Publications

Submitted for publication:

  1. Mark Hughes, Vishnu Jejjala, P Ramadevi, Pratik Roy, and Vivek Kumar Singh. Colored Jones polynomials and the volume conjecture. arXiv preprint arXiv:2502.18575, 2025.
  2. Mark Hughes, Seungwon Kim, and Maggie Miller. Branched covers of twist-roll spun knots. arXiv preprint arXiv:2402.11706, 2024.
  3. Mark Hughes. Knotted surfaces in 4-manifolds and their diagrams. Lectures from the 2024 Georgia Topology Summer School, 2024. [PDF]

Accepted or published:

  1. Hughes, Mark, Seungwon Kim, and Maggie Miller. Band diagrams of immersed surfaces in 4-manifolds. Algebraic & Geometric Topology 25(3): 1731-1791, 2025.
  2. Mark Hughes, Seungwon Kim, and Maggie Miller. Non-isotopic splitting spheres for a split link in S4. Proceedings of the London Mathematical Society, 130(4):e70038, 2025.
  3. Jessica Craven, Mark Hughes, Vishnu Jejjala, and Arjun Kar. Illuminating new and known relations between knot invariants. Machine Learning: Science and Technology, 5(4):045061, 2024.
  4. Mark Hughes, Seungwon Kim, and Maggie Miller. Knotted handlebodies in the 4-sphere and 5-ball. Journal of the European Mathematical Society, 2024.
  5. Jessica Craven, Mark Hughes, Vishnu Jejjala, and Arjun Kar. Learning knot invariants across dimensions. SciPost Physics, 14(2):021, 2023.
  6. Jessica Craven, Mark Hughes, Vishnu Jejjala, and Arjun Kar. (K)not machine learning. In Nankai Symposium on Mathematical Dialogues: In celebration of S.S.Chern’s 110th anniversary, 1 2022.
  7. Mark Hughes. Broken Lefschetz fibrations, branched coverings, and braided surfaces. Open Book Series, 5(1):155–184, 2022.
  8. Mark Hughes, Seungwon Kim, and Maggie Miller. Isotopies of surfaces in 4–manifolds via banded unlink diagrams. Geometry & Topology, 24(3):1519–1569, 2020.
  9. Mark Hughes and Seungwon Kim. Immersed Möbius bands in knot complements. Algebraic & Geometric Topology, 20(2):1059–1072, 2020.
  10. Mark Hughes. A neural network approach to predicting and computing knot invariants. Journal of Knot Theory and Its Ramifications, 29(03):2050005, 2020.
  11. Leslie Colton, Cory Glover, Mark Hughes, and Samantha Sandberg. A Reidemeister type theorem for petal diagrams of knots. Topology and its Applications, 267:106896, 2019.
  12. Mark Hughes. Braiding link cobordisms and non-ribbon surfaces. Algebraic & Geometric Topology, 15(6):3707–3729, 2016.
  13. Mark Hughes. A note on Khovanov–Rozansky sl2-homology and ordinary Khovanov homology. Journal of Knot Theory and its Ramifications, 23(12):1450057, 2014.
  14. Anar Akhmedov, Mark Hughes, and B Doug Park. Geography of simply connected non-spin symplectic 4-manifolds with positive signature. Pacific J. Math, 261(2):257–282, 2013.