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, structure, space, models, and change. History On ...

working in number theory and arithmetic aspects of the

Langlands program In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by , it seeks to relate Galois groups in algebraic num ...

. He specialises 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 ...

. Skinner was a

Packard Foundation The David and Lucile Packard Foundation is a private foundation that provides grants to not-for-profit organizations. It was created in 1964 by David Packard (co-founder of HP) and his wife Lucile Salter Packard. Following David Packard's death ...

Fellow from 2001 to 2006, and 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 Simons is a surname of Scandinavian origins and a variant of Sigmundsson, a patronymic surname with roots in proto-Germanic ''*segaz'' and ''*mundō'', giving a rough translation of "protection through victory". Notable people A * Alan ...

Investigator in Mathematics. He was an invited speaker at the International Congress of Mathematicians in

Madrid Madrid ( , ) is the capital and most populous city of Spain. The city has almost 3.4 million inhabitants and a metropolitan area population of approximately 6.7 million. It is the second-largest city in the European Union (EU), and ...

in 2006.

Career

Skinner graduated from the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

in 1993. After completing his PhD with

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, specializing in number theory. He is best known for proving Fermat's Last Theorem, for which he was awar ...

in 1997, he moved to the

as an assistant professor. Since 2006, he has been a Professor of Mathematics at the

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

. In joint work with

, Skinner proved modularity 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. Together with

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 ...

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

modular form In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the Group action (mathematics), group action of the modular group, and also satisfying a grow ...

s. As a consequence, for a

modular elliptic curve A modular elliptic curve is an elliptic curve ''E'' that admits a parametrisation ''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 an ...

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 (e.g. ). The set of all ration ...

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. The 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, 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 (in joint work with

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 ...

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

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