DOCSLIB.ORG

Max-Planck-Institut FüR Mathematik

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Max-Planck-Institut FüR Mathematik Max-Planck-Institut fiir Mathematik Historical Notes on the New Research Institute at Bonn Norbert Schappacher Ich beginne weit vor mir; denn niemand sollte sein Leben be- schreiben, der nicht die Geduld aufbringt, vor dem Datieren der eigenen Existenz wenigstens der H~lfte seiner Grof3eltern zu ge- denken. G~inter Grass, Die Blechtrommel It seems wise to follow this advice with respect to the tition seems to have been decisive in his earlier refusal, young Max-Planck-Institut f~ir Mathematik (MPI) at at the end of 1932, to go to Princeton. 3 Abraham Bonn: not to start describing its own short existence Flexner, the founder of the IAS and author of a report before saying something about at least half of its on European universities, had stopped over in Gbt- grandparents. The MPI began to exist "on paper" in tingen in the summer of 1932, and explained his 1981, and was established as a building on January 20, scheme for the Institute to Weyl. 4 But only after the 1982. Thus, a mere description of its three-year exis- political turnover of 1933 did the attraction of an in- tence cannot bring out its roots and perspectives. Let dependent IAS abroad win out over the politically us begin instead by looking at the most famous (and dominated university department of G6ttingen. strong-going) grandparent. Weyl certainly never regretted his decision to join the IAS. 5 But maybe his influence is reflected in some of the developments of the IAS during the thirties. For The Institute example, while Flexner's original vision of the institute was based on the idea of lonely intellectual heroes In October 1933, Hermann Weyl finally decided to working away in splendid isolation, the School of leave GOttingen to accept a chair at the Institute for Mathematics at the IAS soon began to invite young, Advanced Study (IAS) in Princeton. He was disgusted promising scholars whose reputations (and job situa- with the new Nazi government which went against tions) were not as well established as those of the per- his democratic ideas (he had lived in Switzerland for manent members (so that inviting them carried a cer- 17 years), potentially threatened his Jewish wife (and tain risk). In this respect--and in many others--the children), and had within the space of one summer Norbert Schappacher managed to destroy almost completely what had been the mathematical centre of the world: the Mathema- tisches Institut at Gbttingen. Weyl wrote to the ministry in Berlin: "... While the universities in Germany are now undergoing fundamental changes, I am happy to join a research institute whose foundation was not little inspired by the precept of the traditional German university. ''1 This seemed to me a puzzling statement when I first read it, as I had always considered the unity of teaching and research to be one of the most important features of the "traditional German university." In fact, Weyl himself, in his postwar reflections on "Universities and Science in Germany, ''2 made it the first attribute in his description of the German university as it used to be. What is more, at G6ttingen Weyl had been espe- cially popular among the students, and a student pe- THE MATHEMATICAL INTELLIGENCER VOL. 7, NO. 2 9 1985Springer-Verlag New York 41 Hermann Weyl (left); and Friedrich Hirzebruch (1959) IAS set the standard for what is usually seen today as Kuiper and Tits as invited participants. The ministry the right way to stimulate mathematical research. gave a subsidy of 1000 DM. This contribution slowly Friedrich Hirzebruch was one of those young math- grew over the years. At the 1962 Arbeitstagung, for ex- ematicians who profited from an invitation to the IAS. ample, Hirzebruch still personally distributed 5000 DM His first stay there, 1952-54, left him with the idea among the 22 participants eligible for financial sup- that Germany, too, should have a centre for mathe- port, and collected their signature on the receipts. The matical research, beyond the various university de- direct state subsidy to the Arbeitstagung finally re- partments. But this idea took a long time to materialize mained constant at the sum of 6000 DM. But then, as on a large scale. At first only small steps could be we shall see, there were other ways to finance the taken. ever-growing yearly meeting. In 1983, for example, the state subsidy represented roughly one sixth of the total expenses. Beginnings of the Arbeitstagung In 1957, the big Arbeitstagung we know today was in no way anticipated. At the meetings, the subjects were "When I came to Bonn in 1956, Professor Peschl sug- still fairly close to Hirzebruch's own research interests, gested I should apply for funds from the ministry to not nearly as varied as they are today, and the same organize small conferences. When I expressed this participants might well have gathered by accident at wish while negotiating with the ministry on the oc- the IAS. In Bonn, however, they were meeting for only casion of an offer from another university, the answer a week; inviting mathematicians for longer stays was was 'of course, Herr Professor,' and the money was not yet possible (except for occasional visiting posi- granted. I then wanted to organize a meeting every tions that Hirzebruch managed to obtain. 7) year, with as little administrative work and prepara- The situation was not to change for some time, al- tion as possible. Thus the idea arose . to let the though a flurry of activity, with a view to promoting program be decided by the participants as the confer- mathematical research, was going on in Germany at ence went on. This proved very useful because in this the end of the fifties. To understand this we have to way the most recent results could be presented. ''6 go back several years and--leaving Bonn for a mo- This is how Hirzebruch recalls the beginnings of the ment-focus on a lonely mansion above the small vil- Bonn MathematischeArbeitstagung. The first Tagung was lage of Oberwolfach in the Black Forest, where Wil- held in 1957 with Atiyah, Grauert, Grothendieck, helm S~iss was already having definite ideas about a 42 THE MATHEMATICAL INTELLIGENCER VOL. 7, NO. 2, 1985 German research institute in mathematics while Hir- After Stiss's death, Hellmuth Kneser (Tiibingen) zebruch was still a student at Miinster. took action to secure the further existence of Ober- wolfach, especially with the Ministry of Culture of the Oberwolfach and EUROMAT Land of Baden-Wi~rttemberg, and he asked Hirze- bruch to find out about the willingness of the federal Wilhelm Stiss (1895-1958) appears to have been ministry of the interior to provide help. uniquely talented in efficiently promoting the cause of At the same time things were moving on the Euro- German mathematicians during World War II. Al- pean scene: the European union for the peaceful use though he was probably not well-liked by parts of the of nuclear technology, EURATOM, had been founded Hitler administration, he was tremendously popular in March of 1957. Soon afterwards, a group of Euro- among his colleagues. During the war he was presi- pean mathematicians tried to find out about the pos- dent of the DMV (Deutsche Mathematiker-Vereinigung-- sibilities of creating a European mathematical institute German Mathematical Society), rector of the Freiburg (to be called EUROMAT) within the EURATOM or- University, and president of the Rektorenkonferenz (as- ganization, or within a whole European university sembly of all the rectors of German universities). Thus sponsored by EURATOM. Hirzebruch and H. Kneser he got to know Bernhard Rust, Hitler's minister of ed- were among the nine mathematicians who gathered in ucation, and apparently became very friendly with Brussels in April 1958 to pass a Projet de crdation d'un him. But Rust had already taken to alcohol by this institut europden de recherches mathdmatiques dans le cadre time, and was losing more and more real power as de I'EURATOM. However, this project never came special agencies for all kinds of things were being close to realization. created, restricting the competencies of the traditional Slightly after this project, on July 4, 1958, the Institut ministries. So it was much more important for Stiss to des hautes dtudes scientifiques (IHES), a French version have the support of Ministerialdirektor Mentzel and of the IAS, was founded (on paper; the territory at Werner Osenberg. Mentzel, an old Nazi from G6t- Bures-sur-Yvette was purchased later), with financial tingen who had soon become a high official in Rust's support from nine French companies as well as FIAT ministry, was president of Deutsche Forschungsgemein- (Italy) and EURATOM. schaft (DFG, see below), and was directly involved Then, still in July 1958, Hirzebruch perceived a cer- with the wartime organization of scientific research. tain interest on the part of the federal ministry of the Osenberg was the instigator and principal organizer of interior to do something for mathematical research. the so-called Osenberg-Aktion, which got engineers and Thus--also under the influence of the foundation of scientists off the battlefield to do research supposedly relevant to the war: kriegswichtig. Wilhelm Siiss (1957) In the fall of 1942, Stiss managed to obtain financial support for the publication of kriegswichtige mathemat- ical literature, but he was already thinking in terms of a national mathematical research institute. When an offer from G6ttingen was shaping up in the spring of 1944, officials in Southwest Germany (Baden) were alarmed by the prospect of the influential Siiss leaving their region. This sped matters up considerably, and as of September 1, 1944, the new institute was able to begin functioning in the Lorenzenhof near Oberwol- fach.
Load more

Recommended publications
  • Marcel Berger Remembered
    Marcel Berger Remembered Claude LeBrun, Editor and Translator Gérard Besson EDITOR’S NOTE. Claude LeBrun has kindly assembled this memorial for Marcel Berger. This month also Marcel Berger,1 one of the world’s leading differential marks the conference “Riemannian Geometry Past, geometers and a corresponding member of the French Present and Future: An Homage to Marcel Berger” at Academy of Sciences for half a century, passed away on IHÉS. October 15, 2016, at the age of eighty-nine. Marcel Berger’s contributions to geometry were both broad and deep. The classification of Riemannian holo- nomy groups provided by his thesis has had a lasting impact on areas ranging from theoretical physics to alge- braic geometry. His 1960 proof that a complete oriented even-dimensional manifold with strictly quarter-pinched positive curvature must be a topological sphere is the Claude LeBrun is professor of mathematics at Stony Brook Univer- sity. His email address is [email protected]. Gérard Besson is CNRS Research Director at Institut Fourier, Uni- For permission to reprint this article, please contact: versité Grenoble, France. His email address is g.besson@ujf [email protected]. -grenoble.fr. DOI: http://dx.doi.org/10.1090/noti1605 1Pronounced bare-ZHAY. December 2017 Notices of the AMS 1285 research director by the CNRS. He served as president of the French Mathematical Society (SMF) during the period of 1979–80 and in this capacity helped oversee the foundation of the International Center for Mathematical Workshops (CIRM) in Luminy. In 1985 he then became director of the Institute for Higher Scientific Studies (IHÉS) in Bures-sur-Yvette, a position in which he served until 1993, when he was succeeded by his former student Jean-Pierre Bourguignon.
    [Show full text]
  • All That Math Portraits of Mathematicians As Young Researchers
    Downloaded from orbit.dtu.dk on: Oct 06, 2021 All that Math Portraits of mathematicians as young researchers Hansen, Vagn Lundsgaard Published in: EMS Newsletter Publication date: 2012 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Hansen, V. L. (2012). All that Math: Portraits of mathematicians as young researchers. EMS Newsletter, (85), 61-62. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Editorial Obituary Feature Interview 6ecm Marco Brunella Alan Turing’s Centenary Endre Szemerédi p. 4 p. 29 p. 32 p. 39 September 2012 Issue 85 ISSN 1027-488X S E European M M Mathematical E S Society Applied Mathematics Journals from Cambridge journals.cambridge.org/pem journals.cambridge.org/ejm journals.cambridge.org/psp journals.cambridge.org/flm journals.cambridge.org/anz journals.cambridge.org/pes journals.cambridge.org/prm journals.cambridge.org/anu journals.cambridge.org/mtk Receive a free trial to the latest issue of each of our mathematics journals at journals.cambridge.org/maths Cambridge Press Applied Maths Advert_AW.indd 1 30/07/2012 12:11 Contents Editorial Team Editors-in-Chief Jorge Buescu (2009–2012) European (Book Reviews) Vicente Muñoz (2005–2012) Dep.
    [Show full text]
  • Life and Work of Friedrich Hirzebruch
    Jahresber Dtsch Math-Ver (2015) 117:93–132 DOI 10.1365/s13291-015-0114-1 HISTORICAL ARTICLE Life and Work of Friedrich Hirzebruch Don Zagier1 Published online: 27 May 2015 © Deutsche Mathematiker-Vereinigung and Springer-Verlag Berlin Heidelberg 2015 Abstract Friedrich Hirzebruch, who died in 2012 at the age of 84, was one of the most important German mathematicians of the twentieth century. In this article we try to give a fairly detailed picture of his life and of his many mathematical achievements, as well as of his role in reshaping German mathematics after the Second World War. Mathematics Subject Classification (2010) 01A70 · 01A60 · 11-03 · 14-03 · 19-03 · 33-03 · 55-03 · 57-03 Friedrich Hirzebruch, who passed away on May 27, 2012, at the age of 84, was the outstanding German mathematician of the second half of the twentieth century, not only because of his beautiful and influential discoveries within mathematics itself, but also, and perhaps even more importantly, for his role in reshaping German math- ematics and restoring the country’s image after the devastations of the Nazi years. The field of his scientific work can best be summed up as “Topological methods in algebraic geometry,” this being both the title of his now classic book and the aptest de- scription of an activity that ranged from the signature and Hirzebruch-Riemann-Roch theorems to the creation of the modern theory of Hilbert modular varieties. Highlights of his activity as a leader and shaper of mathematics inside and outside Germany in- clude his creation of the Arbeitstagung,
    [Show full text]
  • EMS Newsletter September 2012 1 EMS Agenda EMS Executive Committee EMS Agenda
    NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Editorial Obituary Feature Interview 6ecm Marco Brunella Alan Turing’s Centenary Endre Szemerédi p. 4 p. 29 p. 32 p. 39 September 2012 Issue 85 ISSN 1027-488X S E European M M Mathematical E S Society Applied Mathematics Journals from Cambridge journals.cambridge.org/pem journals.cambridge.org/ejm journals.cambridge.org/psp journals.cambridge.org/flm journals.cambridge.org/anz journals.cambridge.org/pes journals.cambridge.org/prm journals.cambridge.org/anu journals.cambridge.org/mtk Receive a free trial to the latest issue of each of our mathematics journals at journals.cambridge.org/maths Cambridge Press Applied Maths Advert_AW.indd 1 30/07/2012 12:11 Contents Editorial Team Editors-in-Chief Jorge Buescu (2009–2012) European (Book Reviews) Vicente Muñoz (2005–2012) Dep. Matemática, Faculdade Facultad de Matematicas de Ciências, Edifício C6, Universidad Complutense Piso 2 Campo Grande Mathematical de Madrid 1749-006 Lisboa, Portugal e-mail: [email protected] Plaza de Ciencias 3, 28040 Madrid, Spain Eva-Maria Feichtner e-mail: [email protected] (2012–2015) Society Department of Mathematics Lucia Di Vizio (2012–2016) Université de Versailles- University of Bremen St Quentin 28359 Bremen, Germany e-mail: [email protected] Laboratoire de Mathématiques Newsletter No. 85, September 2012 45 avenue des États-Unis Eva Miranda (2010–2013) 78035 Versailles cedex, France Departament de Matemàtica e-mail: [email protected] Aplicada I EMS Agenda .......................................................................................................................................................... 2 EPSEB, Edifici P Editorial – S. Jackowski ........................................................................................................................... 3 Associate Editors Universitat Politècnica de Catalunya Opening Ceremony of the 6ECM – M.
    [Show full text]
  • The Convexity Radius of a Riemannian Manifold
    THE CONVEXITY RADIUS OF A RIEMANNIAN MANIFOLD JAMES DIBBLE Abstract. The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver’s method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius. 1. Introduction A subset X of a Riemannian manifold M is strongly convex if any two points in X are joined by a unique minimal geodesic γ : [0, 1] → M and each such geodesic maps entirely into X. It is well known that there exist functions inj, r : M → (0, ∞] such that, for each p ∈ M, inj(p) = max R> 0 exp | is injective for all 0 <s<R p B(0,s) and r(p) = max R> 0 B(p,s) is strongly convex for all 0 <s<R , where B(0,s) ⊂ TpM denotes the Euclidean ball of radius s around the origin. The number inj(p) is the injectivity radius at p, and r(p) is the convexity radius at p. The conjugate radius at p is defined, as is customary, to be rc(p) = min T > 0 ∃ a non-trivial normal Jacobi field J along a unit-speed geodesic γ with γ(0) = p, J(0) = 0, and J(T )=0 , and the focal radius at p is introduced here to be rf (p) = min T > 0 ∃ a non-trivial normal Jacobi field J along a unit-speed geodesic γ with γ(0) = p, J(0) = 0, and kJk′(T )=0 .
    [Show full text]
  • Géométrie De Riemann
    1/9 Data Géométrie de Riemann Thème : Géométrie de Riemann Origine : RAMEAU Domaines : Mathématiques Autres formes du thème : Géométrie elliptique Géométrie riemannienne Riemann, Géométrie de Notices thématiques en relation (7 ressources dans data.bnf.fr) Termes plus larges (4) Espaces généralisés Géométrie différentielle Géométrie différentielle globale Géométrie non-euclidienne Termes plus précis (2) Géométrie riemannienne globale Surfaces à courbure constante Termes reliés (1) Géométrie non-riemannienne data.bnf.fr 2/9 Data Documents sur ce thème (87 ressources dans data.bnf.fr) Livres (87) Utilisation du calcul , Claude Jeanperrin, Paris : Semi-riemannian geometry , Stephen C. Newman, tensoriel dans les Ellipses , DL 2019 (2019) Hoboken, NJ : Wiley géométries riemanniennes (2019) Golden ratio in the elliptical , Daniel Favre (biologiste), Initiation à la géométrie de , François Rouvière, Paris : honeycomb [S.l.] : [Daniel Favre] , cop. Riemann Calvage & Mounet , DL (2016) [2016] (2016) 2016 Spectral theory in , Olivier Lablée, Zuricḧ : A spinorial approach to , Zuricḧ : European Riemannian geometry European mathematical Riemannian and conformal mathematical society , cop. (2015) society , cop. 2015 geometry 2015 (2015) Tensors and Riemannian , Nail' Khairullovich An introduction to , Leonor Godinho, Cham : geometry Ibragimov, Berlin : De Riemannian geometry Springer , 2014 (2015) Gruyter : Higher education (2014) press , cop. 2015 The geometrization , Gang Tian, John Morgan Geometric control theory , Cham : Springer
    [Show full text]
  • FOUR VERTEX THEOREM and ITS CONVERSE Dennis Deturck, Herman Gluck, Daniel Pomerleano, David Shea Vick
    THE FOUR VERTEX THEOREM AND ITS CONVERSE Dennis DeTurck, Herman Gluck, Daniel Pomerleano, David Shea Vick Dedicated to the memory of Björn Dahlberg Abstract The Four Vertex Theorem, one of the earliest results in global differential geometry, says that a simple closed curve in the plane, other than a circle, must have at least four "vertices", that is, at least four points where the curvature has a local maximum or local minimum. In 1909 Syamadas Mukhopadhyaya proved this for strictly convex curves in the plane, and in 1912 Adolf Kneser proved it for all simple closed curves in the plane, not just the strictly convex ones. The Converse to the Four Vertex Theorem says that any continuous real- valued function on the circle which has at least two local maxima and two local minima is the curvature function of a simple closed curve in the plane. In 1971 Herman Gluck proved this for strictly positive preassigned curvature, and in 1997 Björn Dahlberg proved the full converse, without the restriction that the curvature be strictly positive. Publication was delayed by Dahlberg's untimely death in January 1998, but his paper was edited afterwards by Vilhelm Adolfsson and Peter Kumlin, and finally appeared in 2005. The work of Dahlberg completes the almost hundred-year-long thread of ideas begun by Mukhopadhyaya, and we take this opportunity to provide a self-contained exposition. August, 2006 1 I. Why is the Four Vertex Theorem true? 1. A simple construction. A counter-example would be a simple closed curve in the plane whose curvature is nonconstant, has one minimum and one maximum, and is weakly monotonic on the two arcs between them.
    [Show full text]
  • Max-Planck-Institut F¨Ur Mathematik Bonn
    Max-Planck-Institut fur¨ Mathematik Bonn Arbeitstagung 2009 9. Arbeitstagung der zweiten Serie Max-Planck-Institut fur¨ Mathematik Preprint Series 2009 (40) Arbeitstagung 2009 9. Arbeitstagung der zweiten Serie Max-Planck-Institut Mathematisches Institut fur¨ Mathematik der Universitat¨ Bonn Vivatsgasse 7 Endenicher Allee 60 53111 Bonn 53115 Bonn Germany Germany MPI 09-40 Contents List of Participants Program Lectures: M. Kontsevich Symplectic geometry of homological algebra A. Klemm Dualities and Symmetries in String Theory W. Ziller Manifolds of Positive Curvature A. Licata Categorical sl2-Actions P. Teichner The Kervaire Invariant Problem (after Hill, Hopkins and Ravenel) F. Oort Hecke Orbits G. Harder The Fundamental Lemma N. A’Campo Tete-ˆ a-T` eteˆ twists and geometric Monodromy Anton Mellit Elliptic dilogarithms and parallel lines W. Klingenberg Holomorphic Discs in the Space of Oriented Lines via Mean Curvature Flow and Applications W. Muller¨ Analytic Torsion and Cohomology of hyperbolic 3-manifolds D. Lebedev From archimedean L-factors to Topological Field Theories G. Mikhalkin Tropical Geometry T. Kobayashi Discontinuous Groups on pseudo-Riemannian Spaces M. Belolipetsky Counting Lattices M. Bourdon Quasi-conformal geometry and word hyperbolic Coxeter groups O. Lorscheid Geometry over the field with one element Name First Name Institution A'Campo Norbert Universität Basel Ageev Oleg MPIM Ahmadian Razieh University of Teheran Alexandrov Alexander Intitute for Central Sciences RAS Amerik Ekaterina MPIM/Université Paris-Sud Angel
    [Show full text]
  • Local Estimate on Convexity Radius and Decay of Injectivity Radius in A
    LOCAL ESTIMATE ON CONVEXITY RADIUS AND DECAY OF INJECTIVITY RADIUS IN A RIEMANNIAN MANIFOLD SHICHENG XU Abstract. In this paper we prove the following pointwise and curvature- free estimates on convexity radius, injectivity radius and local behavior of geodesics in a complete Riemannian manifold M: 1 (1) the convexity radius of p, conv(p) ≥ min{ 2 inj(p), foc(Binj(p)(p))}, where inj(p) is the injectivity radius of p and foc(Br(p)) is the focal radius of open ball centered at p with radius r; (2) for any two points p, q in M, inj(q) ≥ min{inj(p), conj(q)}−d(p, q), where conj(q) is the conjugate radius of q; 1 (3) for any 0 <r< min{inj(p), 2 conj(Binj(p)(p))}, any (not necessar- ily minimizing) geodesic in Br(p) has length ≤ 2r. We also clarify two different concepts on convexity radius and give ex- amples to illustrate that the one more frequently used in literature is not continuous. 1. Introduction Let M n be a complete Riemannian manifold of dimension n without boundary. The injectivity radius of a point p M, inj(p), is defined to be the supremum of radius of open metric balls centered∈ at p that contains no cut points of p. The conjugate radius of p, conj(p), is defined as the supre- mum of the radius of open balls centered at the origin of the tangent space TpM which contains no critical point of exponential map expp : TpM M. An open set U M is called convex, if any two points in U are joined→ by a unique minimal⊂ geodesic in M and its image lies in U.
    [Show full text]
  • Preface Issue 3-2012
    Jahresber Dtsch Math-Ver (2012) 114:117–118 DOI 10.1365/s13291-012-0050-2 PREFACE Preface Issue 3-2012 Hans-Christoph Grunau Published online: 24 July 2012 © Deutsche Mathematiker-Vereinigung and Springer-Verlag 2012 Although the problem of finding periodic solutions of Hamiltonian systems is easily explained, it is in many cases quite difficult to solve and in most cases still open. This question—among others—gave rise to the development of symplectic geome- try. In this context, Alan Weinstein conjectured in 1978 that every hypersurface of the standard symplectic R2n of so called contact type admits a closed orbit. Being of contact type generalises the notion of an object being star-shaped. The survey ar- ticle of Frederica Pasquotto provides “A short history of the Weinstein conjecture”. Some cases of this conjecture have been solved while in its full generality, it is still open. Herbert von Kaven from Detmold in North Rhine-Westphalia established the eponymous foundation which awards usually every year the von Kaven prize to a young and promising mathematician. The decision is made by the German Research Foundation’s (DFG) mathematics review board. During the 2011 annual meeting of “Deutsche Mathematiker-Vereinigung”, that year’s von Kaven prize was awarded to the DFG-Heisenberg-fellow Christian Sevenheck. His field of research is complex al- gebraic geometry and in particular mirror symmetry. Sometimes it is possible to find correspondences between two seemingly completely different situations, the so called A-model and the B-model, which may arise e.g. in algebraic geometry and string the- ory respectively.
    [Show full text]
  • Geometry of Positive Curvature the Work of Wolfgang Meyer
    GEOMETRY OF POSITIVE CURVATURE THE WORK OF WOLFGANG MEYER JOST ESCHENBURG Fifteen years ago, Detlef Gromoll gave a talk at M¨unster in hon- our of Wolfgang Meyer. He summarized what he considered Wolfgang Meyer’s most important achievements by the following four short state- ments, where M always denotes a complete n-dimensional Riemannian manifold with sectional curvature K and M˜ its universal covering. [1] “Most” compact M have infinitely many closed geodesics. [2] Every noncompact M with K > 0 is contractible. [3] There is an exotic 7-sphere with K ≥ 0. 1 ˜ Sn [4] 4 − ǫ ≤ K ≤ 1, n odd ⇒ M ≈ (“homeomorphic”). [1]-[3] are in joint papers with Detlef Gromoll, [4] with Uwe Abresch. I would like to add another result which puts [4] into a context: 1 ˜ Sn [5] 4 <K< 1 ⇒ M ≈ . This is the famous sphere theorem of Marcel Berger and Wilhelm Klin- genberg which was written up extremely carefully by Detlef Gromoll and Wolfgang Meyer. Their paper became the Springer Lecture Notes volume 55, “Riemannsche Geometrie im Großen”, “Riemannian geom- etry in the Large”, which is almost the title of this conference. Every differential geometer of my generation who knew some German learned Riemannian geometry from this textbook. The main theorem in [1] was also influenced by another research area of Wilhelm Klingenberg: closed Geodesics and the Morse theory of the free loop space of a compact manifold. Closed geodesics are the critical points of the energy function on the space LM of free loops λ : S1 → M. By Morse theory, the number of critical points of index k is bounded from below by the k-th Betti number bk.
    [Show full text]
  • Annual Report for the Fiscal Year July 1, 1982
    The Institute for Advanced Study Annual Report 1982/83 The Institute for Advanced Study Annual Report for the Fiscal Year July 1, 1982-June 30, 1983 The Institute for Advanced Study Olden Lane Princeton, New Jersey 08540 U.S.A. Printed by Princeton University Press Designed by Bruce Campbell It is fundamental to our purpose, and our Extract from the letter addressed by the express desire, that in the appointments to Founders to the Institute's Trustees, the staff and faculty, as well as in the dated June 6, 1930, Newark, New admission of workers and students, no Jersey. account shall be taken, directly or indirectly, of race, religion or sex. We feel strongly that the spirit characteristic of America at its noblest, above all, the pursuit of higher learning, cannot admit of any conditions as to personnel other than those designed to promote the objects for which this institution is established, and particularly with no regard whatever to accidents of race, creed or sex. f:2-33^ Table of Contents Trustees and Officers Administration Four Caroline Bamberger Fuld Louis Bamberger Board of Trustees Daniel Bell Howard C. Kauffmann Henry Ford II Professor President of Social Sciences Exxon Corporation Harvard University G. Daniel Mostow Thornton F. Bradshaw Henry Ford II Professor Chairman of the Board and of Mathematics Chief Executive Officer Yale University RCA John R. Opel Charles L. Brown President and Chairman of the Board and Chief Executive Officer Chief Executive Officer International Business Machines American Telephone and Telegraph Company Howard C. Petersen Philadelphia, Pennsylvania Fletcher L. Byrom Denver, Colorado Martin E.
    [Show full text]