Abstract

Tiling of sphere by n-gons must have n = 3, 4, 5. The study of tilings of sphere by congruent triangles (n = 3) was started in 1922 and completed in 2002. Tilings of sphere by congruent pentagons (n = 5) is much more complicated. There are five possible edge lengths combinations: a²b²c, a³bc, a³b², a⁴b, a⁵. We have completed the classification for four combinations. The remaining is the almost equilateral combination a⁴b.

Triangles are rigid, and pentagons are flexible. We need to develop various techniques, some general and applicable to all pentagonal tilings, and some specific to particular edge combinations. Some of these techniques may lead to additional research topics.

The research is joint work with Yohji Akama of Tohoku University, Wang Erxiao of Zhejiang Normal University, My PhD student Lu Hoiping, and others in the Hong Kong University of Science and Technology.

About the Speaker

A native in Shanghai, Prof. Min Yan received BS from Fudan University and PhD from the University of Chicago, after selected among three other students of Fudan University to enroll in a program initiated by Shiing-Shen Chern for young Chinese math students to study in the United States.  He then held positions at Pennsylvania State University and the University of Michigan, before joining the Hong Kong University of Science and Technology in 1992.  Prof. Yan's research interests include integrable systems, Hopf algebra, geometric topology, and combinatorics.  Besides research papers of a broad scope, he has published a textbook in topology as well as one jointly in calculus.  He is a Professor in the Department of Mathematics and the Director of International Affairs in the School of Science.