Xujiang Tang
Undergraduate in Mathematics
Algebraic Topology, Finite Groups, Equivariant Homotopy Theory
Email: txj_262538@163.com
Website: txj2006.github.io
GitHub: github.com/TXJ2006
ORCID: 0009-0008-1127-6420
Research Profile
Early-stage researcher in pure mathematics, with current work centered on Quillen-type p-subgroup complexes, finite group topology, subgroup-complex homology, and equivariant homotopy-theoretic methods. I am especially interested in the interface between atom/crosscut models, centralizer and orbit-carrier geometry, group cohomology, classifying-space methods, and stable or proper equivariant homotopy theory.
Research Interests
- Algebraic topology and equivariant homotopy theory; subgroup complexes, classifying spaces, stable homotopy-theoretic structures, and geometric fixed point methods.
- Finite group theory; Quillen’s p-subgroup conjecture, elementary abelian p-subgroups, centralizer structures, group cohomology, and FRUL-WOS sphere methods.
- Formalized mathematics; Lean, Mathlib, proof engineering, and long-term formalization of algebraic and topological arguments.
- Additional interests: machine learning theory, optimization, stochastic processes, and operator-theoretic methods.
Education
Yangtze University College of Arts and Sciences, Jingzhou, China
B.Sc. in Mathematics and Applied Mathematics, expected June 2027
- Selected coursework: mathematical analysis, linear algebra, probability and statistics, differential equations, computational modeling, optimization theory, numerical computation, data structures, Python, R, and MATLAB.
- Selected marks: Optimization Theory 97/100; Numerical Computation Methods 96/100.
Great Bay University, China
Visiting Student, 2025-present
- Research in theoretical mathematics and machine learning theory.
Publications and Manuscripts
Submitted Manuscripts and Preprints
X. Tang. “Centralizer Energy, FRUL-WOS Spheres, and Quillen’s p-Subgroup Conjecture.” Submitted to Annals of Mathematics.
- Develops an atom/crosscut-complex approach to Quillen-type p-subgroup complexes using centralizer-energy descent, orbit-carrier Mayer-Vietoris methods, controlled-flat certificates, class-2 commutator-polar data, and protected cross-polytope obstructions.
X. Tang. “Geometric Fixed Point Tomography and Spoke Bokstedt Periodicity.” Submitted to Algebraic & Geometric Topology.
X. Tang and C. Fan. “Out-of-Distribution Generalization Error Bounds for Successful Prediction of Deep Autoregressive Algorithms.” Submitted to NeurIPS 2026.
X. Tang. “Quartic Difficulty: Assessing the Learnability of Unsupervised Learning Algorithms.” Submitted to COLT.
Published and Accepted Papers
Q. Li and X. Tang. “HKGEduRec: A Knowledge Graph-Enhanced Dynamic Hybrid Framework for Educational Recommendation with Cold-Start Mitigation.” IEEE ICMEIM 2025, EI-indexed.
X. Tang and Q. Li. “Logical Gene Encoding: A Bio-Inspired Approach for Energy-Efficient Automated Reasoning.” IEIT 2025, EI-indexed. DOI: 10.2991/978-94-6463-803-5_81.
Q. Li and X. Tang. “Robust Optimal Reinsurance and Investment with Inflation Risk: A Game-Theoretic Approach and Explicit Solutions.” AIMS Mathematics, accepted, 2025.
Selected Research Experience
Finite Group Theory and Quillen’s p-Subgroup Conjecture
Independent research, 2025-present
- Developed a subgroup-complex approach involving atom complexes, centralizer energy, FRUL-WOS spheres, orbit carriers, and controlled fillings.
- Current focus: homological and equivariant-topological methods for Quillen-type problems and related subgroup-complex obstructions.
Algebraic Topology and Equivariant Homotopy Theory
Independent research, 2025-present
- Research on geometric fixed point tomography, spoke Bokstedt periodicity, and stable homotopy-theoretic structures.
Formal Proof and Lean
Formalized mathematics, 2026-present
- Study of Lean, Mathlib, proof engineering, and long-term formalization of advanced arguments in algebra and topology.
Theoretical Machine Learning and Optimization
Research projects, 2024-present
- Work on learnability, generalization guarantees, out-of-distribution prediction, and optimization-theoretic aspects of learning algorithms.
Additional Applied Research
Mathematical modeling, spatial omics, long-sequence data, and quantitative finance, 2023-present
- Epidemic prevention and population-mobility modeling in Jingzhou; spatial omics data processing; epilepsy-related long-sequence modeling using Koopman/operator-theoretic methods; stochastic-process models and robust financial decision problems.
Visiting Position and Training
- Zhejiang University Lean Formalization Summer School, 2026. Formal proof, Lean, Mathlib, and computer-assisted theorem proving.
- Neural Networks and Python Implementation, short winter training with Prof. Mark Vogelsberger. Grade: A.
Honors, Competitions, and Activities
- Kaggle Silver Medal, Jigsaw Toxic Comment Classification Challenge.
- Regional Gold Medal, WorldQuant International Quant Championship.
- Third Prize, UCAS Graduate AI Forum.
- Mathematical Modeling Competition, Hua Zhong Cup; National College Students Statistical Modeling Competition; multiple national second prizes in mathematical modeling competitions.
- Reviewer, ICLR 2026 Workshop.
Professional Experience
- Peking University Open-Source LLM Group, Jun.-Aug. 2024. Contributed to LLM deployment and retrieval-augmented generation systems.
- Deloitte, Jul.-Sep. 2024. Consulting workflows, teamwork, and communication.
- Guolian Securities, Jul.-Sep. 2024. Statistical methods in securities research and quantitative workflows.
Selected Academic Contacts and Collaborations
- William Redman, Johns Hopkins University.
- Ziyue Qiao, Great Bay University.
Skills
Mathematics: algebraic topology, finite group theory, homotopy theory, representation theory, optimization, numerical analysis, stochastic processes, differential equations, causal inference, and statistical modeling.
Formal proof and programming: Lean, Mathlib, Python, PyTorch, NumPy, Pandas, MATLAB, R, C++, LaTeX, Git/GitHub, and Linux.
Languages: Mandarin Chinese; English.