A series is said to be lacunary if, in a precise sense, "almost all" of its coefficients are zero. This is a notion that can be explored from a purely combinatorial perspective; however, we can gain a good deal of insight by introducing a new piece of machinery. We will define a particular class of functions known as modular forms and investigate the ways in which the extra structure of "modularity" can help us understand when the Fourier series of such functions are lacunary.
This talk is accessible to everyone.