Jack Thorne (mathematician)

Jack A. Thorne (born June 13, 1987 ) is a British mathematician and professor at Cambridge University . He deals with algebraic number theory and the Langlands program .

Thorne studied mathematics at Cambridge University from 2004 with a bachelor's degree in 2007 and a master's degree in 2008 and received his doctorate in 2012 under Benedict Gross (and Richard Taylor ) at Harvard University (The arithmetic of simple singularities). He was then a Clay Research Fellow (2012 to 2017). He was also a Junior Fellow of the Society of Fellows at Harvard from 2012 to 2014. He became a Reader in 2013 and Professor at Cambridge University in 2018. From 2014 he was a Staff Fellow at Trinity Hall in Cambridge.

In the appreciation for the SASTRA Ramanujan Prize he was recognized as one of the leading representatives of algebraic number theory of his generation. and in particular his contributions to the modularity of Galois representations and arithmetic invariant theory were highlighted, the latter subject of his dissertation, which led to new bounds for certain Selmer groups and the number of rational and integer points on different classes of algebraic curves . He has also been recognized for being a driving force in the elimination of Taylor-Wiles constraints on the modularity of Galois representations, such as in three papers with Laurent Clozel and his discovery of a surprising theorem on automorphism enhancement by Galois- Representations in a paper in the American Journal of Mathematics from 2015. His work with Chandrasekhar Khare on potential automorphism and the Leopoldt conjecture led to a proof of the potential version of the Shimura-Taniyama conjecture for elliptic curves over imaginary-quadratic number fields . Another breakthrough was the proof that elliptic curves are beyond modular. ${\displaystyle \mathbb {Q} _{\infty }}$

In 2017 he received the Whitehead Prize and an ERC Starting Grant. In 2018 he was invited speaker at the International Congress of Mathematicians in Rio de Janeiro ( Potential automorphy of Ĝ-Local Systems ) and received the SASTRA Ramanujan Prize . In 2020 he received an ERC Horizon Grant. For 2020/21 he received the EMS Prize .

Fonts (selection)

• Vinberg's representations and arithmetic invariant theory , Algebra & Number Theory, Volume 7, 2013, S 2331–2368 (revised version of his dissertation)
• with Laurent Clozel : Level-raising and symmetric power functoriality , Part 1, Compositio Mathematica, Volume 150, 2014, pp. 729–748, Part 2, Annals of Mathematics, Volume 181, 2015, pp. 303–359, Part 3, Duke Math. J., Volume 166, 2017, pp. 325-402
• On the automorphy of l-adic Galois representations with small residual image , Journal of the Institute of Mathematics of Jussieu, Volume 11, 2012, pp. 855-920 ,. Arxiv (with appendix by Robert Guralnick, Florian Herzig, Richard Taylor, Jack Thorne: Adequate Subgroups, pp. 907–920, Arxiv )
• with Michael Harris , Kai-Wen Lan, R. Taylor : On the Rigid Cohomology of Certain Shimura Varieties , Research in Mathematical Sciences, Volume 3, 2016, Arxiv 2013
• Automorphy of some residually dihedral Galois representations , Mathematische Annalen, Volume 364, 2016, pp. 589–648, Arxiv
• Automorphy lifting for residually reducible l-adic Galois representations , J. Amer. Math. Soc., Volume 28, 2015, pp. 785-870
• with Chandrasekhar Khare : Potential automorphy and the Leopoldt conjecture , Amer. J. Math., Volume 139, 2017, pp. 1205-1273, Arxiv
• with P. Allen, Frank Calegari , Ana Caraiani , Toby Gee , D. Helm, B. Le Hung, J. Newton, Peter Scholze , R. Taylor: Potential automorphy over CM fields , Arxiv 2018
• Elliptic curves over are modular ${\displaystyle \mathbb {Q} _{\infty }}$ , J. Eur. Math. Soc., Volume 21, 2019, pp. 1943-1948. Arxiv
• with Gebhard Böckle, Michael Harris , Chandrasekhar Khare: Ĝ-local systems on smooth projective curves are potentially automorphic , Acta Mathematica, Volume 223, 2019, pp. 1–111. Arxiv

Web links

• Homepage at the University of Cambridge , with CV

Individual evidence

1. ↑ Jack Thorne in the Mathematics Genealogy Project (English)
2. ↑ Liu and Thorne awarded SASTRA Ramanujan Prize, Notices AMS, January 2019, p. 113
3. ↑ Arxiv
4. ↑ Biography of the winners of the EMS Prize