Nam Hung Tran Nguyen

Introduction:  "What is a random surface?" was a plenary talk given by Scott Sheffield (Massachusetts Institute of Technology, USA) at International Congress of Mathematicians (ICM) 2022. This post will discuss about certain minor details that are simple and interesting regarding this talk.  1. The construction of the problem    Consider k identical regular triangles. We want to glue them in a way to make into a closed surface (i.e. a polyhedron whose faces are regular triangles). By double counting , the number of triangles times three equals the number of edges of the polyhedron times two, thus k  must be even  or k = 2n. If we consider the planar version of this problem (i.e. all triangles lie on a plane), the positions of the triangles are clear  and you may view these triangles as triangular bricks on the floor of your house. However, when these triangles are at arbitrary positions in the 3-dimensional space, the angle between two adjacent ...

I. Current 1. Reinhard Diestel (Universitat Hamburg)              Reinhard Diestel was born in 1959. He obtained a PhD from the University of Cambridge in 1986 and his doctoral advisor was Béla Bollobás. He is the author of the textbook "Graph Theory", which has more than 400 pages and was published by Springer. In this book, as he wrote in the Preface, " I have broken with the tradition of attempting to cover both theory and applications: this book offers an introduction to the theory of graphs as part of (pure) mathematics; it contains neither explicit algorithms nor 'real world' applications. ".         Currently, he holds the chair of discrete mathematics at the University of Hamburg. He is also the editor of Journal of Combinatorial Theory, Series B, which is a Q1 journal as shown  here . Some of his doctoral students, including Daniela Kuhn and Maya Stein, are now well-known mathematicians in the same area. The Diestel-Le...

   Introduction: We are familiar with the definition of a tree in graph theory. Meanwhile, in set theory, the term tree also refers to a (partially ordered) set that satisfies certain conditions. In this post, I will try to relate these two definitions of tree.  1. What is a tree in set theory?     Since a graph-theoretic tree is very familiar, I will start with a set-theoretic tree. First, the preliminaries will be recalled. A partial order   on a set S is a relation <= such that:     - a <= a for all a belonging to S (reflexive).     - If a, b are elements of S and a <= b, b <= a, then a = b (antisymmetric).     - If a, b, c are elements of S and a <= b, b <= c, then a <= c (transitive).     If a <= b and a is not equal to b, we might say that a is strictly smaller than b , denoted by a < b. If for any two different elements a, b of S, there is an element...