My research lies primarily in the realm of group theory and topological dynamics, with an additional interest in theoretical and formal problems in cognitive science.
Group theory: growth of groups, self-similar groups, automaton groups, groups of intermediate growth, topological full groups, groups of bounded type, iterated monodromy groups
Dynamical systems: étale groupoids, Cantor dynamics, AF-by-discrete groupoids, Bratteli diagrams, symbolic dynamics, Schreier dynamics, expansivity, orbit equivalence
Probability: random walks on groups and Schreier graphs
Cognitive science: consciousness, self-reference, metacognition, observer position, structural organization of experience, mathematical formalization
[1] Zheng Kuang, Growth of groups with incompressible elements I, Groups Geom. Dyn. (2026), DOI 10.4171/GGD/954, preliminary version: arXiv:2402.16238
[4] (Book preprint) Zheng Kuang, Structural Compatibility between Third-Order Consciousness and AF-by-Discrete, 2026, (English translation) TBA; Source of truth: zenodo.22202015 (bilingual Chinese-English research monograph)
[3] Zheng Kuang, Near full groups of bounded type, II, 2026, arXiv:2607.26572
[2] Zheng Kuang, Near full groups of bounded type: full group completion, 2026, arXiv:2607.25729
[1] Zheng Kuang, Growth of finitely generated subgroups of the topological full groups of inverse semigroups of bounded type, 09.2024, arXiv:2409.19491
supplementary to my research at TAMU
Growth of groups: beamer
A group possibly with exponential growth: pdf (Last update: Dec 22, 2021)
Notes on Poincaré metrics: pdf
Some clarifications on groups with purely non-Hausdorff singularities: pdf
Another example of using orbital graphs to find incompressible elements: pdf
Survey on intermediate growth: slides (presented to GSO on 9/21/2023)
Growth of groups with finitely many incompressible elements: slides, scripts recorded
Research Statement: pdf
Smale spaces and groups of intermediate growth: poster
Ph.D. defense: slides