INFOMATMars 2019 KAREN UHLENBECK ER ÅRETS ABELPRISVINNER
“for her pioneering achievements in geometric partial differential equa- tions, gauge theory and integrable systems, and for the fundamental im- pact of her work on analysis, geometry and mathematical physics.”
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
EUROPEAN MATHEMATICAL Matematisk kalender SOCIETY 2019: Norsk Matematisk Forening oppfordrer sterkt alle Mars: sine medlemmer om å melde seg inn i European 19. Offentliggjøring av Abelprisen for 2019, Oslo Mathematical Society. Som medlem av NMF får Mai: man rabatt på årsmedlemskapet i EMS. Innmeld- 20.-22. Abelprisutdeling, Oslo ing og betaling av årsmedlemskap skjer på August: 5.-7. Nordisk konferanse i kombinatorikk, Køben- http://www.euro-math-soc.eu/ems_payment_ havn new/ems_payment_new.html
DEN 13. NORDISKE KONFERANSEN I KOMBINATORIKK, København, 5.-7. SURVEY BY THE EMS EDUCATION august COMMITTEE https://norcom2019.math.aau.dk Dear Presidents, Student transition from school-level mathematics Dette er en konferanse i en serie, der det er en kon- to university-level mathematics, often referred to feranse hvert tredje år. Temaer er kombinatorikk, as the secondary-tertiary transition (STT) is an kodeteori, diskret matematikk. Plenumsforedrag enduring, complicated and multi-faceted process. ved Kathie Cameron, Jack Edmonds og Olav STT is a long-standing issue of concern, which Geil. has merited significant attention in mathemat- ics education research and practice. At its 2018 meeting in Cyprus, the EMS Education Commit- tee recognized that our knowledge about successful ways of deal- Utlysninger ing with STT is still insufficient and that moving forward requires a large-scope effort on the part ABELSTIPEND 2019/2020 of all parties involved, including mathematics lecturers, school teachers, education research- Hvert år deler Norsk Matematisk Forening ut Abel- ers, policymakers and students in transition. As stipend til studenter opptatt ved masterprogram i part of this effort, the Committee is conducting matematiske fag ved norske læresteder. Stipendet a survey among mathematicians. The goal of the har som formål å stimulere lovende studenter til survey is to collect videre studier og forskning i matematiske fag, ved and report to the mathematics community infor- å dekke utgifter i forbindelse med kortere/lengre mation needed in order to devise national and in- opphold ved et utenlandsk lærested. ternational actions that can essentially improve the state of the art with respect to STT. Søknadsfristen er 15. april, og det kan da søkes om We would be thankful to you if you distributed midler for studieåret 2019/2020. Søknad sendes til the survey below among the members of your [email protected]. For mer infor- national mathematical society. The completion of masjon, se https://web.matematikkforeningen.no/ the survey takes about 15 minutes. The survey is aktiviteter/ open until September 15, 2019.
https://docs.google.com/forms/d/e/1FAIpQLSd cxoDW63m1h7nmdacQkhtWS8cGHH84K4a8 OU-fWVnqIEuGJA/viewform NYHETER
For more background information about STT, we OLA BRATTELI AND HIS DIA- refer to GRAMS http://euro-math-soc.eu/sites/default/files/STT-sur- vey-%2015-02-2019.pdf https://arxiv.org/abs/1903.01524
With kind regards, This article discusses the life and work of Pro- Volker Mehrmann,President of the EMS fessor Ola Bratteli (1946--2015). Family, fellow students, his advisor, colleagues and coworkers review aspects of his life and his outstanding HAR DU ET EKSEMPLAR AV PRO- mathematical accomplishments. CEEDINGS FRA ICM I OSLO 1936? Hilsen IMU ønsker å komplettere sitt arkiv av fysiske ek- Magnus Landstad semplarer av proceedings fra de internasjonale kongressene, og skriver:
As you know, the IMU Archive is located in the IMU Secretariat in Berlin. It is our goal to collect Nyheter all IMU related material in the IMU Archive. While we have scanned copies of all proceedings of all the ICMs starting from 1893, we do not possess all ANDREAS ALBERG, OSLO hardcopies of all proceedings. KATEDRALSKOLE, VANT Thus we would like to inquire our members if you ABELKONKURRANSEN have a physical copy of the proceedings of some of the early ICMs, and if you would be willing to – Laginnsatsen var veldig god i år, det var jo donate them to us. We can cover the shipping ex- bare to poeng som skilte oss tre i toppen. Resul- penses. tatet er noe av det sterkeste i finalen noen sinne, The missing proceedings are: nå har jeg tro på at vi skal greie å hevde oss i 1893 Chicago OL, sier vinner Andreas Alberg, som også vant 1893 The Evanston Colloquium Abelkonkurransen i fjor. 1897 Zurich Andreplassen gikk til Erik Mingjun Ma fra 1900 Paris Trondheim katedralskole, og Thomas Thrane 1904 Heidelberg fra samme skole fikk tredjeplassen. Fjerdeplas- 1912 Cambridge (UK) sen gikk til Erik Mjaanes fra Oslo International 1920 Strasbourg School, femteplassen til Olav Hellebust Haaland 1924 Toronto fra Fagerlia videregående skole og sjetteplas- 1928 Bologna sen til Jon-Magnus Rosenblad fra Valler vide- 1932 Zurich regående skole. 1936 Oslo PGS Utfordrerprisen gikk til den unge lovende 1962 Stockholm [vols. 2-4 missing] Zejia He fra Oslo International School. Hennes 1966 Moscow [vols. 2-4 missing] lave alder og solide resultater gjør at hun er en For further inquires, please contact the IMU Ar- kandidat som har potensialet og kunnskapen til å chivist, Ms Birgit Seeliger
ABELPRISEN 2019 TIL only of isolated points, is in higher dimensions KAREN UHLENBECK replaced by a set of codimension 3. The methods used in these revolutionary papers Karen Keskulla Uhlenbeck is a founder of modern are now in the standard toolbox of every geom- Geometric Analysis. Her perspective has perme- eter and analyst. They have been applied with ated the field and led to some of the most dramatic great success in many other partial differential advances in mathematics in the last 40 years. equations and geometric contexts. In particular, Geometric analysis is a field of mathematics where the bubbling phenomenon appears in many works techniques of analysis and differential equations are in partial differential equations, in the study of the weaved with the study of geometrical and topologi- Yamabe problem, in Gromov’s work on pseudo- cal problems. Specifically, one studies objects such holomorphic curves, and also in physical applica- as curves, surfaces, connections and fields which tions of instantons, especially in string theory. are critical points of functionals representing geo-  metric quantities such as energy and volume. For Gauge theory and Yang-Mills equations. example, minimal surfaces are critical points of the After hearing a talk by Atiyah in Chicago, Uh- area and harmonic maps are critical points of the lenbeck became interested in gauge theory. She Dirichlet energy. Uhlenbeck’s major contributions pioneered the study of Yang-Mills equations from include foundational results on minimal surfaces a rigorous analytical point of view. Her work and harmonic maps, Yang-Mills theory, and inte- formed a base of all subsequent research in the grable systems. area of gauge theory. Gauge theory involves an auxiliary vector bundle over a Riemannian mani- Minimal surfaces and bubbling analysis. fold. The basic objects of study are connections An important tool in global analysis, preceding the on this vector bundle. After a choice of a triviali- work of Uhlenbeck, is the Palais-Smale compact- sation (gauge), a connection can be described by ness condition. This condition, inspired by earlier a matrix valued 1-form. Yang-Mills connections work of Morse, guarantees existence of minimis- are critical points of gauge-invariant functionals. ers of geometric functionals and is successful in Uhlenbeck addressed and solved the fundamental the case of 1-dimensional domains, such as closed question of expressing Yang-Mills equations as geodesics. an elliptic system, using the so-called Coulomb Uhlenbeck realised that the condition of Palais- gauge. This was the starting point for both Uh- Smale fails in the case of surfaces due to topologi- lenbeck’s celebrated compactness theorem for p cal reasons. The papers of Uhlenbeck, coauthored connections with curvature bounded in L , and with Sacks, on the energy functional for maps of for her later results on removable singularities surfaces into a Riemannian manifold, have been ex- for Yang-Mills equations defined on punctured tremely influential and describe in detail what hap- balls. The regularity theory for Yang-Mills equa- pens when the Palais-Smale condition is violated. A tions in higher dimensions was carried out much minimising sequence of mappings converges out- later by Gang Tian and Terence Tao. Uhlenbeck’s side a finite set of singular points and by using res- compactness theorem was crucial in non abelian caling arguments, they describe the behaviour near Hodge theory and, in particular, in the proof of the singularities as bubbles or instantons, which are the properness of Hitchin’s map and Corlette’s the standard solutions of the minimising map from important result on the existence of equivariant the 2-sphere to the target manifold. harmonic mappings. In higher dimensions, Uhlenbeck in collaboration Another major result of Uhlenbeck is her joint with Schoen wrote two foundational papers on work with Yau on the existence of Hermitian minimising harmonic maps. They gave a profound Yang-Mills connections on stable holomorphic understanding of singularities of solutions of non- vector bundles over complex n-manifolds, gener- linear elliptic partial differential equations. The alising an earlier result of Donaldson on complex singular set, which in the case of surfaces consists surfaces. This result of Donaldson-Uhlenbeck- ABELPRISEN 2019
Yau links developments in differential geometry LITT OM KAREN UHLENBECK and algebraic geometry, and is a foundational result for applications of heterotic strings to particle phys- Karen Uhlenbeck (born August 24, 1942) grad- ics. uated from the University of Michigan in 1964. Uhlenbeck’s ideas laid the analytic foundations for She received her Ph.D. from Brandeis Univer- the application of gauge theory to geometry and sity in 1968 with a thesis on The Calculus of topology, to the important work of Taubes on the Variations and Global Analysis. Uhlenbeck gluing of self-dual 4- manifolds, to the ground- has made “pioneering contributions to global breaking work of Donaldson on gauge theory and analysis and gauge theory that resulted in ad- 4- dimensional topology, and to many other works vances in mathematical physics and the theory in this area. The book of Uhlenbeck and Dan Freed of partial differential equations.” She has taught on “Instantons and 4-Manifold Topology” instruct- at MIT, Berkeley, the University of Illinois in ed and inspired a generation of differential geom- both Champaign-Urbana and Chicago, and eters. She continued to work in this area, and in since 1988 has held the Third Sid W. Richard- particular had important results with Lesley Sibner son Foundation Regents’ Chair in Mathematics and Robert Sibner. at the University of Texas. She was a MacAr- thur Fellow in 1983, and has been elected to Integrable systems and harmonic mappings. the American Academy of Arts and Sciences The study of integrable systems has its roots in 19th (1985) and the National Academy of Sciences century classical mechanics. Using the language of (1986). On December 1, 2000, she received a gauge theory, Uhlenbeck and Hitchin realised that National Medal of Science for “special recog- harmonic mappings from surfaces to homogene- nition by reason of [her] outstanding contribu- ous spaces come in 1-dimensional parametrised tions to knowledge” in the area of mathemat- families. Based on this observation, Uhlenbeck ics. She has also served as Vice-President of the described algebraically harmonic mappings from American Mathematical Society. In 1990 she spheres into Grasmannians relating them to an in- became only the second woman (after Emmy finite dimensional integrable system and Virasoro Noether in 1932) to give a Plenary Lecture at an actions. This seminal work lead to a series of fur- International Congress of Mathematics. ther foundational papers by Uhelenbeck and Chuu- Lian Terng on the subject, and the creation of an Uhlenbeck is a active and fruitful school. co-founder of the The impact of Karen Uhlenbeck’s pivotal work IAS/Park City goes beyond geometric analysis. A highly influen- Mathematics In- tial early article was devoted to the study of regu- stitute and the pro- larity theory of a system of non-linear elliptic equa- gram for Women tions, relevant to the study of the critical map of and Mathematics higher order energy functionals between Riemann- in Princeton. In ian manifolds.This work extends previous results 2007 she received by Nash, De Giorgi and Moser on regularity of so- the AMS Steele lutions of single non-linear equations to solutions Prize for a Semi- of systems. nal Contribution Karen Uhlenbeck’s pioneering results have had to Mathematical fundamental impact on contemporary analysis, ge- Research for her ometry and mathematical physics, and her ideas foundational con- and leadership have transformed the mathematical tributions in ana- landscape as a whole. lytic aspects of mathematical gauge theory that appeared in two papers in the Communications in Mathematical Physics in 1982.