Leopoldina News 04

Total Page:16

File Type:pdf, Size:1020Kb

Leopoldina News 04 Leopoldina news Deutsche Akademie der Naturforscher Leopoldina – Special edition: Nationale Akademie der Wissenschaften Annual Assembly 2011 Halle (Saale), 21 October 2011 04|2011 Dear members and friends of the Leopoldina, we can look back on a highly successful Annu- al Assembly in Halle. I am extremely grateful to all members who showed their dedication to the Leopoldina and helped to generate such a high level of academic discussion. I would like to say a special thank you to Vice-Presidents Prof. Dr. Bärbel Friedrich ML and Prof. Dr. Michael Hecker ML, who were responsible for prepa- ring the academic side of the assembly. I was pleased to see how many people attended the event and followed the interdisciplinary dialogue between the humanities, the natural Leopoldina Vice-President Martin J. Lohse welcomed the participants at the start of the three-day Annual Assembly of sciences and the life sciences. The speeches the Leopoldina in Halle. Photo: Markus Scholz given by Federal Chancellor Angela Merkel and Minister-President of Saxony-Anhalt, Rei- ner Haseloff, also attracted large audiences. Leopoldina Annual Assembly 2011 However, as we all know, after the Annual Assembly is before the Annual Assembly! So explored questions about life I’d like to take a peek into the future and look ahead to the next Annual Assembly, which “What is life?” – the Leopoldina’s Annu- various perspectives adopted by the na- will be held in Berlin from 22 to 24 September al Assembly, which took place from 23 to tural sciences, life sciences and huma- 2012. The topic of this inspiring event will be 25 September in the Kongress- und Kul- nities. The spectrum stretched from the “The role of science in global change”. turzentrum in Halle, put this question origins and development of life, to the at the heart of its academic discussions. diversity and limits of life, to the possi- At the start of his welcome address, Le- bilities of creating artificial life. Over 600 Kind regards, opoldina Vice-President Prof. Dr. Mar- guests attended the three-day Annual tin J. Lohse ML, said that there were Assembly. Among them were 100 pupils no simple answers to the question. He and several Thai students, who had been explained that disciplines vary widely in invited by the Society of German Natural their approaches to the topic, and that Scientists and Doctors (GDNÄ) and had the question can even mean entirely dif- the opportunity to speak to the outstan- ferent things to scientists and scholars ding researchers during the event. from different fields. The comprehensive (mab) Speeches 3 Prizes and Medals 4 programme for the Annual Assembly re- Scientific Lectures 10 flected this diversity. The topics covered Detailed reports are available on the Events 14 a wide range of issues and discussed the following pages. Publishing Details 15 People 16 2 04|2011 // Leopoldina / Newsletter Impressions Jörg Hacker, President of the Leopoldina, welcomed Chancellor Angela Merkel and Minister-President of Saxony-Anhalt, Reiner Haseloff, at the Kongress- und Kulturzentrum in Halle (from left to right). Photo: David Ausserhofer View of the banquet hall on the opening day of the Annual Assembly 2011. The Leopoldina New members – including Prof. Dr. Heidi welcomed well over 600 international guests to the three-day event in Halle. Pfeifer ML, shown here – received their Photos (3): Markus Scholz diploma from the President. The Junge Akade- mie, which was founded by the Leopoldina and the Berlin-Bran- denburg Academy of Sciences and Humanities, also participated in the Annual Assembly with its “vita-bios- chaim” event. State Secretary Cornelia Quennet-Thielen (center) attended a plenary session of the members of the Junge Akademie. 04|2011 // Leopoldina / Newsletter 3 “There are plenty of topics on which policymakers need expert advice.” In her speech, Chancellor Merkel underlined the importance of the Leopoldina. Jörg Hacker, President of the Leopoldina, and Reiner Haseloff, Minister-President of Saxony-Anhalt, also spoke about the Academy’s role in the research sector in Germany and around the world. This year, the German Chancellor, Dr. Angela Merkel visited the Leopoldi- na Annual Assembly for the first time. In her speech on the opening day, she talked about the importance of scientific advice for policymakers and about the Leopoldina’s role as the German Natio- nal Academy of Sciences in Germany and worldwide. At the start of her speech, Chancellor Merkel said: “There is now one voice that speaks for the German sci- entific community as a whole.” She went on to say that the Leopoldina represents the entire range of the sciences and hu- manities and promotes cooperation bet- ween different scientific and academic institutions. “As a result,” she said, “the public is listening more to what science has to say,” and its voice is being heard internationally. Germany had closed a Chancellor Angela Merkel at the Annual Assembly 2011. Photo: David Ausserhofer gap by designating the Leopoldina as its National Academy of Sciences. The Chancellor emphasised the va- must reach the political sphere and must context. He went on to say that the third lue of the science-based policy advice not be ignored there. The Leopoldina main factor for Germany’s development that the Leopoldina provides: “There takes its scientific responsibility – which into a Republic of Science is continuous are plenty of topics on which policyma- is always also a responsibility towards so- and open communication between sci- kers need expert advice.” In this context, ciety – very seriously.” ence and society, as Germany is a scep- Merkel specifically mentioned the state- In his speech, Prof. Jörg Hacker ML, tical and difficult nation “when it comes ments and recommendations on Pre- President of the Leopoldina, focused fi- to new technologies and living with risks implantation Genetic Diagnosis and on nally on the future role of the Leopoldina and uncertainties.” “Public debate on energy research provided by experts this in the German and international scien- scientific topics is especially important year: “I ask the Leopoldina to continue to tific sphere, in light of the fact that po- in times of increasing uncertainty and intervene and advise us in this way.” In liticians, academics and representatives where ever more complex issues – from Merkel’s opinion, scientific advice serves of other relevant groups plan to develop combating acute infections, to problems as an essential basis for sustainable deci- Germany into a “Republic of Science”. on the financial markets, to questions of sions: “We need the facts to be compiled, Hacker asserted that while science educational policy – demand well-consi- analysed and evaluated in order to make certainly requires reliable funding, “a dered and sometimes fast responses. In sound decisions.” And while such decisi- science republic cannot be built on fi- addition, Hacker stated that science can ons can never be based solely on scienti- nancial support alone; intangible factors only thrive in an international context fic facts, they should never run contrary such as legal framework conditions are and a Republic of Science must be an in- to them, either. just as important in making a location ternational beacon. “That’s why we want In his words of welcome, the Mi- attractive.” Here too, in creating condi- to become a key partner who helps define nister-President of Saxony-Anhalt, Dr. tions that are favourable to science, the the agenda of international science and Reiner Haseloff, said that as politicians Leopoldina has an important advisory research, both through our work in the today cannot possibly keep abreast of all function. Hacker made particular refe- large associations of science academies the latest developments, they have to rely rence to legislation on stem-cell research and in a bilateral context.” (mab) on the advice of independent experts. and the implementation of the EU Di- “But the findings of science and research rective on animal experiments in this 4 04|2011 // Leopoldina / Newsletter At the Annual Assembly, the Leopoldina honoured outstanding researchers with awards and medals Cothenius-Medals: Bert Hölldobler, Anna M. and Ulrich Wobus The ethologist and evolutionary biologist Bert Hölldobler (right) President Jörg Hacker and the General Secretary Jutta Schnitzer- received the Cothenius Medal from Leopoldina President Jörg Ungefug presented the Medal to Anne M. Wobus and Ulrich Wobus Hacker for his research on the social organization of insects. (center) for their works in the field of cell biology and genetic Photo: David Ausserhofer research. Photo: Markus Scholz The Leopoldina members Prof. Dr. Bert He has received numerous high-level the institute was re-founded and became Hölldobler ML (Würzburg), Prof. Dr. awards including the German Research part of the Leibniz Association. Anna M. Anna M. Wobus and Prof. Dr. Ulrich Foundation’s Leibniz Prize and the Kör- Wobus is a pioneer in stem cell research Wobus (both Gatersleben) received the ber Prize. Bert Hölldobler has always in Germany. She is also committed to the golden Cothenius Medal for their scien- understood how important it is to formu- social aspects of stem cell research and is tific life’s work. late his scientific findings for a wider au- today a leading figure internationally in dience. In 1991 he received the American her branch of research. Her name is also Prof. Dr. Bert Hölldobler (born 1936) Pulitzer Prize for his book “The Ants”, a linked to the establishment of embryonic is
Recommended publications
  • 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.
    [Show full text]
  • Replication of Picornaviruses I
    JouRNAL oF VnoLoGy, Dec. 1975, p. 1512-1527 Vol. 16, No. 6 Copyright ©) 1975 American Society for Microbiology Printed in U.SA. Replication of Picornaviruses I. Evidence from In Vitro RNA Synthesis that Poly(A) of the Poliovirus Genome is Genetically Coded KAROLINE DORSCH-HASLER, YOSHIAKI YOGO,' AND ECKARD WIMMER* Department ofMicrobiology, St. Louis University School ofMedicine, St. Louis, Missouri 63104, and Department ofMicrobiology, School ofBasic Health Sciences, State University ofNew York at Stony Brook, Stony Brook, New York 11794 * Received for publication 3 July 1975 A crude replication complex has been isolated from poliovirus-infected HeLa cells and used for synthesis of poliovirus replicative intermediate (RI) RNA, replicative form (RF) RNA, and single-stranded (SS) RNA in vitro. All three classes of virus-specific RNA synthesized in vitro are shown to contain poly(A). Poly(A) of RF and of SS RNA [RF-poly(A) and SS-poly(A)] has a chain length (50 to 70 nucleotides) that is shorter than that of poly(A) of in vivo-synthesized RNAs. Poly(A) of RI [RI-poly(A)], however, is at least 200 nucleotides long and, therefore, larger than poly(A) of RI isolated from HeLa cells 4 h after infection. The crude membrane-bound replication complex contains a terminal adenylate transferase activity that is stimulated by Mn2+ and the addition of an (Ap),AoH primer. This transferase activity is found also in extracts of mock-infected cells. Partial purification of the replication complex in a stepwise sucrose gradient, in which the viral replicase is associated with the smooth cytoplasmic membrane fraction, does not remove the terminal transferase.
    [Show full text]
  • Abstract Book (Pdf)
    6th EMBO/EMBL Conference on Science and Society Science and Security 28 – 29 October 2005 at the European Molecular Biology Laboratory Heidelberg, Germany Organising Committee: Andrew Moore (EMBO, Chair), Halldòr Stefànsson (EMBL), Alessandra Bendiscioli (EMBO), Frank Gannon (EMBO), Iain Mattaj (EMBL) Welcome message n September this year, plans for a new bio-defence laboratory in Montana, USA, were Iunveiled. In the $66.5 million facility, researchers will apply similar scientific knowledge to that which makes bio-terrorism or biological warfare a possibility in the first place. The double-edged sword of science application can hardly be more evident. How successfully can we prevent the misuse of research findings that otherwise give us important insights into the workings of nature and prospects of useful applications? What would be the consequences of tackling this problem by constraining research, the mobility of researchers and the funding and publication of their research? Could we, indeed, ever successfully define “research that should not be done”? How much thought should scientists give to the downstream consequences of their work when deciding what to research, or which experiments to do? In June this year, the USA announced that it would delay the introduction of compulsory biometric passports for travellers from 27 countries in Europe and the Asia-Pacific region until October 2006. But whenever they appear, biometric passports will be part of normal life in the future. In the era of international terrorism, this could, indeed, lead to a safer world; an example of a beneficial use of science. On the other hand, it increases the perception by normal citizens that they are being unnecessarily “watched” by an all- seeing, all-controlling state – the so-called Big Brother of Orwell’s 1984.
    [Show full text]
  • “Let There Be Life”
    Focus: Brave New World “We have reason to believe that the disease is created by a man-made super pathogen...” AND MAN SAID, “LETa short story THERE BE LIFE” By Lawrence Valverde e have reason to believe the nearly 200 scientists simmered with “Wdisease is caused by a man- mumbled comments. The researcher made super-pathogen. The construc- whose speech had been interrupted tion seems to be loosely based on the straightened himself and raised his smallpox virus, but with significant voice in response. modifications, including genes encod- “I hear your concern, Dr. Boots, ing immune system antagonists. It but we have not confirmed whether or also seems to have been specifically not this is, in fact, a terrorist act…” engineered to resist known antivi- “Who else would do such a thing, ral…” Dr. Cervantes?” Dr. Boots demanded. “What do you mean specifically “It wasn’t necessarily done on engineered!” boomed an overweight purpose…” said Dr. Cervantes—the man as he hauled himself out of speaker—but he was interrupted by his chair. “Are you proposing that the clamor that erupted as scientists terrorists may have the technology jump up from their seats. Dr. Cervantes to synthetically create their own vi- frowned. Trying to speak over the ruses?” The surrounding panel of crowd was clearly a lost cause. When credit: Clipart courtesy FCIT. http://etc.usf.edu/clipart credit: Clipart courtesy FCIT. fall 2008 • Harvard Science Review 9 valverde.indd 9 2/9/2009 11:24:54 PM Focus: Brave New World did this whole business with artificially Dr. Boots sputtered.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • Profile of Eckard Wimmer
    PROFILE Profile of Eckard Wimmer he finding caused an uproar. vitalism—the belief that chemicals in liv- Researchers at Stony Brook Uni- ing systems are somehow distinct from Tversity in New York had engi- the chemicals in inorganic systems, such neered poliovirus in a test tube as salt and rocks. That notion was shat- (1). The discovery, led by Eckard Wimmer, tered in 1828, when German chemist elected in 2012 to the National Academy Friedrich Wöhler synthesized the organic of Sciences, dispelled the belief that compound urea from inorganic pre- viruses require a live host to grow cursors (5). and spread. By the 1940s, theoretical physicists and The thought of synthetic viruses terrified biochemists had begun to wonder about an American public still reeling from 9/11 what constitutes life. Wimmer was en- and the subsequent anthrax attacks. What thralled. Biochemistry squared perfectly if the technology to engineer viruses with his worldview, the idea that something wound up in the hands of bioterrorists? as seemingly profound as life could be pared However, today, just a decade later, it is down to its simplest—chemical—form. widely accepted that the ability to engineer While completing his second post- viruses also allows researchers to develop doctoral fellowship at the University of viruses that work as synthetic vaccines, British Columbia in Vancouver in the to carry genetic material into a cell for use mid-1960s, Wimmer attended a talk on in gene therapies, or to preferentially viruses and had his eureka moment. “It attack cancer cells (2). was clear, even though it wasn’t men- Wimmer says his motivations for engi- tioned in that talk, that if viruses can be neering polio were strictly scientific.
    [Show full text]
  • Bert Lawrence Semler
    Curriculum Vitae: Bert Lawrence Semler Contact Information Department of Microbiology and Molecular Genetics School of Medicine, Med Sci B237 University of California Irvine, CA 92697 USA E-mail: [email protected] Phone: (949) 824-7573 FAX: (949) 824-2694 Education 1970-1974 University of California, Irvine Bachelor of Science - Biological Sciences 1974-1979 University of California, San Diego Doctor of Philosophy - Biology Research and Professional Experience 1972-1974 Undergraduate research with Professor H. W. Moore Department of Chemistry, University of California, Irvine 1975-1979 Graduate student with Professor John J. Holland Department of Biology, University of California, San Diego 1979-1983 Postdoctoral fellow with Professor Eckard Wimmer, Department of Microbiology, State University of New York at Stony Brook 1983-1987 Assistant Professor, Department of Microbiology and Molecular Genetics College of Medicine, University of California, Irvine 1987-1991 Associate Professor, Department of Microbiology and Molecular Genetics College of Medicine, University of California, Irvine 1991-2018 Professor, Department of Microbiology and Molecular Genetics School of Medicine, University of California, Irvine 1996-2006 Chair, Department of Microbiology and Molecular Genetics School of Medicine, University of California, Irvine 2000-2010 Associate Director, Center for Virus Research University of California, Irvine 2010-present Director, Center for Virus Research University of California, Irvine 2018-present Distinguished Professor, Department
    [Show full text]
  • IMU-Net 88: March 2018 a Bimonthly Email Newsletter from the International Mathematical Union Editor: Martin Raussen, Aalborg University, Denmark
    IMU-Net 88: March 2018 A Bimonthly Email Newsletter from the International Mathematical Union Editor: Martin Raussen, Aalborg University, Denmark CONTENTS 1. Editorial: ICM 2018 2. IMU General Assembly meeting in São Paulo 3. CDC Panel Discussion and Poster Session during ICM 2018 4. Fields medalist Alan Baker passed away 5. CWM: Faces of women in mathematics 6. Report on the ISC general assembly 7. ICIAM 2019 congress 8. Abel Prize 2018 to Robert Langlands 9. 2018 Wolf prizes to Beilinson and Drinfeld 10. MSC 2020: Revision of Mathematics Subject Classification 11. Subscribing to IMU-Net ------------------------------------------------------------------------------------------------------- 1. EDITORIAL: ICM 2018 Dear Colleagues, After so many months of work and expectation, the year of the Congress has finally arrived! Preparations are well under way: the bulk of the scientific program has been defined, the proceedings are being finalized (the papers by plenary and invited speakers will be distributed to all the participants at the Congress), travel grants have been awarded to participants from the developing world, communications and posters are being selected as I write, and registration of participants is also taking place right now. Keep in mind that the deadline for early advance registration, with reduced registration fee, is April 27. Much of our effort over the last couple of years has been geared towards advertising the Congress, domestically and abroad, as we take the occasion as a historic opportunity to popularize mathematics in our society and, especially, amongst the Brazilian youth. I believe we are being very successful. The Biennium of Mathematics 2017-2018, formally proclaimed by the Brazilian national parliament, encompasses a wide range of outreach initiatives throughout the country, and raised the profile of mathematics in mainstream media to totally unprecedented levels.
    [Show full text]
  • Arxiv:2104.06941V2 [Math.AG] 26 May 2021
    RIEMANN-HILBERT CORRESPONDENCE FOR ALEXANDER COMPLEXES LEI WU Abstract. We establish a Riemann-Hilbert correspondence for Alexander complexes (also known as Sabbah specialization complexes) by using relative holonomic D-modules in an equivariant way, which particularly gives a \global" approach to the correspondence for Deligne's nearby cycles. Using the corre- spondence and zero loci of Bernstein-Sato ideals, we obtain a formula for the relative support of the Alexander complexes. Contents 1. Introduction 1 2. Sheafification of sheaves of modules over commutative rings 8 3. Relative maximal and minimal extensions along F 17 4. Alexander complex of Sabbah 34 5. Comparison 35 References 40 1. Introduction Let f be a holomorphic function on a complex manifold X with D the divisor of f and let Ux be a small open neighborhood of x 2 D. Then we consider the fiber product diagram ∗ ∗ ∗ Uex = (Ux n D) ×C Ce Ce exp f ∗ Ux n D C ∗ ∗ ∗ arXiv:2104.06941v3 [math.AG] 1 Sep 2021 where exp: Ce ! C is the universal cover of the punctured complex plane C . ∗ The deck transformation induces a C[π1(C )]-module structure on the compactly i supported cohomology group Hc(Uex; C), which is called the i-th (local) Alexander module of f. Taking Ux sufficiently small, the Alexander modules contain the information of the cohomology groups of the Milnor fibers around x together with their monodromy action. As x varies along D, all the local Alexander modules ∗ give a constructible complex of sheaves of C[π1(C )]-modules, which recovers the Deligne nearby cycle of the constant sheaf along f (see [Bry86]).
    [Show full text]
  • An Introduction to Algebraic D-Modules
    AN INTRODUCTION TO ALGEBRAIC D-MODULES WYATT REEVES Abstract. This paper aims to give a friendly introduction to the theory of algebraic D-modules. Emphasis is placed on examples, computations, and intuition. The paper builds up the basic theory of D-modules, concluding with a proof of the Kashiwara equivalence of categories. We assume knowledge of basic homological algebra, algebraic geometry, and sheaf theory. Contents 1. Introduction 1 2. Differential Operators and D-modules 2 3. Derived Categories 3 4. Filtrations and Gradings 5 5. Pullback of D-modules 6 6. Pushforward of D-modules 9 Acknowledgments 15 References 15 1. Introduction Linearization is a wonderful thing. Let G be a Lie group acting on a smooth manifold X and let E ! X be a G-equivariant vector bundle over X. By generalizing the notion of a Lie derivative, we obtain an action of g on Γ(X; E): let s 2 Γ(X; E) and X 2 g. Define X · s 2 Γ(X; E) to be the section such that d (X · s)(p) = exp(Xt) · s (exp(−Xt) · p) : dt t=0 This action of g on Γ(X; E) should be thought of as the linearization of the action of G on E. The study of this linearized g action has historically been quite fruitful, leading for example to the resolution of the Kazhdan-Lusztig conjectures by Beilinson and Berstein [1]. A group action can be thought of as a map from a group G to the automorphisms of a space X. Analogously, a Lie algebra action can be thought of as a map of g into the derivations of X.
    [Show full text]
  • Department of Mathematics 1
    Department of Mathematics 1 Department of Mathematics Chair • Shmuel Weinberger Professors • Laszlo Babai, Computer Science and Mathematics • Guillaume Bal, Statistics and Mathematics • Alexander A. Beilinson • Danny Calegari • Francesco Calegari • Kevin Corlette • Marianna Csörnyei • Vladimir Drinfeld • Todd Dupont, Computer Science and Mathematics • Matthew Emerton • Alex Eskin • Benson Farb • Robert A. Fefferman • Victor Ginzburg • Denis Hirschfeldt • Kazuya Kato • Carlos E. Kenig • Gregory Lawler, Mathematics and Statistics • Maryanthe Malliaris • J. Peter May • Andre Neves • Bao Châu Ngô • Madhav Vithal Nori • Alexander Razborov, Mathematics and Computer Science • Luis Silvestre • Charles Smart • Panagiotis Souganidis • Sidney Webster • Shmuel Weinberger • Amie Wilkinson • Robert Zimmer Associate Professors • Simion Filip • Ewain Gwynne Assistant Professors • Sebastian Hurtado-Salazar • Dana Mendelson • Nikita Rozenblyum • Daniil Rudenko Instructors • Lucas Benigni • Guher Camliyurt • Stephen Cantrell • Elliot Cartee • Mark Cerenzia 2 Department of Mathematics • Andrea Dotto • Mikolaj Fraczyk • Pedro Gasper • Kornelia Hera • Trevor Hyde • Kasia Jankiewicz • Justin Lanier • Brian Lawrence • Zhilin Luo • Akhil Mathew • Henrik Matthieson • Cornelia Mihaila • Lucia Mocz • Benedict Morrissey • Davi Obata • Lue Pan • Wenyu Pan • Beniada Shabani • Danny Shi • Daniel Stern • Ao Sun • Xuan Wu • Zihui Zhao • Jinping Zhuge Senior Lecturers • John Boller • Lucas Culler • Jitka Stehnova • Sarah Ziesler Lecturer • Meghan Anderson Assistant Instructional
    [Show full text]