Christopher McLean Skinner (born June 4, 1972) is an American mathematician and professor at Princeton University.
[1] Skinner and Wiles proved modularity results for residually reducible Galois representations in joint work.
[2] Skinner and Eric Urban proved many cases of Iwasawa–Greenberg main conjectures for a large class of modular forms.
[3] As a consequence, for a modular elliptic curve over the rational numbers, they prove that the vanishing of the Hasse–Weil L-function L(E, s) of E at s = 1 implies that the p-adic Selmer group of E is infinite.
These results were used by Manjul Bhargava, Skinner, and Wei Zhang to prove that a positive proportion of elliptic curves satisfy the Birch–Swinnerton-Dyer conjecture.