Aleksa Milojević of ETH Zurich presents a discrete mathematics seminar on random geometric graphs, the model Geo_d(n,p) formed by scattering n points uniformly on a d-dimensional sphere and joining nearby pairs so each edge occurs with probability p. He walks through a simplified version of recent work by Ma, Shen, and Xie that used this model to improve lower bounds on Ramsey numbers R(k,Ck), sharpening their quantitative analysis. The second half addresses a conjecture of Bubeck, Ding, Eldan, and Rácz on when Geo_d(n,p) converges in total variation distance to the classical Erdos-Renyi graph G(n,p), previously confirmed only at the extremes p=Theta(1) and p=Theta(1/n). Milojević outlines a proof covering the intermediate regime, joint work with Zach Hunter and Benny Sudakov. Delivered at the Institute for Advanced Study's Simonyi Classroom, the talk is aimed at researchers in probabilistic combinatorics and graph theory.