Dr. Sanjay Kumar Singh's Homepage

Academic Details

• Associate Professor (June 2022, Now), Mathematics, Indian Institute of Science Education and Research, Bhopal, India.
• Assistant Professor (Aug, 2015- June 2022), Mathematics, Indian Institute of Science Education and Research, Bhopal, India.
• Assistant Professor (Oct, 2013- Aug 2015), Institute of Mathematics Polish Academy of Sciences (IMPAN), Warsaw, Poland.
• Visiting Researcher (Jan, 2013- April 2013), Centro de Investigación en Matemáticas A.C., Mathematics Research Center, Mexico.
• Ph.D., Mathematics (June 2013), Tata Institute of Fundamental Research , Mumbai.

Research Interest

Publications:

1. Brill-Noether loci and generated torsionfree sheaves over nodal and cuspidal curves, (with Usha Bhosle), Manuscripta Mathematica, May 2013, Volume 141, Issue 1-2, Pages 241-271.
2. Hitchin pairs on an integral curve, (with Usha Bhosle and A.J. Parameswaran), Bulletin des Sciences Mathematiques, Volume 138, Issue 1, January-February 2014, Pages 41-62.
3. Diagonal property of the symmetric product of a smooth curve,(with Indranil Biswas), Comptes Rendus Mathematique, Volume 353, Issue 5, May 2015, Pages 445-448.
4. Weak point property and sections of Picard bundles on a compactified jacobian over a nodal curve, (Usha N. Bhosle), Proc. Indian Acad. Sci. Math. Sci. 126 (2016), No. 3, Pages 329-339.
5. Weight distribution of a subclass of Z₂-double cyclic codes (with Nupur Patanker) Finite Fields and Their Applications, Volume 57, May 2019, Pages 29-46.
6. A note on generalized derivations with multilinear polynomials in prime rings (with Dr. Shailesh Kumar Tiwari) Communications in Algebra 48 (2020), Vol No. 4, Pages 1770-1788.
7. Fourier-Mukai Transform on a compactified Jacobian (with Usha N. Bhosle) International Mathematics Research Notices(IMRN), Vol-2020, Issue-13, Pages 3991-4015, July 2020.
8. On Geometric Goppa Codes from Elementary Abelian p-Extensions of F_p^s(x)$ (with Nupur Patanker) Problems of Information Transmission Volume 56, Pages 253-269, Oct 2020.
9. Projective Poincare and Picard bundles for moduli spaces of vector bundles over nodal curves (with Usha N. Bhosle and Arusha C.) Bulletin des Sciences Mathematiques, Volume 166, February 2021.
10. Affine variety codes over a hyperelliptic curve (with N. Patanker) Problems of Information Transmission Volume 57, Pages 84-97 Jan 2021.
11. Second Order parallel tensor on generalized f.pk-space form and hypersurfaces of generalized f.pk-space form (with Punam Gupta) Differential Geometry-Dynamical Systems, Vol.23, 2021, pp. 59-66.
12. Vector Bundle satisfying the Point property (with Punam Gupta) Journal of Algebra and Application, Vol. 21, No. 04, 2250069 (2022).
13. Comprehensive quasi-Einstein spacetime with application to general relativity (with Punam Gupta) International Journal of Geometric Methods in Modern Physics, Vol. 19, No. 02, 2250016 (2022).
14. Clairaut semi-invariant submersion from Kahler manifold (with Punam Gupta) Afrika Matematika, 33, 8 (2022).
15. A Note on Parabolic Bundles on Nodal Curves (with C. Arusha) International Journal of Mathematics(IJM), VOl 33, No 03,2022.
16. Generalized g-derivations on prime rings (with Vincenzo De Filippis, Shailesh Kumar Tiwari) Accepted in Journal of Algebra and Application, Sept 2021.
17. Generalized Hamming weights of toric codes over hypersimplices and square-free affine evaluation codes (with N. Patanker) Accepted in Advances in Mathematics of Communications, 2021.
18. Quaternary affine variety codes over a Klein-like curve (with N. Patanker) Indian Journal of Pure and Applied Mathematics.
19. Generalization of trace codes to places of higher degree (with N. Patanker) Preprint.

Book Chapter/Survey Paper:

1. Clairaut Submersion, (with Punam Gupta), Book title: Advanced Topics of Topology, Intech Open.

Workshop/ School/ Conference conducted

• Discussion Meeting on Algebra and Geometry Department of Mathematics, IISER Bhopal (16-18 Aug 2023) Pictures.

• Annual Foundation Schools-II (AFS) at IIT, Patna (22 May-17 June 2023) .

• Teacher's Enrichment Workshops (TEW)on "Algebra \& Multivariate Calculus" at Dr. Harisingh Gour University, Sagar (8 Jan 2021 to 14 Feb 2021) INSA-NCM joint TEW 2021.

• National Conference on "Commutative Algebra and Algebraic Geometry (CAAG)" at IISER, Bhopal (02-06 July 2019).

• Annual Foundation Schools-I (AFS)" at IISER, Bhopal (03-29 December 2018).

• Science Academies' Lecture Workshop on "Geometry and Topology" at IISER, Bhopal (20-21 January 2018). Poster

Teaching

• Introduction to Differentiable Manifolds and Lie Groups (MTH 508/608) in 2nd Sem 2023/24.

• Introduction to Riemannian Geometry (MTH 513/613) in 1st Sem 2023/24.

• Complex Variables (MTH204) in 2nd Sem 2022/23.

• Introduction to Analytic Number Theory (MTH422/523) in 2nd Sem 2021/22.

• Commutative Algebra (MTH 518/618) in 1st Sem 2021/22.

• Algebra I (MTH 601, PhD 1st year course) in 2nd Sem 2020/21.

• Fields and Galois Theory (MTH 401) in 1st Sem 2020/21.

• Differential Geometry of Curves and Surfaces (MTH 406) in 2nd Sem 2019/20.

• Introduction to Groups and Symmetry (MTH 203) in 1st Sem 2019/20.

• Topology II (MTH 516/616) in 2nd Sem 2018/19.

• Commutative Algebra (MTH 618) in 1st Sem 2018/19.

• Introduction to Algebraic Topology (MTH 507) in 2nd Sem 2017/18.

• Commutative Algebra (MTH 518) in 1st Sem 2017/18.

• Differential Geometry of Curves and Surfaces (MTH 406) in 2nd Sem 2016/17.

• Multivariable Calculus and Differential Equations (MTH 201) in 1st Sem 2016/17.

• Introduction to Algebraic Geometry (MTH 517/617) in 2nd Sem 2015/16.

• Real Analysis II (MTH403) in 1st Sem 2015/16.

Reading course

• The Arithmetic of Elliptic and Hyperelliptic curves (2nd Sem, 2016/17) to Nupur Patenker (Int PhD student).

• Algebraic geometry (2st Sem, 2016/17) to Arusha C. (PhD student).

• Compact Riemann surfaces (1st Sem, 2016/17) to Arusha C. (PhD student).

• Algebraic geometry in coding theory and cryptography (1st Sem, 2016/17) to Nupur Patenker (Int PhD student).

Tutor

• Linear Algebra (MTH 102) in 2nd Sem 2017/18

• Probability and Statistics (MTH 201) in 2nd Sem 2015/16

• Complex Variables (MTH 204) in 2nd Sem 2018/19

BS MS project Students

• Mihir Manojkumar More (2022/23), (BS-MS 5th Year student, IISER Bhopal).

• Project Title: Some Topics in Tropical Geometry and Brill-Noether Theory.

• Amajit Sarma (2020/21), (Now a Ph.D. Student at Indiana University Bloomington, USA).

• Project Title: Some Topics in Algebraic Geometry over Finite Fields and Algebraic Coding Theory.

• Satvik Goswami (2018/19), (Now an Associate Solution Advisor in Risk Financial Advisory, Deloitte USI).

• Project Title: Applications of Algebraic Geometry to Coding Theory.

• Grishma G Palkar (2016/17), (Now a Ph.D. student in the Department of Mathematics, University of Pittsburgh (USA)).

• Project Title: Representations of the Fundamental group of compact Riemann surface and Vector Bundles.

PhD Students

• Priya

  (Thesis submission: ----.
• Thesis Title: ---.
• PhD Awarded: -----.

• C. Arusha

  (Thesis submission: Dec 2020).
• Thesis Title: SOME PROBLEMS ON VECTOR BUNDLES OVER NODAL CURVES.
• PhD Awarded: 31/03/2021.

• Nupur Patanker

  (Thesis submission: Nov 2020).
• Thesis Title: SOME PROBLEMS IN ALGEBRAIC CODING THEORY.
• PhD Awarded: 17/05/2021.

Post Doc

• Dr Pranjal Srivastava (PhD, IIT Gandhi Nagar) June 2023- .
• Dr Shailesh Kumar Tiwari (PhD, IIT Delhi) Sep 2018- Dec 2019 (now faculty in IIT Patna).

Summer Project Students

• Summer 2023

• Representation of Fundamental Groups of Topological Spaces: Shashank Gupta (BHU, Varanasi), Anuradha Yadav (IIT Ropar).
• Topics in Differentail Geometry Priyansh Shukla (BHU, Varanasi).
• Warped Product of Finsler Spaces: Abhishek Pandey (Central University of Punjab, Bathinda).

• Summer 2022

  • Astheno-Kahler Manifolds: Nidhi Yadav (Dr. Harisingh Gour Vishwavidyalaya Sagar).
  • An Introduction to Riemannian Geometry: Kirti Gupta (Dr. Harisingh Gour Central University Sagar).
  • An Introduction to Bundles and Holonomy Groups in Riemannian Geometry: Ashutosh Kumar Upadhyay (University of Allahabad, Prayagraj), Sonali priyadarsini Behara (ISI Bangalore).

• Summer 2021

  • Commutative Algebra: Shruti Priya(NIT Rourkela), Jaya Sharma (IIT Roorkee), Debashis Mohanty(Bhubaneswar), Rigen Tamang (IIT KGP), Vikrant Shukla(BHU), Aritra Roy (BHU)
  • Topics in Algebra: Mihir More (IISER Bhopal), Saumya Jain (IISERB), Pratikshya Dutta (Jorhat Institute of Science and Technology, Guwahati).
  • Connection in Geometry: Disha Adak (Jadhavpur University), Apratim Choudhury(NISER Bhubaneswar), Tarun Saxena(University of Allahabad)
  • Algebraic Coding Theory: Charu Garg (IIT Gandhi Nagar)

• Summer 2017

  • Finite Fields and Algebraic codes: Sarbindu Dolui (BHU), Subhadip Pal (Pondichery University)
  • Topics in Algebra Shayon Bhadra (Tezpur University)
  • Groups and Symmetry: Nishu Mittal (Delhi University)

Project

• DST SERB Project (Jan 2017-Jan 2020) (Closed)

• Project Title: Vector bundles satisfying the point property
• Project JRF:
  • 1. Duttatrey Nath Srivastava (MSc, CBS Mumbai,Now PhD student in School of Mathematics and Statistics, University of Canterbury, NEW ZEALAND).(Homepage)
  • 2. Anu Dhochak (MSc)
  • 3. Mayank Mishra (BS-MS, IISER, Bhopal)
  • 4. Sudipta Das (MSc, Jadavpur University)
  • 5. Raneeta Dutta (MSc, IIT Chennai)
  • 6. S. Maniknandan (PhD, HRI Allahabad)
  • 7. Bivas Khan (PhD, IIT Chennai)
  • 8. Pradip Das (PhD, HRI Allahabad)

Other Institute Duties

• Sports Faculty Adviser (2019)
• DUGC Convener (2018)
• DPGC Convener (2022)
• Institute Club Chairperson (2022)
• Associate Dean, Students' Affairs (ADOSA) (Oct 2022-now)
• Chairperson and Member of the Selection and Screening Committee of a few Non-Academic Positions

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