (May 20-24, 2024) Oklahoma State University, Stillwater, Oklahoma, USA.
L-functions associated to Jacobi forms, Workshop on Number theory (February 20-25, 2023) NISER Bhubaneswar, India.
Spaces of cusp forms spanned by eta quotients and applications, L- functions, circle method and applications (June 27-July 01, 2022), ICTS Bangalore, India.
Some identities for the partition function, 34th Automorphic Forms Workshop (March 17-19, 2022), Provo, Utah, USA.
Modular forms and associated L- functions, DST-CIMS, BHU (July 10, 2021).
Some identities for the partition function, Math Symposium, IISER Bhopal (March 25-26, 2021).
On the Fourier coefficients of modular forms, TIFR Mathematics Students' Seminar (Aug 04, 2020).
Non-vanishing of Fourier-Jacobi coefficients of Hermitian cusp form, Virtual Math Fest 2020 (July 20-26,2020).
Determining Siegel modular forms by their fundamental Fourier coefficients, (August 08, 2019), Postdoc seminar, HRI, Allahabad.
Fundamental Fourier coefficients of Siegel modular forms of half-integral weight, In-house symposium (March 28-29, 2019), IISc. Bangalore.
Fundamental Fourier coefficients of Siegel modular forms, Workshop on number theory (November 30-December 06, 2018), NISER Bhubaneswar, India.
Non-vanishing of the Fourier-Jacobi coefficients of modular forms, Workshop on modular forms (October 03-14, 2018) at KSOM Kozhikode, India.
Characteristic twist of certain Dirichlet series attached to modular form, Workshop on modular forms (February 22-24, 2018), KSOM Kozhikode, India.
Rankin-Cohen bracket of Jacobi forms and certain Dirichlet series, Discussion Meeting on Automorphic Forms (December 21-27, 2016), NISER Bhubaneswar, India.
Construction of certain Siegel cusp forms, Conference on Modular Forms (September 04, 2016), IISER Bhopal, India.
Construction of certain Siegel and Jacobi cusp forms, Building Bridges: 3rd EU/US Summer School & Workshop on Automorphic Forms and Related Topics (July 11-22, 2016), University of Sarajevo, Bosnia and Herzegovina.
Rankin-Cohen brackets on Siegel modular forms and special values of certain Dirichlet series, The 2016 Gainesville International Number Theory Conference (March 17-21, 2016), University of Florida, Gainesville, USA.
Rankin-Cohen brackets on Siegel modular forms of genus two and certain Dirichlet series, 30th Automorphic Forms Workshop (March 07-10, 2016) Wake Forest University, Winston-Salem, North Carolina, USA.
The Adjoint of some linear maps constructed using Rankin-Cohen brackets and special values of certain Dirichlet series, Thesis Colloquium, April 25, 2016, NISER, Bhubaneswar, India.
Construction of cusp forms using Rankin-Cohen brackets, Workshop on Automorphic Forms (February 10-16, 2016), Kerala School of Mathematics, Kozhikode, Kerala, India.
Adjoint of some linear maps on the space of Jacobi cusp forms, Mathematics Seminar, October 27, 2014, NISER, Bhubaneswar, India.
The Stone-Čech compactification, Mathematics Seminar, September 08, 2014, NISER, Bhubaneswar, India.
Special values of certain L-functions, April 21, 2014, NISER, Bhubaneswar, India.
Evaluation of convolution sums involving divisor functions using elementary methods and modular forms, State of the art seminar, February 19, 2013, NISER, Bhubaneswar, India.

Workshops & Conferences attended:

Nurturing Future Leadership Program (October 21-25, 2024) IIT(ISM) Dhanbad.
36th Automorphic Forms Workshop (May 20-24, 2024) Oklahoma State University, Stillwater, Oklahoma, USA.
NCM Workshop on Representations Theory of Real Groups and Automorphic Forms (October 02-07, 2023) HRI Prayagraj.
Workshop on Number theory (February 20-25, 2023) NISER Bhubaneswar, India.
NCM Workshop on Jacobi forms (December 12-24, 2022) IIT Guwahati.
Workshop on Analytic Number Theory (April 05 - 09, 2021) IIT Kanpur & ISI Kolkata.
Math Symposium (March 25 - 26, 2021), IISER Bhopal .
Virtual Math Fest 2020 (July 20 - 26, 2020), online .
International conference on "class group of number fields and related topics" (October 16 - 19, 2019), HRI Allahabad.
Algebraic and Analytic Aspects of Automorphic Forms(February 25 - March 07, 2019), ICTS, Bangalore.
International Conference in Number Theory (December 10 - 14, 2018), Kerala School of Mathematics, Kozhikode, India .
Workshop on number theory (November 30 - December 06, 2018), NISER Bhubaneswar, India.
Workshop on modular forms (October 03 - 14, 2018), Kerala School of Mathematics, Kozhikode, India.
Workshop on modular forms (February 12 - 24, 2018), Kerala School of Mathematics, Kozhikode, India.
ATM workshop in Analytic Number Theory (December 26 - 30, 2017), Indian Statistical Institute (ISI), Kolkata, India.
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.
Conference on Modular Forms (September 04, 2016), IISER Bhopal, India.
Number Theory Conference on "Arithmetic Geometry and L- functions" (August 17 - 21, 2016), Kerala School of Mathematics, Kozhikode, India.
Building Bridges: 3rd EU/US Summer School & Workshop on Automorphic Forms (July 11 - 22, 2016), University of Sarajevo, Bosnia and Herzegovina.
Advanced Instructional School in Analytic Theory of Algebraic Numbers (June 13 - July 02, 2016), School of Computer Applications, KIIT University, Bhubaneswar, India.
The 2016 Gainesville International Number Theory Conference (March 17 - 21, 2016), University of Florida, Gainesville, USA.
30th Automorphic Forms Workshop (March 07 - 10, 2016), Wake Forest University, Winston-Salem, North Carolina, USA.
Workshop on Automorphic Forms (February 10 - 16, 2016), Kerala School of Mathematics, Kozhikode, India.
ATM workshop in Analytic Number theory (October 19 - 24, 2015), The Institute of Mathematical Sciences (IMSc), Chennai.
Advanced Instructional School in Analytic Number Theory (June 01 - 20, 2015), School of Computer Applications, KIIT University, Bhubaneswar, India.
International conference on "Automorphic Forms and Applications" (February 13 - 14, 2015), Kerala School of Mathematics, Kozhikode, India.
Workshop on "Jacobi Forms and Modular forms of half-integral weight" (February 02 - 12, 2015), Kerala School of Mathematics, Kozhikode, India.
Winter School on "Modular Functions of One and Several Variables" (December 08 - 17, 2014), Goa University, Goa, India.
Advanced Instructional School in Algebraic Number Theory (July 07 - 26, 2014), Chennai Mathematical Institute, Chennai, India.
Discussion Meeting on Algebraic Curves (February 19 - March 05, 2014), Harish-Chandra Research Institute, Allahabad, India,
International CIMPA Research School and conference on "Fourier Analysis of Groups in Combinatorics" (November 18 - 30, 2013), NEHU Shillong, India,
Advanced Instructional School in Analytic Number Theory (June 10 - 29, 2013), School of Computer Applications, KIIT University, Bhubaneswar, India.
The Legacy of Srinivasa Ramanujan Conference (December 17 - 22, 2012), University of Delhi, Delhi, India.
School on Modular Forms (October 03 - 19, 2012), Kerala School of Mathematics, Kozhikode, India.
Annual Foundation School-III (July 06 - 31, 2012), Harish-Chandra Research Institute, Allahabad, India.
Annual Foundation School-II, (June 04 - 30, 2012), University of Pune, Pune, India.
Annual Foundation School-I (December 05 - 31, 2011), IISER, Pune, India.
Workshop on Differential Geometry (May 02 - 11, 2011), Banaras Hindu University, Varanasi, India.
ATM School in Geometric Complex Analysis (March 21 - April 02, 2011), University of Delhi, Delhi, India.
Advanced Training Programme in Functional Analysis (June 21 - July 03, 2009), Banaras Hindu University, Varanasi, India.

Academic visits:

NISER Bhubaneswar (Jan 05-12, 2024).
NISER Bhubaneswar (July 10-21, 2023).
NISER Bhubaneswar (May 16-July 15, 2022).
IIT Kanpur (September 17-25, 2021).
NISER Bhubaneswar (May 02, 2018 - June 01, 2018).
University of Florida, Gainesville USA (March 12 - 21, 2016).
Harish-Chandra Research Institute (HRI), Allahabad (July 01 - 25, 2015).
Harish-Chandra Research Institute (HRI), Allahabad (November 24 - December 06, 2014).

Warden, Prafulla C. Ray Hostel (May 31, 2024- present).
Associate Counsellor, Cultural Council of Gymkhana IIT(BHU), 2023- present.
Warden, Dr. S. Ramanujan Hostel (May 31, 2023- May 30, 2024).
Member, Institute Core Course and Monitoring Committee (2022 - present).
Member, Department Library Committee (2021 - present).
Convener, DUGC (2022 - 2023).
Convener, Department Timetable Committee (2022 - 2023).
Convener, Department Examination Committee (2022 - 2023).
Member, Department Space Committee (2022 - 2023).
Member, Department R & D Committee (2022- 2023).
Member, DUGC (2021 - 2022).
Member, Department Timetable Committee (2021 - 2022).
Member, Institute Teaching and Learning Cell (2021 - 2022).

SEED grant (2021), IIT(BHU) Varanasi, India.
Start-up Research Grant (2022-2024), Science and Engineering Research Board (SERB) India.
MATRICS (2022-2025), Science and Engineering Research Board (SERB) India.

Graduate Students:

Chanchal Malik: 2024-

Animesh Sarkar: 2021-

Md. Shahvez Alam: 2021-

Babita: 2024 (Thesis Title: Asymptotic behaviour of certain Lambert series associated to automorphic forms and moments of divisor function)

Postdoc(s):

Dr. Anup Kumar Singh (2023): NBHM postdoctoral Fellow, Current Position: Assistant Professor at University of Allahabad.