Explore a 57-minute lecture on the quantitative development of the orbit method using microlocal analysis and its applications to representation theory and automorphic forms. Delve into local applications, including asymptotic expansions of relative characters, and global applications such as moment estimates and subconvex bounds for L-functions. Examine the research presented in two papers, one co-authored with Akshay Venkatesh, which form the basis of this talk delivered at the Hausdorff Center for Mathematics.