In Progress:

• Knot Invariants On Additivity of Crossing Number

• Reflection length function in affine George group

• From GKH to Incompressible Surface

• Exploring Cubic Skein Modules

• Extension of Plan's Thoerem

Preprints:

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

• "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

• "Independence Complexes of Circle Graphs" Bakshi R, Guo A, Ibarra D, Montoya-Vega G, Mukherjee S, Silvero M, Spreer J : https://arxiv.org/abs/2412.01125

• "On the notion of Khovanov A-adequacy" L. Buchanan, H. Guo, G. Montoya-Vega, Y. Rong, M. Silvero: https://arxiv.org/abs/2502.17637

• "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

Publications:

• "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)