GTA Seminar| Title: Classification of Edge-to-edge Monohedral Tilings of the Sphere
Speaker: Hoi Ping LUK (The Hong Kong University of Science & Technology)
Date: July 4th, 2024 at 11 a.m.
Room: F2.2 Polo II ECT, UTAD
Online: https://videoconf-colibri.zoom.us/j/93648996782)
Abstract: The studies on tilings of the sphere can be traced back to Plato (5 Platonic solids) and Archimedes (13 Archimedean solids). We study edge-to-edge monohedral tilings of the sphere. The classification of these tilings was initiated by D. Sommerville in 1923. The first major breakthrough was achieved by Y. Ueno and Y. Agaoka in 2002. A significant progress has seen been made. However, the remaining cases have been the most difficult to classify. They are also of the utmost importance because they give rise to the majority of the tilings. We have recently classified all of them and hence completed the whole classification celebrating the problem’s centenary. The process involved new techniques ranging from combinatorics, geometry, algebra and number theory. The full classification reveals the structural relations between different tilings. All the tilings can be categorised into 3 types: Platonic type, earth map type, and sporadic type. In this talk, we will give an overview of the classification and highlight how some of the tools can be applied to the studies of tilings of other classes. This is a joint work with Ho Man Cheung and Min Yan.
