I will present some results on the 1d Super-Conformal Field Theory (SCFT) living on a 1/2-BPS line defect in a 4d N=4 SCFT. The main realization of this setup being Wilson lines in N=4 Super-Yang-Mills (SYM). After reviewing what the modern numerical bootstrap have to say about this problem I will describe how analytic bootstrap methods can efficiently produce the perturbative expansion at strong coupling in the planar theory. NOTE: This will be an online seminar using Zoom. Please register at integrability-london.weebly.com to receive the link