Introduction
Jack A. Thorne (born 1987) is a British mathematician working in number theory and arithmetic aspects of the Langlands Program.He specialises in algebraic number theory. Thorne was awarded the Whitehead Prize in 2017, and he was an invited speaker at the International Congress of Mathematicians in 2018. He was also awarded the 2018 SASTRA Ramanujan Prize for his contributions to the field of mathematics. He shared the prize with Yifeng Liu.
Career
Thorne read mathematics at Trinity Hall, Cambridge. After completing his PhD with Benedict Gross and Richard Taylor at Harvard University in 2012, he was a Clay Research Fellow. Currently, he is a Professor of Mathematics at the University of Cambridge, where he has been since 2015, and is also a fellow at Trinity Hall, Cambridge.
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. WithGebhard Böckle, Michael Harris (mathematician), and Chandrashekhar Khare, he has applied techniques from modularity lifting to the Langlands conjectures over function fields. With Kai-Wen Lan, Michael Harris (mathematician), and Richard Taylor (mathematician), Thorne constructed Galois representations associated to non-self dual regular algebraic cuspidal automorphic forms for GL(n) over CM fields. Thorne's 2015 joint work with Chandrashekhar Khare on potential automorphy and the Leopoldt conjecture has led to a proof of a potential version of the Shimura-Taniyama Conjecture for elliptic curves over imaginary quadratic fields.
In 2018, Thorne was an invited speaker at the International Congress of Mathematicians in Rio de Janeiro.