Lorentzian polynomials link continuous convex analysis and discrete convex analysis via tropical geometry. The tropical connection is used to produce Lorentzian polynomials from discrete convex functions. The talk will be accessible to a general audience: No specific background beyond linear algebra and multivariable calculus are required for most of the presentation. In addition, I advertise the talk to people with interests in at least one of the following topics: graphs, convex bodies, stable polynomials, projective varieties, partition functions, tropicalizations, Schur polynomials, highest weight representations. Based on joint work with Petter Brändén.