In this talk, I describe two applications of algebraic topology to the physical layer of wireless transmissions. Algebraic topology is the study of invariants of shape using abstract algebra. Building upon the growing field of topological data analysis and topological signal processing, I show how distorted radio signals can be analyzed using this field of mathematics. I will present how topology helps with unsupervised automatic modulation classification and synchronization in a noisy environment. This talk is self-contained and background in topology is not assumed.