We will explore the interplay between combinatorics and coarse geometry in this talk. Specifically, I will explain a new combinatorial proof of the sharp Assoud—Nagata dimension upper bound proven by Le Donne—Rajala. With the same method one can also prove that volume noncollpased doubling metric measure space with polynomial volume growth has asymptotic dimension bounded by its polynomial growth order. This is joint work with Jing Yu. The purpose of this talk is to advertise this relatively less popular field of research. I will go through basic examples and make the talk very accessible.
