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'''Jack A. Thorne''' {{post-nominals|FRS}} (born 1987) is a [[United Kingdom|British]] [[mathematician]] working in number theory and arithmetic aspects of the [[Langlands program|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]].<ref>{{Cite web|url=https://sas.sastra.edu/ramanujan/Ramanujan-Awards.php|title=Srinivasa Ramanujan Centre (SRC)|website=sas.sastra.edu|access-date=2019-02-22}}</ref><ref>{{cite web |last1=Maeve Forti |title=Yifeng Liu wins prestigious award in mathematics |url=https://news.yale.edu/2018/10/25/yifeng-liu-wins-prestigious-award-mathematics |website=YaleNews |publisher=Yale University |access-date=3 February 2019|date=2018-10-25 }}</ref><ref>{{cite news |title=Yale, Cambridge profs. get SASTRA-Ramanujan Award |journal=The Hindu |date=December 22, 2018 |url=https://www.thehindu.com/news/national/tamil-nadu/yale-cambridge-profs-get-sastra-ramanujan-award/article25803389.ece |access-date=3 February 2019}}</ref> In April 2020 he was elected a [[Fellow of the Royal Society]].<ref>{{Cite web|url=https://royalsociety.org/news/2020/04/outstanding-scientists-elected-as-fellows-and-foreign-members-of-the-royal-society/|title=Outstanding scientists elected as Fellows and Foreign Members of the Royal Society|website=royalsociety.org|language=en-GB|access-date=2020-04-30}}</ref> Also in 2020 he received the EMS Prize of the [[European Mathematical Society]].<ref>[https://8ecm.si/prizes EMS Prize 2020]</ref>
'''Jack A. Thorne''' {{post-nominals|FRS}} (born 1987) is a [[United Kingdom|British]] [[mathematician]] working in number theory and arithmetic aspects of the [[Langlands program|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 awarded the 2018 [[SASTRA Ramanujan Prize]] for his contributions to the field of mathematics. He shared the prize with [[Yifeng Liu]].<ref>{{Cite web|url=https://sas.sastra.edu/ramanujan/Ramanujan-Awards.php|title=Srinivasa Ramanujan Centre (SRC)|website=sas.sastra.edu|access-date=2019-02-22}}</ref><ref>{{cite web |last1=Maeve Forti |title=Yifeng Liu wins prestigious award in mathematics |url=https://news.yale.edu/2018/10/25/yifeng-liu-wins-prestigious-award-mathematics |website=YaleNews |publisher=Yale University |access-date=3 February 2019|date=2018-10-25 }}</ref><ref>{{cite news |title=Yale, Cambridge profs. get SASTRA-Ramanujan Award |journal=The Hindu |date=December 22, 2018 |url=https://www.thehindu.com/news/national/tamil-nadu/yale-cambridge-profs-get-sastra-ramanujan-award/article25803389.ece |access-date=3 February 2019}}</ref> In April 2020 he was elected a [[Fellow of the Royal Society]].<ref>{{Cite web|url=https://royalsociety.org/news/2020/04/outstanding-scientists-elected-as-fellows-and-foreign-members-of-the-royal-society/|title=Outstanding scientists elected as Fellows and Foreign Members of the Royal Society|website=royalsociety.org|language=en-GB|access-date=2020-04-30}}</ref> In 2020 he received the EMS Prize of the [[European Mathematical Society]],<ref>[https://8ecm.si/prizes EMS Prize 2020]</ref> and in 2021 he was awarded a [[Breakthrough Prize in Mathematics#2022|New Horizons in Mathematics Prize]].


== Education ==
== Education ==
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Thorne's paper on adequate representations<ref>{{Cite journal|last=Thorne|first=Jack|date=October 2012|title=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=Journal of the Institute of Mathematics of Jussieu|language=en|volume=11|issue=4|pages=855–920|doi=10.1017/S1474748012000023|issn=1475-3030|arxiv=1107.5993|s2cid=15994406}}</ref> significantly extended the applicability of the Taylor-Wiles method. His paper on deformations of reducible representations<ref>{{Cite journal|last=Thorne|first=Jack|date=2015|title=Automorphy lifting for residually reducible 𝑙-adic Galois representations|url=https://www.ams.org/home/page/|journal=Journal of the American Mathematical Society|language=en|volume=28|issue=3|pages=785–870|doi=10.1090/S0894-0347-2014-00812-2|s2cid=3945032|issn=0894-0347|doi-access=free}}</ref> generalized previous results of [[Christopher Skinner|Chris Skinner]] and [[Andrew Wiles]] from two-dimensional representations to ''n''-dimensional representations. With Gebhard Böckle, [[Michael Harris (mathematician)|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 (mathematician)|Richard Taylor]], Thorne constructed [[Galois representation]]s associated to non-self dual regular algebraic cuspidal [[automorphic form]]s for GL(''n'') over CM fields.<ref>{{Cite journal|last1=Harris|first1=Michael|last2=Lan|first2=Kai-Wen|last3=Taylor|first3=Richard|last4=Thorne|first4=Jack|date=2016-10-26|title=On the rigid cohomology of certain Shimura varieties|journal=Research in the Mathematical Sciences|language=En|volume=3|issue=1|doi=10.1186/s40687-016-0078-5|issn=2197-9847|arxiv=1411.6717|s2cid=119142230}}</ref> Thorne's 2015 joint work with Khare on potential automorphy and [[Leopoldt's conjecture]]<ref>{{Cite journal|last1=Thorne|first1=Jack A.|last2=Khare|first2=Chandrashekhar B.|date=2017-09-13|title=Potential Automorphy and the Leopoldt conjecture|journal=American Journal of Mathematics|language=en|volume=139|issue=5|pages=1205–1273|doi=10.1353/ajm.2017.0030|issn=1080-6377|arxiv=1409.7007|s2cid=117991797}}</ref> has led to a proof of a potential version of the [[modularity conjecture]] for [[elliptic curve]]s over imaginary quadratic fields.<ref>Liu and Thorne Awarded SASTRA Ramanujan Prize, Notices of the American Mathematical Society, January 2019, https://www.ams.org/journals/notices/201901/rnoti-p113.pdf</ref>
Thorne's paper on adequate representations<ref>{{Cite journal|last=Thorne|first=Jack|date=October 2012|title=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=Journal of the Institute of Mathematics of Jussieu|language=en|volume=11|issue=4|pages=855–920|doi=10.1017/S1474748012000023|issn=1475-3030|arxiv=1107.5993|s2cid=15994406}}</ref> significantly extended the applicability of the Taylor-Wiles method. His paper on deformations of reducible representations<ref>{{Cite journal|last=Thorne|first=Jack|date=2015|title=Automorphy lifting for residually reducible 𝑙-adic Galois representations|url=https://www.ams.org/home/page/|journal=Journal of the American Mathematical Society|language=en|volume=28|issue=3|pages=785–870|doi=10.1090/S0894-0347-2014-00812-2|s2cid=3945032|issn=0894-0347|doi-access=free}}</ref> generalized previous results of [[Christopher Skinner|Chris Skinner]] and [[Andrew Wiles]] from two-dimensional representations to ''n''-dimensional representations. With Gebhard Böckle, [[Michael Harris (mathematician)|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 (mathematician)|Richard Taylor]], Thorne constructed [[Galois representation]]s associated to non-self dual regular algebraic cuspidal [[automorphic form]]s for GL(''n'') over CM fields.<ref>{{Cite journal|last1=Harris|first1=Michael|last2=Lan|first2=Kai-Wen|last3=Taylor|first3=Richard|last4=Thorne|first4=Jack|date=2016-10-26|title=On the rigid cohomology of certain Shimura varieties|journal=Research in the Mathematical Sciences|language=En|volume=3|issue=1|doi=10.1186/s40687-016-0078-5|issn=2197-9847|arxiv=1411.6717|s2cid=119142230}}</ref> Thorne's 2015 joint work with Khare on potential automorphy and [[Leopoldt's conjecture]]<ref>{{Cite journal|last1=Thorne|first1=Jack A.|last2=Khare|first2=Chandrashekhar B.|date=2017-09-13|title=Potential Automorphy and the Leopoldt conjecture|journal=American Journal of Mathematics|language=en|volume=139|issue=5|pages=1205–1273|doi=10.1353/ajm.2017.0030|issn=1080-6377|arxiv=1409.7007|s2cid=117991797}}</ref> has led to a proof of a potential version of the [[modularity conjecture]] for [[elliptic curve]]s over imaginary quadratic fields.<ref>Liu and Thorne Awarded SASTRA Ramanujan Prize, Notices of the American Mathematical Society, January 2019, https://www.ams.org/journals/notices/201901/rnoti-p113.pdf</ref>


In 2018, Thorne was an invited speaker at the [[International Congress of Mathematicians]] in [[Rio de Janeiro]].<ref>{{Cite web|url=http://www.icm2018.org/portal/en/invited-section-lectures-speakers|title=Invited Section Lectures - Speakers {{!}} ICM 2018|website=www.icm2018.org|access-date=2018-11-30|archive-url=https://web.archive.org/web/20181208144537/http://www.icm2018.org/portal/en/invited-section-lectures-speakers|archive-date=8 December 2018|url-status=dead}}</ref><ref>{{Citation|last=plusmathsorg|title=ICM 2018: Jack Thorne|date=2018-08-09|url=https://www.youtube.com/watch?v=axKZ7YMsNrQ|access-date=2019-02-22}}</ref>
In 2018, Thorne was an invited speaker at the [[International Congress of Mathematicians]] in [[Rio de Janeiro]].<ref>{{Cite web|url=http://www.icm2018.org/portal/en/invited-section-lectures-speakers|title=Invited Section Lectures - Speakers {{!}} ICM 2018|website=www.icm2018.org|access-date=2018-11-30|archive-url=https://web.archive.org/web/20181208144537/http://www.icm2018.org/portal/en/invited-section-lectures-speakers|archive-date=8 December 2018|url-status=dead}}</ref><ref>{{Citation|last=plusmathsorg|title=ICM 2018: Jack Thorne|date=2018-08-09|url=https://www.youtube.com/watch?v=axKZ7YMsNrQ|access-date=2019-02-22}}</ref>.

In joint work with James Newton<ref>{{Cite journal|last=Newton|first=James|last2=Thorne|first2=Jack A.|date=2020-07-17|title=Symmetric power functoriality for holomorphic modular forms|url=http://arxiv.org/abs/1912.11261|journal=arXiv:1912.11261 [math]}}</ref><ref>{{Cite journal|last=Newton|first=James|last2=Thorne|first2=Jack A.|date=2020-09-15|title=Symmetric power functoriality for holomorphic modular forms, II|url=http://arxiv.org/abs/2009.07180|journal=arXiv:2009.07180 [math]}}</ref>, Thorne has established symmetric power functoriality for all holomorphic modular forms. Thorne was awarded a [[Breakthrough Prize in Mathematics#2022|New Horizons in Mathematics Prize]] in 2021 "For transformative contributions to diverse areas of algebraic number theory, and in particular for the proof, in collaboration with James Newton, of the automorphy of all symmetric powers of a holomorphic modular newform."<ref>{{Cite web|title=Breakthrough Prize – Winners Of The 2022 Breakthrough Prizes In Life Sciences, Fundamental Physics And Mathematics Announced|url=https://breakthroughprize.org/News/65|access-date=2021-09-10|website=breakthroughprize.org|language=en}}</ref>


== References ==
== References ==

Revision as of 22:25, 10 September 2021

Jack Thorne
FRS
Born
Jack A. Thorne

(1987-06-13) 13 June 1987 (age 37)
Hereford, England
NationalityBritish
Alma materUniversity of Cambridge
Awards
Scientific career
FieldsMathematics
Institutions
ThesisThe Arithmetic of Simple Singularities (2012)
Doctoral advisorRichard Taylor, Benedict Gross

Jack A. Thorne FRS (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 awarded the 2018 SASTRA Ramanujan Prize for his contributions to the field of mathematics. He shared the prize with Yifeng Liu.[1][2][3] In April 2020 he was elected a Fellow of the Royal Society.[4] In 2020 he received the EMS Prize of the European Mathematical Society,[5] and in 2021 he was awarded a New Horizons in Mathematics Prize.

Education

Thorne read mathematics at Trinity Hall, Cambridge. He completed his PhD with Benedict Gross and Richard Taylor at Harvard University in 2012.

Career and research

Thorne was a Clay Research Fellow.[6] Currently, he is a Professor of Mathematics at the University of Cambridge,[7] where he has been since 2015, and is also a fellow at Trinity Hall, Cambridge.

Thorne's paper on adequate representations[8] significantly extended the applicability of the Taylor-Wiles method. His paper on deformations of reducible representations[9] 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 representations associated to non-self dual regular algebraic cuspidal automorphic forms for GL(n) over CM fields.[10] Thorne's 2015 joint work with Khare on potential automorphy and Leopoldt's conjecture[11] has led to a proof of a potential version of the modularity conjecture for elliptic curves over imaginary quadratic fields.[12]

In 2018, Thorne was an invited speaker at the International Congress of Mathematicians in Rio de Janeiro.[13][14].

In joint work with James Newton[15][16], Thorne has established symmetric power functoriality for all holomorphic modular forms. Thorne was awarded a New Horizons in Mathematics Prize in 2021 "For transformative contributions to diverse areas of algebraic number theory, and in particular for the proof, in collaboration with James Newton, of the automorphy of all symmetric powers of a holomorphic modular newform."[17]

References

  1. ^ "Srinivasa Ramanujan Centre (SRC)". sas.sastra.edu. 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. ^ "Outstanding scientists elected as Fellows and Foreign Members of the Royal Society". royalsociety.org. Retrieved 30 April 2020.
  5. ^ EMS Prize 2020
  6. ^ "Jack Thorne | Clay Mathematics Institute". www.claymath.org. Retrieved 22 February 2019.
  7. ^ "Professor Jack Thorne". Trinity Hall. Retrieved 22 February 2019.
  8. ^ 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. S2CID 15994406.
  9. ^ 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. S2CID 3945032.
  10. ^ 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. S2CID 119142230.{{cite journal}}: CS1 maint: unflagged free DOI (link)
  11. ^ 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. S2CID 117991797.
  12. ^ Liu and Thorne Awarded SASTRA Ramanujan Prize, Notices of the American Mathematical Society, January 2019, https://www.ams.org/journals/notices/201901/rnoti-p113.pdf
  13. ^ "Invited Section Lectures - Speakers | ICM 2018". www.icm2018.org. Archived from the original on 8 December 2018. Retrieved 30 November 2018.
  14. ^ plusmathsorg (9 August 2018), ICM 2018: Jack Thorne, retrieved 22 February 2019
  15. ^ Newton, James; Thorne, Jack A. (17 July 2020). "Symmetric power functoriality for holomorphic modular forms". arXiv:1912.11261 [math].
  16. ^ Newton, James; Thorne, Jack A. (15 September 2020). "Symmetric power functoriality for holomorphic modular forms, II". arXiv:2009.07180 [math].
  17. ^ "Breakthrough Prize – Winners Of The 2022 Breakthrough Prizes In Life Sciences, Fundamental Physics And Mathematics Announced". breakthroughprize.org. Retrieved 10 September 2021.
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