Christopher Skinner
Christopher Skinner | |
|---|---|
| Born | 4 June 1972 Little Rock, Arkansas |
| Alma mater | University of Michigan, Princeton University |
| Known for | Main conjecture of Iwasawa theory for modular curves |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Princeton University |
| Thesis | Deformations of Galois Representations (1997) |
| Doctoral advisor | Andrew Wiles |
| Doctoral students | Ellen Eischen |
Christopher McLean Skinner (born June 4, 1972) is an American mathematician and professor at Princeton University. He works in algebraic number theory and arithmetic aspects of the Langlands program.
Early life and education
[edit]Skinner was born on June 4, 1972 in Little Rock, Arkansas.[1] Skinner graduated with a B.A. from the University of Michigan in 1993.[1] He received a Ph.D. from Princeton University in 1997 under the supervision of Andrew Wiles.[1]
Career
[edit]Skinner was a member of the Institute for Advanced Study from 1997 to 2000.[1] He was then an associate professor of mathematics at the University of Michigan from 2000 to 2004, and then a full professor from 2004 to 2006.[1] He became a professor of mathematics at Princeton University in 2006.[1]
Research
[edit]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. 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 by Manjul Bhargava, Skinner, and Wei Zhang to prove that a positive proportion of elliptic curves satisfy the Birch–Swinnerton-Dyer conjecture.[4][5]
Awards and honors
[edit]Skinner was a Packard Foundation Fellow from 2001 to 2006[1][6] and a Sloan Research Fellow from 2001 to 2002.[1] He was named an inaugural Fellow of the American Mathematical Society in 2013.[7] In 2015, he was named a Simons Investigator in Mathematics.[8][9]
He was an invited speaker at the International Congress of Mathematicians in Madrid in 2006.[10]
References
[edit]- ^ a b c d e f g h "Curriculum Vitae" (PDF). Christopher Skinner. Archived from the original (PDF) on 3 August 2012.
- ^ Skinner, Christopher; Wiles, Andrew (1999). "Residually reductible representations and modular forms" (PDF). Publications Mathématiques de l'IHÉS. 89: 5–126.
- ^ Urban, Eric; Skinner, Christopher (1 January 2014). "The Iwasawa Main Conjectures for GL2". Inventiones Mathematicae. 195 (1): 1–277. Bibcode:2014InMat.195....1S. CiteSeerX 10.1.1.363.2008. doi:10.1007/s00222-013-0448-1. ISSN 1432-1297. S2CID 120848645.
- ^ Bhargava, Manjul; Skinner, Christopher; Zhang, Wei (7 July 2014). "A majority of elliptic curves over $\mathbb Q$ satisfy the Birch and Swinnerton-Dyer conjecture". arXiv:1407.1826 [math.NT].
- ^ Baker, Matt (10 March 2014). "The BSD conjecture is true for most elliptic curves". Matt Baker's Math Blog. Retrieved 24 February 2019.
- ^ "Skinner, Christopher M." The David and Lucile Packard Foundation. Retrieved 24 February 2019.
- ^ "American Mathematical Society". www.ams.org. Retrieved 24 February 2019.
- ^ "FACULTY AWARD: Skinner named Simons Investigator in Mathematics". Princeton University. Retrieved 24 February 2019.
- ^ "Simons Investigators". Simons Foundation. 10 July 2018. Retrieved 24 February 2019.
- ^ "ICM Plenary and Invited Speakers | International Mathematical Union (IMU)". www.mathunion.org. Retrieved 24 February 2019.
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