DOCSLIB.ORG

Bois-Marie INSTITUTDESHAUTESÉTUDESSCIENTIFIQUES

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

NEWSLETTER - 2012 bois-marie INSTITUTDESHAUTESÉTUDESSCIENTIFIQUES editorial Not so long ago, opening the history of mathematics,which attracted over 80 000 visitors, mathematics to everyone was will prompt other initiatives with a similar scope, to help the a challenge that felt very general public dare look at mathematics without fear and with daunting.This science fascinates us as much as it scares us,sitting pleasure. as it does at the intersection of so many paths we walk down IHÉS has been carrying out a complementary project since every day: technological progress, philosophical enquiry, September 2011, aimed at high school and university students. educational strategies. This fascination and fright can be The Tour de France des déchiffreurs has travelled in approximately explained by the fact that mathematics challenges us, throwing twenty French towns; thousands of people have been able to back to us our lack of understanding of the world around us. discover fundamental research in mathematics and theoretical However, mathematics is very much with us, very real and physicists from a fresh perspective.A more modest undertaking present everywhere, so closely woven in the fabric of our daily in terms of resources, it was also a great success. Because the life that we don’t notice it. Lying in wait in its abstraction, its general public is obviously curious about mathematics, IHÉS very first rampart of defence, it does not reveal itself easily and will continue its efforts to try and inspire young people and to its beauty is only known by mathematicians. firmly establish the presence of fundamental research in the And yet, it was the wish of the mathematical community to public sphere. gain increased exposure and esteem.The Mathematics,A Beautiful Two projects in this vein are underway. The celebrations Elsewhere exhibition, at the Fondation Cartier pour l’art marking the centenary of Henri Poincaré’s passing,coordinated contemporain offered a wonderful showcase and timeframe for by the Institut Henri Poincaré, will take place this autumn. A this. IHÉS very much hopes that this unprecedented venture in documentary film for general release in 2013, directed by Olivier Peyon and produced by Haut et Court and Zadig Productions, will take us to the heart of the complexity of mathematical issues today. contents scientific events . 2 - 3 awards ...................................... 4 Schlumberger chair . 5 research at IHÉS . 6 - 7 Fiftieth Anniversary Campaign . 8 campaign in the U.S. 9 events . 10 - 11 exhibition at the Fondation Cartier . 12 - 13 Tour de France des déchiffreurs . .14 - 15 a point of view from ... / forthcoming events . 16 © Ergo-Robots: artificial curiosity and language -View of the exhibition Mathematics,A Beautiful Elsewhere, from 21 October 2011 to 18 March 2012 at the Fondation Cartier pour l’art contemporain, Paris. - Photo Pierre-Yves Dinasquet Institut des Hautes Études Scientifiques | Le Bois-Marie, 35 route de Chartres, F-91440 Bures-sur-Yvette, France Telephone: +33 1 60 92 66 00 | Email: [email protected] | Website: www.ihes.fr scientific events gravitation 1/2 From 6 October 2011 to 15 March 2012, 7 Thibault Damour (IHÉS),Cedric Deffayet (APC) and Pierre Vanhove (CEA-Saclay IPhT & IHÉS) organised symposium in honour of Yuri Manin eight seminar sessions on the theoretical and experimental aspects of gravitation. 71/2, a symposium organised by Ivan Penkov With the idea of recreating the atmosphere of (Jacobs University,Bremen) took place at IHÉS the Manin seminar in Moscow (1984-1986), Évariste Galois on 5, 6 and 7 March 2012. The event was in the four speakers were each invited to give a honour of mathematician Yuri I. Manin, lecture, consisting of two 75 minute sessions. A conference on Differential Equations and Galois Professor at the Max Planck Institute in Bonn The lectures were given byAlexander Beilinson Theory was organised from 17 to 21 October 2011 and former member of the IHÉS Scientific (University of Chicago), Vladimir Drinfeld at IHÉS to present the significant results of the Council, and the symposium was held on the (University of Chicago), Mikhail Kapranov past few years in this field. occasion of his 75th birthday. (Yale University) and Maxim Kontsevich (IHÉS). wall crossing From 10 to 12 November 2011, Maxim Kontsevich (IHÉS) and Andrew Neitzke (UT Austin) made a “The meeting in honour ofYuri Manin was a tribute by Russian series of presentations on wall crossing,a relatively mathematicians to a Russian mathematician.The range of different ways to recent phenomenon that appears in several areas, practice and share mathematics was dazzling.Vladimir Drinfeld showed the such as homological algebra, combinatorics, importance of exchanging ideas to make successive simplifications and improve differential geometry and complex analysis. a demonstration. Mikhail Kapranov highlighted the need for a geometric vision in formulating and solving problems of a very algebraic nature, a vision that enables the manipulation of complicated combinatorics. Publications Finally,Maxim Kontsevich shared his brilliant insights and the amazing mathématiques de l’IHÉS way he always has of reading certain mathematical formulas.” A new Rencontre autour des Publications Claude Sabbah, Mathématiques de l’IHÉS was organised on professor, École polytechnique 20 January 2012,after a first such event in 2011,by Claire Voisin, managing editor of Les Publica- tions Mathématiques de l’IHÉS. Laurent Schwartz seminar For the second year running, F.Merle (Univ.of Cergy-Pontoise & IHÉS) and F.Golse (École polytechnique) jointly organised the Laurent Schwartz Seminar on the subject of Partial Differential Equations and Applications. The seminar took place over a day,comprising 3 or 4 presentations, and generally saw specialists on the subject meeting together once a month, at the École polytechnique or at IHÉS. physics seminar Yuri Manin, Jean-Pierre Serre From 6 February to 26 March 26, 2012, David Ruelle (IHÉS) and Hans Henrik Rugh (Univ.Paris- Sud) organised a seminar,with seven presentations on Dynamical Systems and Nonequilibrium Statistical Mechanics. 2 courses in Arithmetics and Algebraic Geometry at IHÉS Interview with Ahmed Abbes, research success of the first two courses taught by Peter scientific collaboration is so much greater with director at CNRS, long term CNRS visitor at Scholze (Perfectoid Spaces and the Weight- friends. We had the opportunity to jointly IHÉS since 1 May 2011. Ahmed Abbes is a Monodromy Conjecture,October and November organise three conferences, two in France and mathematician, specialised in arithmetic 2011) and Kim Minhyong (Fundamental one in Japan. But we thought it helpful to geometry. Groups, Non-Abelian Cohomology and maintain more regular contact.Todai accepted Diophantine Geometry, February 2012) shows the idea straight away. In 2008, the university You are the person who already has that this format meets a real need.The courses already had the necessary equipment for several conferences to his credit and is are filmed and videos and notes are made conducting video-seminars. also behind a particular initiative: available on the IHÉS website, in order to I then spoke of the project to IHÉS, where it Courses in Arithmetics and Algebraic benefit the greatest number possible. was welcomed with enthusiasm. IHÉS Geometry. Why did you choose this equipped itself with a videoconferencing approach? system in 2010. Since then, the seminar has During the 1960s, IHÉS witnessed a usually been held once a month. Speakers are revolution in algebraic geometry, led by alternately from IHÉS and Todai, and their Alexander Grothendieck, who did much to presentation is transmitted simultaneously by establish the Institute’s international video to the other institute.The audience is reputation.The foundations of this new theory able to interact directly with the speaker, were developed by Grothendieck and his which is the whole point of this new students over ten years or so in his famous technology. Séminaire de Géométrie Algébrique du Bois- The French school of arithmetic geometry has Marie.These presentations were then published kept close links with the Japanese school in a collection of papers (known by the since the 1970s.These were initially developed acronym SGA) which remains to this day the Peter Scholze by Michel Raynaud and Tetsuji Shioda, then « bible » for this topic.This foundational period by Luc Illusie and Kazuya Kato.With Takeshi was extended with Pierre Deligne continuing You love Japan and you run the Paris- Saito, we hope to carry on this tradition for the tradition of the seminar, by presenting Tokyo Arithmetic Geometry Seminar. the benefit of both schools.Our next project is some of the most elegant and profound results How did this come about? Do you have the joint Arithmetic GeometryWeek in Tokyo to in arithmetic and algebraic geometry (Weil any other projects involving Japan? be held from 4 to 8 June 2012. conjecture,Hodge theory,Galois representations The idea came to me during an extended stay and modular forms ...). The new series of at the University of Tokyo (Todai) in courses in arithmetics and algebraic geometry, 2008. Over the past ten years, I have been which I am currently co-organising with working extensively withTakeshi Saito atTodai Christophe Breuil and Laurent Lafforgue, aims on arithmetic geometry ramification.This has to revive the tradition of an in-depth seminar given me the opportunity to discover this on important topics.The courses are likely to wonderful country and has, more importantly, enhance the attractiveness and influence of enabled me to establish relationships of trust IHÉS. and friendship with my Japanese colleagues, There is an abundant supply of generalist or primarily withTakeshi Saito.The pleasure of a thematic seminars in the Paris area at the moment. Because of their format, these * Courses in arithmetic and algebraic geometry are seminars only give a brief presentation of new jointly organised by the Fondation mathématique results, without exploring the new ideas and Jacques Hadamard and IHÉS.
Recommended publications
  • Mathematical

    Mathematical

    2-12 JULY 2011 MATHEMATICAL HOST AND VENUE for Students Jacobs University Scientific Committee Étienne Ghys (École Normale The summer school is based on the park-like campus of Supérieure de Lyon, France), chair Jacobs University, with lecture halls, library, small group study rooms, cafeterias, and recreation facilities within Frances Kirwan (University of Oxford, UK) easy walking distance. Dierk Schleicher (Jacobs University, Germany) Alexei Sossinsky (Moscow University, Russia) Jacobs University is an international, highly selective, Sergei Tabachnikov (Penn State University, USA) residential campus university in the historic Hanseatic Anatoliy Vershik (St. Petersburg State University, Russia) city of Bremen. It features an attractive math program Wendelin Werner (Université Paris-Sud, France) with personal attention to students and their individual interests. Jean-Christophe Yoccoz (Collège de France) Don Zagier (Max Planck-Institute Bonn, Germany; › Home to approximately 1,200 students from over Collège de France) 100 different countries Günter M. Ziegler (Freie Universität Berlin, Germany) › English language university › Committed to excellence in higher education Organizing Committee › Has a special program with fellowships for the most Anke Allner (Universität Hamburg, Germany) talented students in mathematics from all countries Martin Andler (Université Versailles-Saint-Quentin, › Venue of the 50th International Mathematical Olympiad France) (IMO) 2009 Victor Kleptsyn (Université de Rennes, France) Marcel Oliver (Jacobs University, Germany) For more information about the mathematics program Stephanie Schiemann (Freie Universität Berlin, Germany) at Jacobs University, please visit: Dierk Schleicher (Jacobs University, Germany) math.jacobs-university.de Sergei Tabachnikov (Penn State University, USA) at Jacobs University, Bremen The School is an initiative in the framework of the European Campus of Excellence (ECE).
  • Report for the Academic Year 1995

    Report for the Academic Year 1995

    Institute /or ADVANCED STUDY REPORT FOR THE ACADEMIC YEAR 1994 - 95 PRINCETON NEW JERSEY Institute /or ADVANCED STUDY REPORT FOR THE ACADEMIC YEAR 1 994 - 95 OLDEN LANE PRINCETON • NEW JERSEY 08540-0631 609-734-8000 609-924-8399 (Fax) Extract from the letter addressed by the Founders to the Institute's Trustees, dated June 6, 1930. Newark, New jersey. It is fundamental in our purpose, and our express desire, that in the appointments to the staff and faculty, as well as in the admission of workers and students, no 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. TABLE OF CONTENTS 4 BACKGROUND AND PURPOSE 5 • FOUNDERS, TRUSTEES AND OFFICERS OF THE BOARD AND OF THE CORPORATION 8 • ADMINISTRATION 11 REPORT OF THE CHAIRMAN 15 REPORT OF THE DIRECTOR 23 • ACKNOWLEDGMENTS 27 • REPORT OF THE SCHOOL OF HISTORICAL STUDIES ACADEMIC ACTIVITIES MEMBERS, VISITORS AND RESEARCH STAFF 36 • REPORT OF THE SCHOOL OF MATHEMATICS ACADEMIC ACTIVITIES MEMBERS AND VISITORS 42 • REPORT OF THE SCHOOL OF NATURAL SCIENCES ACADEMIC ACTIVITIES MEMBERS AND VISITORS 50 • REPORT OF THE SCHOOL OF SOCIAL SCIENCE ACADEMIC ACTIVITIES MEMBERS, VISITORS AND RESEARCH STAFF 55 • REPORT OF THE INSTITUTE LIBRARIES 57 • RECORD OF INSTITUTE EVENTS IN THE ACADEMIC YEAR 1994-95 85 • INDEPENDENT AUDITORS' REPORT INSTITUTE FOR ADVANCED STUDY: BACKGROUND AND PURPOSE The Institute for Advanced Study is an independent, nonprofit institution devoted to the encouragement of learning and scholarship.
  • Arithmetic Properties of the Herglotz Function

    Arithmetic Properties of the Herglotz Function

    ARITHMETIC PROPERTIES OF THE HERGLOTZ FUNCTION DANYLO RADCHENKO AND DON ZAGIER Abstract. In this paper we study two functions F (x) and J(x), originally found by Herglotz in 1923 and later rediscovered and used by one of the authors in connection with the Kronecker limit formula for real quadratic fields. We discuss many interesting properties of these func- tions, including special values at rational or quadratic irrational arguments as rational linear combinations of dilogarithms and products of logarithms, functional equations coming from Hecke operators, and connections with Stark's conjecture. We also discuss connections with 1-cocycles for the modular group PSL(2; Z). Contents 1. Introduction 1 2. Elementary properties 2 3. Functional equations related to Hecke operators 4 4. Special values at positive rationals 8 5. Kronecker limit formula for real quadratic fields 10 6. Special values at quadratic units 11 7. Cohomological aspects 15 References 18 1. Introduction Consider the function Z 1 log(1 + tx) (1) J(x) = dt ; 0 1 + t defined for x > 0. Some years ago, Henri Cohen 1 showed one of the authors the identity p p π2 log2(2) log(2) log(1 + 2) J(1 + 2) = − + + : 24 2 2 In this note we will give many more similar identities, like p π2 log2(2) p J(4 + 17) = − + + log(2) log(4 + 17) 6 2 arXiv:2012.15805v1 [math.NT] 31 Dec 2020 and p 2 11π2 3 log2(2) 5 + 1 J = + − 2 log2 : 5 240 4 2 We will also investigate the connection to several other topics, such as the Kronecker limit formula for real quadratic fields, Hecke operators, Stark's conjecture, and cohomology of the modular group PSL2(Z).
  • TWAS Fellowships Worldwide

    TWAS Fellowships Worldwide

    CDC Round Table, ICTP April 2016 With science and engineering, countries can address challenges in agriculture, climate, health TWAS’s and energy. guiding principles 2 Food security Challenges Water quality for a Energy security new era Biodiversity loss Infectious diseases Climate change 3 A Globally, 81 nations fall troubling into the category of S&T- gap lagging countries. 48 are classified as Least Developed Countries. 4 The role of TWAS The day-to-day work of TWAS is focused in two critical areas: •Improving research infrastructure •Building a corps of PhD scholars 5 TWAS Research Grants 2,202 grants awarded to individuals and research groups (1986-2015) 6 TWAS’ AIM: to train 1000 PhD students by 2017 Training PhD-level scientists: •Researchers and university-level educators •Future leaders for science policy, business and international cooperation Rapidly growing opportunities P BRAZIL A K I N D I CA I RI A S AF TH T SOU A N M KENYA EX ICO C H I MALAYSIA N A IRAN THAILAND TWAS Fellowships Worldwide NRF, South Africa - newly on board 650+ fellowships per year PhD fellowships +460 Postdoctoral fellowships +150 Visiting researchers/professors + 45 17 Programme Partners BRAZIL: CNPq - National Council MALAYSIA: UPM – Universiti for Scientific and Technological Putra Malaysia WorldwideDevelopment CHINA: CAS - Chinese Academy of KENYA: icipe – International Sciences Centre for Insect Physiology and Ecology INDIA: CSIR - Council of Scientific MEXICO: CONACYT– National & Industrial Research Council on Science and Technology PAKISTAN: CEMB – National INDIA: DBT - Department of Centre of Excellence in Molecular Biotechnology Biology PAKISTAN: ICCBS – International Centre for Chemical and INDIA: IACS - Indian Association Biological Sciences for the Cultivation of Science PAKISTAN: CIIT – COMSATS Institute of Information INDIA: S.N.
  • Twenty Female Mathematicians Hollis Williams

    Twenty Female Mathematicians Hollis Williams

    Twenty Female Mathematicians Hollis Williams Acknowledgements The author would like to thank Alba Carballo González for support and encouragement. 1 Table of Contents Sofia Kovalevskaya ................................................................................................................................. 4 Emmy Noether ..................................................................................................................................... 16 Mary Cartwright ................................................................................................................................... 26 Julia Robinson ....................................................................................................................................... 36 Olga Ladyzhenskaya ............................................................................................................................. 46 Yvonne Choquet-Bruhat ....................................................................................................................... 56 Olga Oleinik .......................................................................................................................................... 67 Charlotte Fischer .................................................................................................................................. 77 Karen Uhlenbeck .................................................................................................................................. 87 Krystyna Kuperberg .............................................................................................................................
  • How to Glue Perverse Sheaves”

    How to Glue Perverse Sheaves”

    NOTES ON BEILINSON'S \HOW TO GLUE PERVERSE SHEAVES" RYAN REICH Abstract. The titular, foundational work of Beilinson not only gives a tech- nique for gluing perverse sheaves but also implicitly contains constructions of the nearby and vanishing cycles functors of perverse sheaves. These con- structions are completely elementary and show that these functors preserve perversity and respect Verdier duality on perverse sheaves. The work also de- fines a new, \maximal extension" functor, which is left mysterious aside from its role in the gluing theorem. In these notes, we present the complete details of all of these constructions and theorems. In this paper we discuss Alexander Beilinson's \How to glue perverse sheaves" [1] with three goals. The first arose from a suggestion of Dennis Gaitsgory that the author study the construction of the unipotent nearby cycles functor R un which, as Beilinson observes in his concluding remarks, is implicit in the proof of his Key Lemma 2.1. Here, we make this construction explicit, since it is invaluable in many contexts not necessarily involving gluing. The second goal is to restructure the pre- sentation around this new perspective; in particular, we have chosen to eliminate the two-sided limit formalism in favor of the straightforward setup indicated briefly in [3, x4.2] for D-modules. We also emphasize this construction as a simple demon- stration that R un[−1] and Verdier duality D commute, and de-emphasize its role in the gluing theorem. Finally, we provide complete proofs; with the exception of the Key Lemma, [1] provides a complete program of proof which is not carried out in detail, making a technical understanding of its contents more difficult given the density of ideas.
  • Kavli IPMU Annual 2014 Report

    Kavli IPMU Annual 2014 Report

    ANNUAL REPORT 2014 REPORT ANNUAL April 2014–March 2015 2014–March April Kavli IPMU Kavli Kavli IPMU Annual Report 2014 April 2014–March 2015 CONTENTS FOREWORD 2 1 INTRODUCTION 4 2 NEWS&EVENTS 8 3 ORGANIZATION 10 4 STAFF 14 5 RESEARCHHIGHLIGHTS 20 5.1 Unbiased Bases and Critical Points of a Potential ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙20 5.2 Secondary Polytopes and the Algebra of the Infrared ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙21 5.3 Moduli of Bridgeland Semistable Objects on 3- Folds and Donaldson- Thomas Invariants ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙22 5.4 Leptogenesis Via Axion Oscillations after Inflation ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙23 5.5 Searching for Matter/Antimatter Asymmetry with T2K Experiment ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ 24 5.6 Development of the Belle II Silicon Vertex Detector ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙26 5.7 Search for Physics beyond Standard Model with KamLAND-Zen ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙28 5.8 Chemical Abundance Patterns of the Most Iron-Poor Stars as Probes of the First Stars in the Universe ∙ ∙ ∙ 29 5.9 Measuring Gravitational lensing Using CMB B-mode Polarization by POLARBEAR ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ 30 5.10 The First Galaxy Maps from the SDSS-IV MaNGA Survey ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙32 5.11 Detection of the Possible Companion Star of Supernova 2011dh ∙ ∙ ∙ ∙ ∙ ∙
  • Opening Ceremony

    Opening Ceremony

    Opening ceremony Sir John Ball, President of the International Mathematical Union Your Majesty, Señor Ruiz Gallardón, Señora Cabrera, Señora Aguirre, Professor Manuel de León, Distinguished guests, Ladies and gentlemen, ¡Bienvenidos al ICM dos mil seis! Welcome to ICM 2006, the 25th International Congress of Mathematicians, and the first ICM to be held in Spain. We offer our heartfelt thanks to the Spanish nation, so rich in history and culture, for its invitation to Madrid. We greatly appreciate that His Majesty King Juan Carlos is honouring mathematics by His presence here today. While celebrating this feast of mathematics, with the many talking-points that it will provide, it is worth reflecting on the ways in which our community functions. Mathematics is a profession of high standards and integrity. We freely discuss our work with others without fear of it being stolen, and research is communicated openly prior to formal publication. Editorial procedures are fair and proper, and work gains its reputation through merit and not by how it is promoted. These are the norms operated by the vast majority of mathematicians. The exceptions are rare, and they are noticed. Mathematics has a strong record of service, freely given. We see this in the time and care spent in the refereeing of papers and other forms of peer review. We see it in the running of mathematical societies and journals, in the provision of free mathematical software and teaching resources, and in the various projects world-wide to improve electronic access to the mathematical literature, old and new. We see it in the nurturing of students beyond the call of duty.
  • The Bloch-Wigner-Ramakrishnan Polylogarithm Function

    The Bloch-Wigner-Ramakrishnan Polylogarithm Function

    Math. Ann. 286, 613424 (1990) Springer-Verlag 1990 The Bloch-Wigner-Ramakrishnan polylogarithm function Don Zagier Max-Planck-Insfitut fiir Mathematik, Gottfried-Claren-Strasse 26, D-5300 Bonn 3, Federal Republic of Germany To Hans Grauert The polylogarithm function co ~n appears in many parts of mathematics and has an extensive literature [2]. It can be analytically extended to the cut plane ~\[1, ~) by defining Lira(x) inductively as x [ Li m_ l(z)z-tdz but then has a discontinuity as x crosses the cut. However, for 0 m = 2 the modified function O(x) = ~(Liz(x)) + arg(1 -- x) loglxl extends (real-) analytically to the entire complex plane except for the points x=0 and x= 1 where it is continuous but not analytic. This modified dilogarithm function, introduced by Wigner and Bloch [1], has many beautiful properties. In particular, its values at algebraic argument suffice to express in closed form the volumes of arbitrary hyperbolic 3-manifolds and the values at s= 2 of the Dedekind zeta functions of arbitrary number fields (cf. [6] and the expository article [7]). It is therefore natural to ask for similar real-analytic and single-valued modification of the higher polylogarithm functions Li,. Such a function Dm was constructed, and shown to satisfy a functional equation relating D=(x-t) and D~(x), by Ramakrishnan E3]. His construction, which involved monodromy arguments for certain nilpotent subgroups of GLm(C), is completely explicit, but he does not actually give a formula for Dm in terms of the polylogarithm. In this note we write down such a formula and give a direct proof of the one-valuedness and functional equation.
  • Algebraic D-Modules and Representation Theory Of

    Algebraic D-Modules and Representation Theory Of

    Contemporary Mathematics Volume 154, 1993 Algebraic -modules and Representation TheoryDof Semisimple Lie Groups Dragan Miliˇci´c Abstract. This expository paper represents an introduction to some aspects of the current research in representation theory of semisimple Lie groups. In particular, we discuss the theory of “localization” of modules over the envelop- ing algebra of a semisimple Lie algebra due to Alexander Beilinson and Joseph Bernstein [1], [2], and the work of Henryk Hecht, Wilfried Schmid, Joseph A. Wolf and the author on the localization of Harish-Chandra modules [7], [8], [13], [17], [18]. These results can be viewed as a vast generalization of the classical theorem of Armand Borel and Andr´e Weil on geometric realiza- tion of irreducible finite-dimensional representations of compact semisimple Lie groups [3]. 1. Introduction Let G0 be a connected semisimple Lie group with finite center. Fix a maximal compact subgroup K0 of G0. Let g be the complexified Lie algebra of G0 and k its subalgebra which is the complexified Lie algebra of K0. Denote by σ the corresponding Cartan involution, i.e., σ is the involution of g such that k is the set of its fixed points. Let K be the complexification of K0. The group K has a natural structure of a complex reductive algebraic group. Let π be an admissible representation of G0 of finite length. Then, the submod- ule V of all K0-finite vectors in this representation is a finitely generated module over the enveloping algebra (g) of g, and also a direct sum of finite-dimensional U irreducible representations of K0.
  • FY 2008 WPI Project Progress Report World Premier International Research Center (WPI) Initiative

    FY 2008 WPI Project Progress Report World Premier International Research Center (WPI) Initiative

    FY 2008 WPI Project Progress Report World Premier International Research Center (WPI) Initiative Host Institution The University of Tokyo Host Institution Head Hiroshi Komiyama Research Center Institute for the Physics and Mathematics of the Universe Center Director Hitoshi Murayama Summary of center project progress HyperSuprimeCam projects are making steady progress, and the MoU Institute for the Physics and Mathematics of the Universe (IPMU) has made to join SDSS-III experiment was signed. steady progress towards the stated goals. The numbers below refer to the (5) Honors and Awards. PI Ooguri received the 2009 Humboldt Research period between April 1, 2008 and March 31, 2009, unless stated otherwise. Award, and Prof. Sugimoto received the 2008 Kimura prize of (1) Organization. The number of administrative and research support staff theoretical physics. Assoc. Prof. Yoshida received the IUPAP Young has exceeded the proposed number of 30. The scientific staff is also Scientist Prize in computational physics, and Assoc. Prof. Komatsu steadily growing, from 63 to 125, well on track towards the proposed (joint appointment with Texas) received the same Prize in astrophysics. goal of 195 (March 2011). PI Nakahata received the 2008 Inoue Prize for Science. PI Inoue received the 2008 JSPS Prize. (2) Internationalization. The WPI program requires more than 30% of the researchers to be non-Japanese. Our current percentage is 48%, and (6) Interdisciplinary activities. As proposed, we hold daily tea at three has fulfilled the mandate. The most significant among the non-Japanese o’clock to encourage informal and interdisciplinary discussions. They members is one full and two associate professors who have moved from are well attended and create desired atmosphere.
  • Oberwolfach Jahresbericht Annual Report 2008 Herausgeber / Published By

    Oberwolfach Jahresbericht Annual Report 2008 Herausgeber / Published By

    titelbild_2008:Layout 1 26.01.2009 20:19 Seite 1 Oberwolfach Jahresbericht Annual Report 2008 Herausgeber / Published by Mathematisches Forschungsinstitut Oberwolfach Direktor Gert-Martin Greuel Gesellschafter Gesellschaft für Mathematische Forschung e.V. Adresse Mathematisches Forschungsinstitut Oberwolfach gGmbH Schwarzwaldstr. 9-11 D-77709 Oberwolfach-Walke Germany Kontakt http://www.mfo.de [email protected] Tel: +49 (0)7834 979 0 Fax: +49 (0)7834 979 38 Das Mathematische Forschungsinstitut Oberwolfach ist Mitglied der Leibniz-Gemeinschaft. © Mathematisches Forschungsinstitut Oberwolfach gGmbH (2009) JAHRESBERICHT 2008 / ANNUAL REPORT 2008 INHALTSVERZEICHNIS / TABLE OF CONTENTS Vorwort des Direktors / Director’s Foreword ......................................................................... 6 1. Besondere Beiträge / Special contributions 1.1 Das Jahr der Mathematik 2008 / The year of mathematics 2008 ................................... 10 1.1.1 IMAGINARY - Mit den Augen der Mathematik / Through the Eyes of Mathematics .......... 10 1.1.2 Besuch / Visit: Bundesministerin Dr. Annette Schavan ............................................... 17 1.1.3 Besuche / Visits: Dr. Klaus Kinkel und Dr. Dietrich Birk .............................................. 18 1.2 Oberwolfach Preis / Oberwolfach Prize ....................................................................... 19 1.3 Oberwolfach Vorlesung 2008 .................................................................................... 27 1.4 Nachrufe ..............................................................................................................