Jack A. Thorne (born 13 June 1987) is a British mathematician working in number theory and arithmetic aspects of the Langlands Program. 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 ...
.
Education
Thorne read mathematics at
Trinity Hall, Cambridge
Trinity Hall (formally The College or Hall of the Holy Trinity in the University of Cambridge) is a constituent college of the University of Cambridge.
It is the fifth-oldest surviving college of the university, having been founded in 1350 by ...
. He completed his PhD with
Benedict Gross
Benedict Hyman Gross is an American mathematician who is a professor at the University of California San Diego, the George Vasmer Leverett Professor of Mathematics Emeritus at Harvard University, and former Dean of Harvard College.Richard Taylor at
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
in 2012.
Career and research
Thorne was a Clay Research Fellow. Currently, he is a Professor of Mathematics at the
University of Cambridge
, mottoeng = Literal: From here, light and sacred draughts.
Non literal: From this place, we gain enlightenment and precious knowledge.
, established =
, other_name = The Chancellor, Masters and Schola ...
, where he has been since 2015, and is also a fellow at
Trinity Hall, Cambridge
Trinity Hall (formally The College or Hall of the Holy Trinity in the University of Cambridge) is a constituent college of the University of Cambridge.
It is the fifth-oldest surviving college of the university, having been founded in 1350 by ...
.
Thorne's paper on adequate representations significantly extended the applicability of the Taylor-Wiles method. His paper on deformations of reducible representations generalized previous results of Chris Skinner and Andrew Wiles from two-dimensional representations to ''n''-dimensional representations. With Gebhard Böckle, Michael Harris, and Chandrashekhar Khare, he has applied techniques from modularity lifting to the Langlands conjectures over function fields. With Kai-Wen Lan, Harris, and Richard Taylor, Thorne constructed
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 i ...
s associated to non-self dual regular algebraic cuspidal
automorphic form
In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of ...
s for GL(''n'') over CM fields. Thorne's 2015 joint work with Khare on potential automorphy and
Leopoldt's conjecture In algebraic number theory, Leopoldt's conjecture, introduced by , states that the p-adic regulator of a number field does not vanish. The p-adic regulator is an analogue of the usual
regulator defined using p-adic logarithms instead of the usual ...
elliptic curve
In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...
s over imaginary quadratic fields.
In joint work with James Newton, Thorne has established symmetric power functoriality for all holomorphicmodular forms.
Awards and honors
Thorne was awarded the
Whitehead Prize
The Whitehead Prize is awarded yearly by the London Mathematical Society to multiple mathematicians working in the United Kingdom who are at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C. Whiteh ...
in 2017. In 2018, Thorne 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 Nevanlinna Prize (to be rename ...
in Rio de Janeiro. He was awarded the 2018
SASTRA Ramanujan Prize
The SASTRA Ramanujan Prize, founded by Shanmugha Arts, Science, Technology & Research Academy (SASTRA) located near Kumbakonam, India, Srinivasa Ramanujan's hometown, is awarded every year to a young mathematician judged to have done outstanding ...
for his contributions to the field of mathematics. He shared the prize with Yifeng Liu. In April 2020 he was elected a
Fellow of the Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...
Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number ...