Eric Urban
Eric Jean-Paul Urban is a professor of mathematics at Columbia University working in number theory and automorphic forms, particularly Iwasawa theory.Career
Urban received his PhD in mathematics from Paris-Sud University in 1994 under the supervision of Jacques Tilouine. He is a professor of mathematics at Columbia University.Research
Together with Christopher Skinner, Urban proved many cases of Iwasawa–Greenberg main conjectures for a large class of modular forms. As a consequence, for a modular elliptic curve over the rational numbers, they prove that the vanishing of the Hasse–Weil L-function L of E at s = 1 implies that the p-adic Selmer group of E is infinite. Combined with theorems of Gross-Zagier and Kolyvagin, this gave a conditional proof of the conjecture that E has infinitely many rational points if and only if L = 0, a form of the Birch–Swinnerton-Dyer conjecture. These results were used to prove that a positive proportion of elliptic curves satisfy the Birch–Swinnerton-Dyer conjecture.Selected publications
