Walter Baily's research focused on areas of algebraic groups, modular forms and number-theoretical applications of automorphic forms. One of his significant works was with Armand Borel, now known as the Baily–Borel compactification, which is a compactification of a quotient of a Hermitian symmetric space by an arithmetic group (that is, a linear algebraic group over the rational numbers).[3] Baily and Borel built on the work of Ichirō Satake and others.