Zhufeng Yao

Interests:

I study discrete subgroups of Lie groups. Recently, I’ve been working on the dynamical aspects of Θ-positive representations (see this paper by Guichard–Wienhard), focusing on the associated entropy, geodesic currents and fractal properties of their limit maps and limit sets. I am also interested in the geometry of Anosov subgroups.

I am also a fan of Touhou Project and Dota 2.

My point of view on artificial intelligence:

I am strongly against the abuse of AI, like plagiarism, hiding usage, and posting AI-generated manuscripts without proper organization, writing and review. I am also strongly against the companies and media that are hyping for advertising, and thus misrepresenting the nature of mathematical work.

On the other hand, I believe AI itself will hugely help the development of mathematics as long as it is used properly.  At present, as a tool, it greatly improves the efficiency in discovering connections between known mathematical objects, and makes mathematics learning more accessible to humans. I use it to discuss math, conduct literature reviews, and do grammar, vocabulary, and proof checks. I keep learning to use it more properly and ensure transparency in my AI usage. I label the papers where AI initiated decisive mathematical observations as "AI-insight", and those where AI helped to develop, check, or present proofs based on central ideas provided by the authors as "AI-assisted". These labels cannot describe contributions perfectly in individual cases. In related papers, the contributions made by AI will be comprehensively recorded. 

Personally, I do not attribute ideas generated by AI to myself. Moreover, these ideas shall also be properly credited to the math precedents that might have brought AI's attention there, and I will list them after a literature review. For AI-insight papers, I consider my personal role as verifying, formalizing, and understanding the work and taking responsibility under the existing system. However, this stance applies only to myself; I deeply respect and credit the rigorous mathematical efforts and contributions made by my co-authors.

 I believe this is an age of mathematical revolution, though with many difficulties to be resolved. I learn and reflect to work in alignment with pursuing knowledge.

Preprints and Publications:

1. Critical exponent rigidity for Θ-positive representations, preprint, (arXiv:2505.17559 [math.DG]), to appear on Transactions of American Mathematical Society.

2. Entropy rigidity for maximal representations, preprint, (arxiv: 2601.03585 [math.DG]).

3. Hausdorff Dimension of Anosov Subgroups' Limit Sets with Special Self-Affine Complexity, preprint, (arXiv:2604.18365 [math.DG]).

4. Geometric finiteness in paracomplex hyperbolic spaces,  joint with Tianqi Wang and Tengren Zhang, preprint, (arXiv:2609.07628 [math.DG]).

5. Non-Hitchin Borel Anosov representations from surface groups to SL(3k, R), joint with Junming Zhang, preprint, (arXiv:2609.12809 [math.GT]). AI-insight.