Explore open problems in the geometry of complex supercurves in this 49-minute lecture by Jeffrey Rabin from the University of California, San Diego. Delivered as part of the Workshop on Supergeometry and Bracket Structures in Mathematics and Physics at the Fields Institute, delve into topics such as split supercurves, elliptic supercurves, spectral supercurves, divisors, duality, line bundles, Obl maps, Jacobi inversion, theta functions, prime forms, and super Riemann surfaces. Gain insights into the current challenges and potential research directions in this advanced area of mathematical physics.