Title: Singular modular forms and small representations.

Abstract: The Fourier coefficients a(T) of Siegel modular forms are naturally indexed by n by n symmetric integer matrices T. An interesting phenomenon when n > 1 is that some non-zero modular forms have Fourier coefficients a(T) which vanish except when rank(T) < n. I will review these singular modular forms, and relations to number theory. Then, I will discuss the interpretation with automorphic representations, and describe the construction of singular modular forms for groups of type A-D-E.