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Jack Thorne (mathematician)

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.[1][2][3]

Jack Thorne
Born1987 (age 31–32)
Hereford, England
Alma materTrinity Hall, Cambridge
Scientific career
ThesisThe Arithmetic of Simple Singularities (2012)
Doctoral advisorRichard Taylor, Benedict Gross


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[4]. Currently, he is a Professor of Mathematics at the University of Cambridge[5], where he has been since 2015, and is also a fellow at Trinity Hall, Cambridge.

Thorne's paper on adequate representations[6] significantly extended the applicability of the Taylor-Wiles method. His paper on deformations of reducible representations[7] generalized previous results of Chris Skinner and Andrew Wiles from two dimensional representations to n-dimensional representations. With Gebhard 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.[8] Thorne's 2015 joint work with Chandrashekhar Khare on potential automorphy and the Leopoldt conjecture[9] has led to a proof of a potential version of the Shimura-Taniyama Conjecture for elliptic curves over imaginary quadratic fields[10].

In 2018, Thorne was an invited speaker at the International Congress of Mathematicians in Rio de Janeiro.[11][12]


  1. ^ "Srinivasa Ramanujan Centre (SRC)". Retrieved 22 February 2019.
  2. ^ Maeve Forti (25 October 2018). "Yifeng Liu wins prestigious award in mathematics". YaleNews. Yale University. Retrieved 3 February 2019.
  3. ^ "Yale, Cambridge profs. get SASTRA-Ramanujan Award". The Hindu. 22 December 2018. Retrieved 3 February 2019.
  4. ^ "Jack Thorne | Clay Mathematics Institute". Retrieved 22 February 2019.
  5. ^ "Professor Jack Thorne". Trinity Hall. Retrieved 22 February 2019.
  6. ^ Thorne, Jack (October 2012). "On the automorphy of l-adic Galois representations with small residual image With an appendix by Robert Guralnick, Florian Herzig, Richard Taylor and Jack Thorne". Journal of the Institute of Mathematics of Jussieu. 11 (4): 855–920. arXiv:1107.5993. doi:10.1017/S1474748012000023. ISSN 1475-3030.
  7. ^ Thorne, Jack (2015). "Automorphy lifting for residually reducible 𝑙-adic Galois representations". Journal of the American Mathematical Society. 28 (3): 785–870. doi:10.1090/S0894-0347-2014-00812-2. ISSN 0894-0347.
  8. ^ Harris, Michael; Lan, Kai-Wen; Taylor, Richard; Thorne, Jack (26 October 2016). "On the rigid cohomology of certain Shimura varieties". Research in the Mathematical Sciences. 3 (1). arXiv:1411.6717. doi:10.1186/s40687-016-0078-5. ISSN 2197-9847.
  9. ^ Thorne, Jack A.; Khare, Chandrashekhar B. (13 September 2017). "Potential Automorphy and the Leopoldt conjecture". American Journal of Mathematics. 139 (5): 1205–1273. arXiv:1409.7007. doi:10.1353/ajm.2017.0030. ISSN 1080-6377.
  10. ^ Liu and Thorne Awarded SASTRA Ramanujan Prize, Notices of the American Mathematical Society, January 2019,
  11. ^ "Invited Section Lectures - Speakers | ICM 2018". Retrieved 30 November 2018.
  12. ^ plusmathsorg (9 August 2018), ICM 2018: Jack Thorne, retrieved 22 February 2019

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