About me

Hi! I am Jian-Ci Xiao (萧建慈), who is currently an associate research fellow in the School of Mathematics at Nanjing University of Aeronautics and Astronautics. During 2022 and 2023, I was a postdoctoral fellow in the Department of Mathematics at the Chinese University of Hong Kong, collaborating with Professor De-Jun Feng. Before that, I was a PhD student in the School of Mathematical Sciences at Zhejiang University, supervised by Professor Huo-Jun Ruan.

Research Interests

My interests focus mainly on fractal sets’ geometric and topological properties and dimension theory. Some specific topics include the embedding problem of self-similar/self-affine sets, the interiors of self-similar sets and their sumsets or difference sets, homeomorphism criteria between carpet-like fractal sets, etc.

Publications and preprints

Preprints

1. Self-embedding similitudes of Bedford-McMullen carpets with dependent ratios, arXiv:2412.02123, submitted.
2. The connectedness of Sierpinski sponges with rotational and reflectional components and associated graph-directed systems (with Huo-Jun Ruan), arXiv:2204.09219, to appear in Math. Proc. Cambridge Philos. Soc.

Published

1. A self-similar set with non-locally connected components, J. Fractal Geom. 11 (2024), 389–395.
2. On a self-embedding problem for self-similar sets, Ergod. Th. & Dynam. Sys. 44 (2024), 3002–3011.
3. Estimates on the topological Hausdorff dimensions of fractal squares, Topology Appl. 355 (2024), 109003.
4. Connectedness and local cut points of generalized Sierpinski carpets (with Xin-Rong Dai, Jun Luo, Huo-Jun Ruan and Yang Wang), Asian. J. Math. 27 (2023), 529–570.
5. A note on the interior and dimensions of typical sumsets, Proc. Amer. Math. Soc. 151 (2023), 4799–4806.
6. On the existence of cut points of connected generalized Sierpinski carpets (with Huo-Jun Ruan and Yang Wang), Ann. Fenn. Math. 48 (2023), 229–254.
7. When does a Bedford-McMullen carpet have equal Hausdorff and topological Hausdorff dimensions (with Huo-Jun Ruan), Fractals 29 (2021), 2150194.
8. Fractal squares with finitely many connected components, Nonlinearity 34 (2021), 1817–1836.
9. Existence and box dimension of general recurrent fractal interpolation functions (with Huo-Jun Ruan and Bing Yang), Bull. Aust. Math. Soc. 103 (2021), 278–290.

Teaching

• Fall 2023, MATH1010, University Mathematics, Chinese University of Hong Kong.
• Fall 2022, MATH6081, Topics in Analysis I, Chinese University of Hong Kong.

Talks

1. Apr. 2024, On a self-embedding problem for self-similar sets, Chongqing University
2. Apr. 2024, On a self-embedding problem for self-similar sets, Workshop on Fractal Geometry, Zhejiang University
3. Sep. 2022, On the existence of cut points of connected generalized Sierpinski carpets, Workshop on Analysis and Probability, Chinese University of Hong Kong
4. Oct. 2021, Existence of general recurrent fractal interpolation functions, Yantai University
5. Apr. 2021, Connected components of fractal squares, Analysis Seminar, University of St Andrews

Contact information

• Email: jcxiao@nuaa.edu.cn
• Office: Building A17, Room 348, Nanjing University of Aeronautics and Astronautics, Nanjing, China