1 Research Interests
A formalizable, computable, generalizable, classifiable, and bridgeable framework for mathematics, physics, and computer science grounded in higher category theory.
On this page you can learn about my
- Research Interests
- Education and Degrees
- Language Proficiency and Certificates
Here is my current research focus
- Research - 1 - A Topos-Theoretic Bridge for Holographic Entanglement Entropy - Preliminaries
Practical techniques for formalizing categorical constructions in proof assistants include leveraging inductive type systems to encode higher-dimensional structures and using homotopy type theory to capture equivalence relations between morphisms.
Intuitions from topological quantum field theories may inform the development of more robust generalizations of categorical composition, particularly in contexts where locality and functoriality are central.
Recent advances in computational category theory have enabled the implementation of automated reasoning tools for n-categories, facilitating the verification of complex coherence conditions in physical models.
Care must be taken when translating abstract categorical results to computational frameworks, as issues of decidability and computational complexity may arise for higher-dimensional structures.
Over-reliance on syntactic encodings of category theory can obscure geometric intuitions, highlighting the need for hybrid approaches that integrate formal syntax with semantic visualization.
Inconsistencies may emerge when combining foundational frameworks (e.g., ZFC vs. homotopy type theory) for categorical modeling, requiring careful attention to metatheoretic assumptions.
Common pitfalls in classifying categorical structures include misapplying equivalence criteria for higher morphisms and overlooking non-trivial coherence constraints in n-functorial compositions.
The integration of higher category theory with quantum circuit design has yielded promising results for classifying topological phases of matter, demonstrating practical utility of abstract formalisms.
Key milestones in this research direction include the formalization of 2-functorial quantum gates and the classification of braided monoidal structures in low-dimensional topological systems.
Completed work includes the development of a computational toolchain for verifying functoriality of quantum operations and the characterization of monoidal equivalences between circuit models.
A concrete illustration of these methods is the construction of a 3-category encoding the compositional structure of fault-tolerant quantum error correction protocols, where 3-morphisms represent error recovery strategies.
Propose a generalization of the Yoneda lemma to (∞,1)-categories that accounts for higher-dimensional natural transformations, and discuss its implications for classifying representable functors in physical contexts.
How might the theory of derivators be adapted to provide a more computationally tractable framework for modeling higher categorical structures in artificial intelligence systems?
A potential resolution involves using derivator-generated homotopy theories to bridge abstract categorical semantics with concrete computational models, enabling the transfer of coherence results to algorithmic implementations.
2 Research Interests
Higher category theory
- Symmetric monoidal \((\infty, n)\)-categories
- Grothendieck toposes
- Topos-theoretic bridging methods
- Extended TQFT
- Higher algebraic stacks / Higher geometry / Motivic homotopy theory
- Categorical logic
- Axiomatic cohesion & cohesive higher toposes
- Internal logic of higher toposes
- Homotopy type theory
Operator algebras
- von Neumann algebras
- Algebraic quantum field theory
- Conformal field theory
- Topological order
- Subfactor theory
Derived algebraic geometry
- Spectral algebraic geometry
- Condensed mathematics
- Arithmetic geometry
Algebraic topology
- Index theory
- Topological modular forms
- Quantum anomalies
Representation theory
- Chiral representation theory
- Quantum geometric representation theory
Holographic duality
- Higher categories in holographic duality
- HaPPY model
- Holographic entanglement entropy
- Quantum information in holographic duality
Applied category theory
- Quantum error correction
- Theoretical computer science
- Theoretical physics
- Math of machine learning
- Math of computation
- Categorical quantum mechanics
- Categorical quantum information
- ZX-calculus
- Categorical symmetry
- Topos quantum theory
Artificial Intellegence
- Quantum artificial intellegence
- Topos in artificial intellegence
Theoretical Computer Science
- Categorical logic
- Topos theory
- Type theory
3 Education and Degrees
Aug 2025 – present
Gap-year self-study
Higher category theory • Operator algebras • Derived algebraic geometry • Extended TQFT • Holographic Entanglement Entropy
Jul 2025
Bachelor of Science in Physics
Tongji University, Shanghai, China
4 Language Proficiency and Certificates
Rong-Kang ZHANG | 張容康 (ちょう · ようこう) | Жункан Чжан
4.1 Overview
CEFR Six-Level Scale
A1 → A2 → B1 → B2 → C1 → C2 (Basic → Independent → Proficient)
Native Native speaker level
🇬🇧 English (C1) • English（C1）Advanced Fluent in academic/business contexts
🇷🇺 Russian (B1) • Русский（B1）Intermediate Travel & work-related conversations
🇯🇵 Japanese (B1) • 日本語（B1）Intermediate Daily conversation
Certificates: JLPT-N1
Elementary Slow-paced daily / basic communication
4.2 Japanese Certificates
5 Programming & Tools
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Programming Languages
- Python (NumPy / Pandas / Matplotlib / Scikit-learn / SciPy)
- C++ (Research-focused applications)
- Haskell / Idris (Theoretical exploration)
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Deep Learning Frameworks
- PyTorch (Sony AI Preferred)
- TensorFlow / Keras (Model Building & Training)
- Hugging Face Transformers & Datasets
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Data Processing
- SQL (Data Extraction & Manipulation)
- Apache Spark (Large-scale Data Processing)
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MLOps & Deployment
- Docker & Kubernetes (Containerization & Orchestration)
- MLflow (Experiment Tracking & Model Registry)
- AWS / GCP (Cloud Services for ML)
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Generative AI & Multimodal
- Diffusers (Stable Diffusion, etc.)
- OpenCV (Computer Vision)
- NLTK / SpaCy (Natural Language Processing)
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Mathematical Tools
- SymPy (Symbolic Mathematics)
- PyMC3 / Stan (Probabilistic Programming)
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Version Control & Collaboration
- Git & GitHub (Team Collaboration & Code Management)
- Quarto / Jupyter (Reproducible Research)
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Visualization
- Matplotlib, Seaborn, Plotly
- Tableau (Interactive Dashboard & Result Presentation)