报告题目：Tight polyhedral

报告学者：Gabriel Kevin Cunningham教授

报告者单位：Wentworth Institute of Technology&University of Massachusetts Boston

报告时间：2024年5月10日（周五）20:00-22:00

报告地点：北区四号教学楼213

报告摘要：It is possible to take the idea of a convex polyhedron and generalize it to a graph structure known as an abstract polyhedron. If there is a fixed p and q such that the faces are all p-cycles and the vertices all have degree q, then the polyhedron is said to be of type {p,q}. In this talk, I will explore the question of finding the smallest abstract polyhedra of each type {p,q}. First we will work completely combinatorially, solving a problem in graph theory. Later, we will define the symmetries of an abstract polyhedron and what it means for an abstract polyhedron to be regular. Then we will try to find small regular polyhedra of each type {p,q}, which is really just a problem in pure group theory. At the end, we will brieflydiscuss further generalizations of these problems.