Research

1. Manohar Kumar, Joydip Mondal and Ramakrishna Nanduri; Componentwise linearity of powers of edge ideals of weighted oriented graphs, (2025), arxiv preprint, https://doi.org/10.48550/arXiv.2509.14637.

2. Manohar Kumar, and Kamalesh Saha; Componentwise linearity of support-two                    monomial ideals and Fröberg's Analogue, (2026) (submitted).

3. Manohar Kumar, and Emiliano Liwski; v-number of Lovász-Saks-Schrijver Ideals and   (parity) binomial edge ideals of graphs, (2026), arxiv preprint                                    https://doi.org/10.48550/arXiv.2608.01199.

4. Manohar Kumar, Joydip Mondal and Ramakrishna Nanduri; Homologicalshift ideals of weighted oriented graphs, (2026), arxiv preprint,  https://doi.org/10.48550/arXiv.2608.02170.

5. Truong Thi Hien, Manohar Kumar, Regularity of symbolic powers of complementary edge ideals, (2026), arxiv preprint, https://doi.org/10.48550/arXiv.2609.06903.

6. Manohar Kumar, N. C. Minh, and Thanh Vu; v-numbers of symbolic-ordinary discrepancy modules, (2026), arXiv preprint, https://doi.org/10.48550/arXiv.2609.22872.

7. Manav Batavia, Omkar Javadekar, Manohar Kumar; The Betti numbers and Golodness of numerical semigroup rings of Sally type, (2026), arXiv preprint, https://doi.org/10.48550/arXiv.2609.26752 .

1.Manohar Kumar and Dipak Kumar Pradhan; Monomial Ideals of VEW graphs, accepted in Journal of Algebra and Its application (2026). 

2. Manohar Kumar, Ramakrishna Nanduri and Kamalesh Saha; Componentwise linearity of edge ideals of weighted oriented graphs,  Journal of Algebraic Combinatorics, 61(3), Paper No. 33  (2025).

3. Manohar Kumar and Ramakrishna Nanduri; Regularity of symbolic and  ordinary powers of weighted oriented graphs and their upper bounds, Communications in Algebra, 53(6), 2565–2583  (2025).

4. Manohar Kumar, Ramakrishna Nanduri and Kamalesh Saha; The slope of the v-function and the Waldschmidt constant, Journal of Pure and Applied Algebra, 229(2), Paper No. 107881 (2025).

5. Manohar Kumar and Ramakrishna Nanduri; Regularity of powers of edge ideals of Cohen-Macaulay weighted oriented forests; Journal of Algebraic Combinatorics, 58(3), 867–893  (2023). 

• Master's Project Title: Primary Decomposition and Symbolic Powers of Ideals (Report).

• Master's Seminar: Gröbner Basis and Buchberger's Algorithm (Slide)

• Talk at ICTP (Video)