报告人：孔诗磊（德国比勒菲尔德大学）

日期：2020年12月14日、12月17日、12月21日、12月24日、12月28日、12月31日

时间：上午10:00开始

地点：数统学院 LD302

摘要：The notion of hyperbolic graphs was invented by M. Gromov in 1980s for the study of geometric group theory. Without reference to any group structure, there are also interesting hyperbolic graphs arising from various subjects, such as contractive iterated function systems in fractal geometry, generalized dyadic cubes in harmonic analysis, and successive partitions on compact metrizable spaces. In each of these cases, the object considered is identified with the boundary of the graph, topologically or H\"older equivalently. In this series of talks, we introduce a key class of hyperbolic graphs, called {\it expansive hyperbolic graphs}, to capture the common properties essentially used in previous study. By using this class, we investigate the relation of hyperbolic graphs to the boundaries, the embeddings of hyperbolic boundaries, as well as the discrete potential theory of random walks on such graphs. These are based on some joint works with Ka-Sing Lau, Xiang-Yang Wang and Ting-Kam Leonard Wong.

具体课程内容见附件。

简介：孔诗磊，香港中文大学博士，现为德国比勒菲尔德大学（University of Bielefeld）博士后，研究方向为分形几何；已在Advances in Mathematics 等著名杂志发表多篇文章。

参考文献：

[1] M. Gromov, Hyperbolic groups, Math. Sci. Res. Inst. Publ., vol.8, Springer-Verlag (1987), 75-263.

[2] W. Woess, Random Walks on Infinite Graphs and Groups. Cambridge University Press, Cambridge (2000).

[3] J. Heinonen,  Lectures on Analysis on Metric Spaces,  Springer, New York (2001).

[4] V. A. Kaimanovich, Random walks on Sierpinski graphs: Hyperbolicity and stochastic homogenization, Fractals in Graz 2001, Trends Math., Birkhäuser, Basel, (2003), 145-183.

[5] S.L. Kong, K.S. Lau and L.T.K. Wong, Random walks and induced Dirichlet forms on self-similar sets, Adv. Math. 320 (2017) 1099-1134.

[6] S.L. Kong, K.S. Lau and X.Y. Wang, Gromov hyperbolic graphs arising from iterations, preprint (2020).

[7] S.L. Kong, K.S. Lau, J. Luo and X.Y. Wang, Hyperbolic graphs induced by iterations and applications in fractals, preprint (2020).

联系人：罗军

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