The celebrated Langlands program is anchored in number theory, representation theory, and algebraic geometry, but involves just about all areas of mathematics. One of its cornerstones is a conjectural link between harmonic analysis and algebraic geometry, mediated by an equality of so-called L-functions, which generalize the Riemann zeta function. A famous case is the relation between modular forms and elliptic curves (which implies Fermat's Last Theorem). The goal of the talk is to give the general audience some idea of what this is all about, and introduce some of the fundamental players. (Familiarity with basic complex analysis, group actions, and quadratic residues will be an advantage.)