In Progress:

• Knot Invariants On Additivity of Crossing Number

• Reflection length function in affine George group

• From GKH to Incompressible Surface

• Extension of Plan's Thoerem

• Last Conjecture of Jones and Jaeger on Skein Module

Preprints:

• "On the Mapping Class Group of nontrivial $S^2$ fiber bundles" Guo H. : https://arxiv.org/abs/2509.16520

• Bakshi, R. P., Christiana, A., Guo, H., Ibarra, D., Kauffman, L. H., Montoya-Vega, G., Mukherjee, S., Przytycki, J. H., & Wang, X. (2025). Fundamentals of cubic skein modules. arXiv preprint arXiv:2511.10959. https://doi.org/10.48550/arXiv.2511.10959 

• "In Search of Homology for Quasigroups of Bol-Moufang Type" Christiana A, Clingenpeel B, Guo H, Oh J, Przytycki J, Zamojska-Dzienio A : https://arxiv.org/abs/2508.21268

• "The Montesinos-Nakanishi 3-move conjecture for links up to 20 crossings" R. Bakshi, B.  Burton, H. Guo, D. Ibarra, G. Montoya-Vega, S. Mukherjee, J. Przytycki: https://arxiv.org/abs/2502.17711

• "Low Dimensional Homology of the Yang-Baxter Operators Yielding the HOMFLYPT Polynomial" A. Christiana, B. Clingenpeel, H. Guo, J. Oh, J. Przytycki, X. Wang, H. Yun: https://arxiv.org/abs/2502.20659 (Accepted by  Homology, Homotopy and Applications)

Publications:

• "Independence complexes of circle graphs" R. Bakshi, H. Guo, D. Ibarra, G. Montoya-Vega, S. Mukherjee, M. Silvero, and J. Spreer,  arXiv:2412.01125, https://doi.org/10.1007/978-3-032-16202-1_17(Matrix Annals, 2025)

• "On the notion of Khovanov A-adequacy" L. Buchanan, H. Guo, G. Montoya-Vega, Y. Rong, and M. Silvero,arXiv:2502.17637, https://doi.org/10.1007/978-3-032-16202-1_19 (Matrix Annals, 2025)

• "The Generalized Kauffman-Harary Conjecture is True"  Bakshi R, Guo H, Montoya-Vega G, Mukherjee S, Przytycki  J: arxiv.org/abs/2301.02645 , https://msp.org/agt/2025/25-4/p06.xhtml/pc(Algebraic Geometry & Topology, 2025)

• "Using Fibonacci Numbers and Chebyshev Polynomials to Express Fox Coloring Groups  and Alexander-Burau-Fox Modules of Diagrams of Wheel Graphs"  Christiana A, Guo H, Przytycki J: https:/arxiv.org/abs/2310.19979 (Contemporary Mathematics, 2024)

• "Pairs of Disjoint Matchings and related classes of graphs". Guo H, Kaempen K, Mo Z,  Qunell S, Rogge J, Song C, Tserunyan A, Zomback J: https://arxiv.org/abs/2005.00671(Involve Journal, 2021)