YMSC Topology Seminar | Edge-to-Edge Tilings of the Sphere by Congruent Polygons

Abstract 

A central problem in tilings of compact surfaces is the classification of edge-to-edge tilings of the sphere by congruent polygons. It is easy to see that the polygon can only be triangle, quadrilateral, or pentagon. The classification of triangular tilings was started by Sommerville in 1924, and completed by Ueno and Agaoka in 2002.

In 2013, Gao, Shi and Yan classified edge-to-edge tilings of the sphere by 12 pentagons, which was the first classification beyond triangular tilings. Now we have completed the whole classification, i.e., quadrilateral and pentagonal tilings. The tilings are generally of two types: Platonic type and earth map type. There are also several sporadic quadrilateral tilings.

About the speaker

 Min YAN, Professor at Hong Kong University of Science and Technology. Research Interests：Integrable systems; Hopf algebra; geometric topology; combinatorics.

Homepage：

https://facultyprofiles.hkust.edu.hk/profiles.php?profile=min-yan-mamyan#proj