Biography:Eric Urban
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 |
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.[1] He is a professor of mathematics at Columbia University.[2]
Research
Together with Christopher Skinner, 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. 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.[4][5]
Awards
Urban was awarded a Guggenheim Fellowship in 2007.[6]
Selected publications
- Urban, Eric (2011). "Eigenvarieties for reductive groups" (in en). Annals of Mathematics. Second Series 174 (3): 1685–1784. doi:10.4007/annals.2011.174.3.7. ISSN 0003-486X. http://annals.math.princeton.edu/2011/174-3/p07.
- Skinner, Christopher; Urban, Eric (2014). "The Iwasawa Main Conjectures for GL2" (in en). Inventiones Mathematicae 195 (1): 1–277. doi:10.1007/s00222-013-0448-1. ISSN 0020-9910. Bibcode: 2014InMat.195....1S. http://link.springer.com/10.1007/s00222-013-0448-1.
References
- ↑ Eric Urban at the Mathematics Genealogy Project
- ↑ "Eric Jean-Paul Urban » Department Directory". Columbia University. https://www.math.columbia.edu/people/directory/name/eric-urban/.
- ↑ Skinner, Christopher; Urban, Eric (2014). "The Iwasawa Main Conjectures for GL2" (in en). Inventiones Mathematicae 195 (1): 1–277. doi:10.1007/s00222-013-0448-1. ISSN 0020-9910. Bibcode: 2014InMat.195....1S. http://link.springer.com/10.1007/s00222-013-0448-1.
- ↑ Bhargava, Manjul; Skinner, Christopher; Zhang, Wei (2014-07-07). "A majority of elliptic curves over $\mathbb Q$ satisfy the Birch and Swinnerton-Dyer conjecture". arXiv:1407.1826 [math.NT].
- ↑ Baker, Matt (2014-03-10). "The BSD conjecture is true for most elliptic curves" (in en). https://mattbaker.blog/2014/03/10/the-bsd-conjecture-is-true-for-most-elliptic-curves/.
- ↑ "Eric Urban". https://www.gf.org/fellows/all-fellows/eric-urban/. Retrieved 9 March 2021.
External links
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