This volume consists of articles by speakers at the Conference on Geometry and Topology held at Harvard University in 2014. Included are: Camillo De Lellis, on the size of the singular set of area-minimizing currents; Simon Donaldson, on Kähler–Einstein metrics and algebraic structures on limit spaces; Mark Gross, on theta functions and mirror symmetry; Nigel Hitchin, on Higgs bundles and diffeomorphism groups; Fernando Marques, on topology of the space of cycles and existence of minimal varieties; William Meeks, on constant mean curvature surfaces; Richard Thomas, on the proof of the KKV conjecture; Claire Voisin, on stable birational invariants and the Luroth problem; and Mu-Tao Wang, on energy, momentum, and center of mass in general relativity.