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From Wikipedia, the free encyclopedia
Eric Jean-Paul Urban is a professor of mathematics at Columbia University working in number theory and automorphic forms, particularly Iwasawa theory.[1]
Eric Urban | |
|---|---|
.jpg) Urban at the Mathematical Research Institute of Oberwolfach in 2018 | |
| Alma mater | Paris-Sud University |
| Awards | Guggenheim Fellowship (2007) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Columbia University |
| Thesis | Arithmétique des formes automorphes pour GL(2) sur un corps imaginaire quadratique (1994) |
| Doctoral advisor | Jacques Tilouine |
Urban received his PhD in mathematics from Paris-Sud University in 1994 under the supervision of Jacques Tilouine.[2] He is a professor of mathematics at Columbia University.[3]
Together with Christopher Skinner, Urban proved many cases of Iwasawa–Greenberg main conjectures for a large class of modular forms.[4] 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. Combined with theorems of Gross-Zagier and Kolyvagin, this gave a conditional proof (on the Tate–Shafarevich conjecture) of the conjecture that E has infinitely many rational points if and only if L(E, 1) = 0, a (weak) form of the Birch–Swinnerton-Dyer conjecture. These results were used (in joint work with Manjul Bhargava and Wei Zhang) to prove that a positive proportion of elliptic curves satisfy the Birch–Swinnerton-Dyer conjecture.[5][6]
Urban was awarded a Guggenheim Fellowship in 2007.[7]
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