Title: Exact superconducting states in attractive Hubbard models with topological flat bands.

Abstract: A good superconductor has two characteristics: large Cooper pair density in the ground state (condensation), and mobile Cooper pair excitations (superfluidity). From a simple BCS perspective, the infinite density of states in flat bands promotes condensation, but the infinite electron mass prevents superfluidity. To the contrary, we find that the short-range entanglement protected by band topology coheres the system into a strongly correlated superconductor. We prove this statement in a large family of attractive Hubbard models with topological flat bands by deriving exact expressions (at fixed particle number) for the pairing ground state and its one- and two-particle excitations. The latter organizes into a set of low-energy bosonic modes (the various pairing channels) and exhibits a universal dependence on the minimal Fubini-Study metric of the flat band wavefunctions. Time permitting, we will discuss extensions to solvable models with unconventional pairing symmetries, and departures from the isolated band limit.