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INFOMATMars 2018

ROBERT P. LANGLANDS ER ÅRETS ABELPRISVINNER

Robert P. Langlands, Institute of Advanced Study, Princeton, USA, er tildelt Abelprisen for 2018 for “sitt visjonære program som knytter sammen representasjonsteori og tallteori”.

INFOMAT kommer ut med 11 nummer i året og gis ut av Norsk Matematisk Forening. Deadline for neste utgave er alltid den 15. i neste måned. Stoff til INFOMAT sendes til arnebs at math.uio.no Foreningen har hjemmeside http://www.matematikkforeningen.no/ Ansvarlig redaktør er Arne B. Sletsjøe, Universitetet i Oslo. ARRANGEMENTER

Matematisk kalender TOPOLOGIMØTE, Oslo, 29.-30. mai 2018 2018: April: On 29-30 May 2018 there will be a topology meet- 16.-20. Sheaves, curves and moduli, Stavanger ing at the University of Oslo covering a broad Mai: range of topics including topological Hochschild 22. Abelprisutdeling, Oslo homology, motivic homotopy theory, symplec- 23. Abelforelesningene, Oslo tic geometry, and low-dimensional geometry. So Cecilia 25.-27. NORDAN-konferanse, Stavanger far, the meeting will feature lectures by: Karlsson, Raphael Zentner, Emanuele Dotto, 29.-30. Topologimøte, Oslo Kristian Moi, Martin Frankland, Grigory Juni: Garkusha. 18.-22. Nordfjordeid Summer school 2018: Combi- natorics and Hodge theory, Nordfjordeid Please visit the meeting’s website https://sites.google.com/site/topologymeetinguio/ September: 13.-14. Nasjonalt matematikermøte, Bergen for more information Desember: 6.-8. Enumeration and Moduli, Oslo

WORKSHOP: NORDFJORDEID SUMMER SHEAVES, CURVES AND MODULI, SCHOOL 2018: COMBINATORICS Stavanger, 16.-20. april 2018 AND HODGE THEORY, Nordfjord- eid, 18.-22. juni 2018 Se webside: http://sheaves.ux.uis.no/workshop2018/ The aim of the sum- mer school is to pro- vide an introduction to the recent advanc- NORDAN, Stavanger, 25.-27. mai 2018 es in combinatorics and representation NORDAN is an annual conference in theory and in par- complex analysis and geometry, and is the largest ticular their interaction with algebraic geometry. meeting place for the Nordic research groups work- The school is aimed at phd students (as well as ing in this branch of mathematics. In addition, the advanced master students and early postdocs) conference attracts attendees from outside the Nor- with a general background in algebra, and with dic region. interests in algebra, geometry or topology. There Speakers: Séverine Biard (Reykjavík), Filippo will be three lecture series and extensive problem Bracci (Roma), Samuele Mongodi (Milano), sessions. Stéphanie Nivoche (Nice), David Witt Nyström Speakers: Petter Brändén (KTH), June Huh (Göteborg), Lars Simon (NTNU), Tuyen Trung (IAS/Princeton), Nicholas Proudfoot (Oregon) Truong (Oslo), Tat Dat Tô (Toulouse), Avgust For more information, se the website: http://www. Tsikh (Krasnoyarsk), Jan Wiegerinck (Amster- mn.uio.no/math/english/research/groups/alge- dam). bra/events/conferences/nordfjordeid2018/index. The registration is open at the website https://sites. html google.com/view/nordan-2018. The registration deadline is April 30, 1918. UTLYSNINGER

ENUMERATION AND MODULI, Oslo 6.-8. desember 2018 Nyheter

A conference in algebraic geometry on the occasion of Geir Ellingsrud’s 70th birthday. For further information, see: http://www.mn.uio. no/math/english/research/ groups/algebra/events/ conferences/Enumeration- andmoduli/index.html

Andreas Alberg sammen med kunnskaps- og integreringsminister Jan Tore Sanner (H) under premieutdelingen. Utlysninger Foto: Universitetsavisa, NTNU

ANDREAS ALBERG TIL TOPPS I STIPENDIAT/POSTDOC VED NTNU ABELKONKURRANSEN Ny stipendiat/postdoc stillling ledig ved IMF i Andreas Alberg, Fagerborg skole i Oslo vant Trondheim. Beskrivelse finnes på https://www. årets Abelkonkurranse. 14-åringen fikk 38 av 40 jobbnorge.no/ledige-stillinger/stilling/148547/ poeng og tok en klar seier. phd-fellowship-postdoctoral-fellowship-in-data- driven-modelling-of-moving-flexible-structures Resultater: Fristen for å søke er 26.mars.2018. 1) Andreas Alberg, Fagerborg skole, 10C, 38p 2) Bjørnar Gullikstad Hem, Nadderud vgs, 3D, 34p 3) Erik Ma, Trondheim katedralskole, 2-STD, ABELSTIPEND 2018/2019 31p 4) Luca S. Marino, St Paul’s school, U8, 28p 4) Philip Bergh Sveen, Nydalen vgs, 1STE, Hvert år deler Norsk Matematisk Forening ut Abel- 28p 6) Sigvart Brendberg, Kristen vgs Trønde- stipend til studenter opptatt ved masterprogram i lag, 3C, 27p 7) Thomas Agung Dibpa Anandita matematiske fag ved norske læresteder. Stipendet Thrane, Trondheim katedralskole, 2STA, 24p 8) har som formål å stimulere lovende studenter til Donny Chan, Møglestu vgs, 3STA, 23p 8) Anna videre studier og forskning i matematiske fag, ved Lyubarskaja, Trondheim katedralskole, 3IB, 23p å dekke utgifter i forbindelse med opphold ved 8) Espen Sund, Stavanger katedralskole, 3STA, et utenlandsk lærested. Vi deler typisk ut mellom 23p 11) Håvard Rognebakke Krogstie, Thora 10.000 og 50.000 kroner til stipendmottagerne. Storm vgs, 2STD, 18p 12) Amund Skretting Bergset, Asker vgs, 3STE, 17p Søknadsfristen er 16. april 2018, og det kan da søkes om midler for studieåret 2018/2019. Søknad sendes til [email protected]. For mer informasjon, se https://web.matematikkfore- ningen.no/aktiviteter/ ABELPRISEN

KOMITEENS BEGRUNNELSE: conjectures, such as the Ramanujan-Peterson and The Norwegian Academy of Science and Letters Selberg conjectures, and the Hasse-Weil conjec- has decided to award the for 2018 to ture for zeta functions. Robert P. Langlands Functoriality for reductive groups over number of the Institute of Advanced Study, Princeton, fields remains out of reach, but great progress has USA, for his visionary program connecting rep- been achieved by the work of many experts, in- resentation theory to . cluding the Fields medallists Drinfeld, Lafforgue The predicts the existence of and Ngô, all inspired by the guiding light of the a tight web of connections between automorphic Langlands program. New facets of the theory have forms and Galois groups. evolved, such as the Langlands conjectures over The great achievement of algebraic number the- local fields and function fields, and the geometric ory in the first third of the 20th century was class Langlands program. Langlands’s ideas have el- field theory. This theory is a vast generalisation of evated automorphic representations to a profound Gauss’s law of quadratic reciprocity. It provides role in other areas of mathematics, far beyond the an array of powerful tools for studying problems wildest dreams of early pioneers such as Weyl and governed by abelian Galois groups. The non- Harish-Chandra. abelian case turns out to be substantially deeper. Langlands, in a famous letter to André Weil in 1967, outlined a far-reaching program that revo- OM ROBERT P. LANGLANDS lutionised the understanding of this problem. (av Alex Bellos) In January 1967, Robert Langlands, a 30-year-old Langlands’s recognition that one should relate associate professor at Princeton, wrote a letter to representations of Galois groups to automorphic the great French mathematician André Weil, aged forms involves an unexpected and fundamental 60, outlining some of his new mathematical in- insight, now called Langlands functoriality. The sights. If you are willing to read it as pure specula- key tenet of Langlands functoriality is that au- tion I would appreciate that, he wrote. If not - I am tomorphic representations of a reductive group sure you have a waste basket handy. should be related, via L-functions, to Galois rep- Langlands’s modesty now reads like an almost resentations in a dual group. comic piece of understatement. His 17-page letter Jacquet and Langlands were able to establish a introduced a theory that created a whole new way first case of functoriality for GL(2), using the of thinking about mathematics: it suggested deep . Langlands’s work on base links between two areas, number theory and har- change for GL(2) proved further cases of func- monic analysis, that previously had been consid- toriality, which played a role in Wiles’s proof of ered unrelated. important cases of the Shimura-Taniyama-Weil In fact, so radical were his insight, and so rich the conjecture. mechanisms he suggested to bridge these mathe- The group GL(2) is the simplest example of a matical fields, that this letter began a project - the non-abelian reductive group. To proceed to the Langlands program - that has enlisted hundreds of general case, Langlands saw the need for a stable the world´s best mathematicians over the last fifty trace formula, now established by Arthur. Togeth- years. No other project in modern mathematics has er with Ngô’s proof of the so-called Fundamental as wide a scope, has produced so many deep re- Lemma, conjectured by Langlands, this had led sults, and has so many people working on it. As to the endoscopic classification of automorphic its depth and breadth has grown, the Langlands representations of classical groups, in terms of program is frequently described as a grand unified those of . theory of mathematics. Functoriality dramatically unifies a number of Robert Phelan Langlands was born in New West- important results, including the modularity of el- minster, greater Vancouver, Canada, in 1936. When liptic curves and the proof of the Sato-Tate con- he was nine, he moved to a small tourist town near jecture. It also lends weight to many outstanding ABELPRISEN the US border, where his parents had a shop selling ent Turkish. An enthusiastic learner of languages, building supply materials. He had no intention of he also speaks German and Russian. going to university until a teacher told him, in front Langlands returned to Yale where he developed of his classmates, that it would be a betrayal of his his twin ideas of functoriality and reciprocity and God-given talents. published them in Problems in the Theory of Au- Langlands enrolled at the University of British Co- tomorphic Forms (1970). In 1972 he returned to lumbia aged 16. He completed his bachelor´s degree Princeton as a professor at the Institute for Ad- in mathematics in 1957, and his master´s degree a vanced Study, where he has been ever since. year later. He moved to for his doc- Throughout the 1970s Langlands continued to torate, completing hís PhD thesis, Semi-groups and work on ideas within his program. In the mid- representations of Lie groups in his first year there. 1980s he turned attention to percolation and In his second year he began to study the work of the conformal invariance, problems from theoretical Norwegian , which would later become physics. In recent years he has been back look- central to his own research. ing at ideas that he pioneered such as one called In 1960, Langlands, joined “endoscopy”. as an instructor, where he rubbed shoulders with Langlands has won many awards, including the Selberg, as well as André Weil and Harish-Chan- first US National Academy of Sciences Award dra, all of whom were at the nearby Institute for in Mathematics in 1988 for his extraordinary vi- Advanced Study. He was especially influenced sion. He shared the 1996 Wolf Prize with Andrew by the work of Harish-Chandra on automorphic Wiles for his path blazing work. Other awards in- forms. Langlands was also learning other areas of clude the 2005 American Mathematical Society mathematics, such as , an area he Steel Prize, the 2006 Nemmers Prize in Mathe- was nudged into by his colleague Salomon Boch- matics and the 2007 in Mathematical ner, who encouraged him to give a course in it. In Sciences (with Richard Taylor). 1962, Langlands was appointed a member in the While at the UBC, aged 19, he married Charlotte Institute´s School of Mathematics. Lorraine Cheverie. He has four children with During the Christmas break of 1966 Langlands Charlotte, and several grandchildren. came up with the basic idea of “functoriality”, a Aged 81, he continues to work at the Institute mechanism for linking ideas in number theory to for Advanced Study, where he is now Emeritus those in automorphic forms. He bumped into Weil Professor, and where he occupies the same office in a corridor in the beginning of January 1967 and once used by . began to explain his discovery. Weil suggested he write up his thoughts in a letter. Langlands swiftly wrote the letter in longhand. Weil had the letter typed up and it was widely circulated among mathematicians. Over the next few years the letter provided many of them with many new, deep and interesting problems and as more people joined the project to prove his conjectures the en- terprise became known as the Langlands program. - There were some fine points that were right that rather surprise me to this day, Langlands later said about the letter. -There was evidence that these L- functions were good but that they would have these consequences for algebraic number theory was by no means certain. Langlands spent the year 1967-68 at the Middle East Technical University in Ankara. He speaks flu-