Explore the mathematical physics of dilute Bosons in two spatial dimensions through this 44-minute lecture from the Erwin Schrödinger International Institute. Examine repulsive potential interactions and discover the proof of the Lee-Huang-Yang formula in two dimensions as predicted by Mora and Castin in 2009. Investigate the excitation spectrum and free energy behavior in the thermodynamical limit while understanding key differences between two-dimensional and three-dimensional systems. Learn why hardcore potential calculations are significantly simpler in two dimensions compared to three dimensions through accessible mathematical proofs. Gain insights into quantum many-body systems and Bose-Einstein condensation from a rigorous mathematical physics perspective.