Christopher McLean Skinner (born June 4, 1972) is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and professor at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

. He works in

algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

and arithmetic aspects of the

Langlands program In mathematics, the Langlands program is a set of conjectures about connections between number theory, the theory of automorphic forms, and geometry. It was proposed by . It seeks to relate the structure of Galois groups in algebraic number t ...

Early life and education

Skinner was born on June 4, 1972, in

Little Rock Little Rock is the List of capitals in the United States, capital and List of municipalities in Arkansas, most populous city of the U.S. state of Arkansas. The city's population was 202,591 as of the 2020 census. The six-county Central Arkan ...

, Arkansas. Skinner graduated with a B.A. from the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

in 1993. He received a Ph.D. from

in 1997 under the supervision of

Andrew Wiles Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is best known for Wiles's proof of Fermat's Last Theorem, proving Ferma ...

Career

Skinner was a member of the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

from 1997 to 2000. 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. He became a professor of mathematics at

in 2006.

Research

Skinner and Wiles proved

modularity Modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. The concept of modularity is used primarily to reduce complexity by breaking a system into varying ...

results for residually reducible

Galois representation In mathematics, a Galois module is a ''G''-module, with ''G'' being the Galois group of some extension of fields. The term Galois representation is frequently used when the ''G''-module is a vector space over a field or a free module over a ring ...

s in joint work. Skinner and

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 superv ...

proved many cases of Iwasawa–Greenberg main conjectures for a large class of

modular form In mathematics, a modular form is a holomorphic function on the complex upper half-plane, \mathcal, that roughly satisfies a functional equation with respect to the group action of the modular group and a growth condition. The theory of modul ...

s. As a consequence, for a

modular elliptic curve A modular elliptic curve is an elliptic curve ''E'' that admits a parametrization ''X''0(''N'') → ''E'' by a modular curve. This is not the same as a modular curve that happens to be an elliptic curve, something that could be called a ...

over the

rational number In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (for example, The set of all ...

s, 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 In arithmetic geometry, the Selmer group, named in honor of the work of by , is a group constructed from an isogeny of abelian varieties. Selmer group of an isogeny The Selmer group of an abelian variety ''A'' with respect to an isogeny ''f'' ...

of ''E'' is infinite. Combined with theorems of Gross– Zagier and

Kolyvagin Victor Alexandrovich Kolyvagin (, born 11 March, 1955) is a Russian mathematician who wrote a series of papers on Euler systems, leading to breakthroughs on the Birch and Swinnerton-Dyer conjecture, and Iwasawa's conjecture for cyclotomic fields ...

, 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 In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory a ...

. These results were used by

Manjul Bhargava Manjul Bhargava (born 8 August 1974) is a Canadian-American mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory at Leiden University, and also holds A ...

, Skinner, and Wei Zhang to prove that a positive proportion of elliptic curves satisfy the

Awards and honors

Skinner was a Packard Foundation Fellow from 2001 to 2006 and a Sloan Research Fellow from 2001 to 2002. He was named an inaugural

Fellow of the American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

in 2013. In 2015, he was named a

Simons Investigator The Simons Foundation is an American private foundation established in 1994 by Marilyn and James Harris Simons, Jim Simons with offices in New York City. As one of the largest charitable organizations in the United States with assets of over $5 ...

in Mathematics. He was an invited speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

in Madrid in 2006.

References

Fellows of the American Mathematical Society 21st-century American mathematicians Princeton University alumni Living people 1972 births University of Michigan alumni {{US-mathematician-stub