The aim of this program is to connect efforts of the mathematical and physical sciences communities to address the latest advances and new challenges on the understanding of multi-messenger astronomy. The IPAM program will comprise four workshops, each addressing a different topic: the generation of catalogs of waveform templates; the discussion of the mathematical modeling of the equations governing strong relativistic systems; parameter estimation of astrophysical sources of gravitational waves; and the state of the art of big data and deep learning techniques for GW data analysis.