DOCSLIB.ORG

The Scientific Context

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Scientific Context Center for Quantum Geometry of Moduli Spaces Proposal for the Danish National Research Foundation The Scientific Context: The role of mathematics in our understanding of nature has been recognized for millennia. Its importance is especially poignant in modern theoretical physics as the cost of experiment escalates and the mathematical complexity of physical theories increases. Major challenge: Discover the mathematical mechanisms to define quantum field theory as a mathematical entity, to justify mathematically the recipes used by physicists, and to unify quantum theory with gravity. Classical and quantum mechanics rests on solid mathematical foundations, which were developed over the last two centuries. In contrast, quantum field theory, which plays a central role in modern theoretical physics, lacks a mathematical foundation. The mathematical difficulties involve averaging over infinite-dimensional spaces, which have defied rigorous interpretation and yet are effective in practice according to explicit recipes in physics. For example, the Standard Model of particle physics successfully predicts to a dozen decimals experimental results from high-energy colliders such as CERN or SLAC. Quantum field theory has enjoyed several important successes in the last two decades where a number of models were constructed despite the difficulties described above. In all these cases, the theory admits a large family of symmetries, and the problematic infinite-dimensional averages reduce to averages over smaller ensembles, called moduli spaces, which are in many cases finite-dimensional and permit mathematically rigorous calculations. Also, low-dimensional models unifying gravity with quantum theory have been developed successfully, and the key geometrical objects are again moduli spaces. Quantum geometry, so-named since the quantization arises from geometric methods designed to make a passage from classical geometry to quantum theory, plays the fundamental role in all these constructions. Quantum geometry of Moduli Spaces combines the many ideas and techniques developed over the last decades and provides the current most promising resolution of the major challenge for a large class of quantum field theories. Center for Quantum Geometry of Moduli Spaces Proposal for the Danish National Research Foundation Research Mission: • In response to this need for a systematic mathematical approach to quantum field theory and string theory, we propose to establish the Center for the Quantum Geometry of Moduli Spaces at the University of Aarhus, with the aspiration to become the world-leading center at this crucial interface between mathematics and theoretical physics. • The conceptual goals of the proposed Center are: • to significantly advance the understanding of moduli spaces and their quantization in order to provide the mathematical underpinnings of contemporary and future physical theories; • to train the next generation of scholars and researchers at the Center to be the world-leading experts on this important confluence of mathematics and theoretical physics; • to build the Center into a world-renowned catalyst of collaborative cutting-edge research and training in the quantum geometry of moduli spaces. • The specific research mission of the proposed Center is to develop the quantum geometry of moduli spaces so as to provide complete mathematical models for a number of quantum field theories. In particular four specific deep research topics will receive our primary attention: The Geometric Langlands Program and Higgs- Topologically twisted quantum Yang-Mills theories .The bundle Moduli Spaces “standard model” of particle physics is a quantum Yang- Mills theory. Toeplitz operators and geometric quantization of Quantum Chern-Simons theory. Two spatial and one time moduli spaces dimension. Combinatorial models for moduli spaces and Quantum gravity so far only in one and two spatial quantum moduli spaces dimensions plus one time dimension. Quantum representation theory and perturbative Relevant for our understanding all quantum field theories. invariants Center for Quantum Geometry of Moduli Spaces Proposal for the Danish National Research Foundation The proposed Center: • To meet these objectives, the Center will build on the existing Niels Bohr Professorship initiative around Professor Nicolai Reshetikhin, the Aarhus based researchers involved in this initiative and the regularly recurring long-term visitors it has attracted to Aarhus, in particular: – Professor Robert Penner, recurring visitor from University of Southern California; – Professor Vladimir Fock. recurring visitor from Strasbourg University; • In addition, – Professor Maxim Kontsevich, IHES Paris, recipient of the 2000 Fields Medal (the mathematical equivalent of the Nobel Prize) and the 2008 Crawford Prize; – Savilian Professor of Geometry Nigel Hitchin, University of Oxford, recipient of the 2000 Sylvester Medal and 2002 Polya Prize; are enthusiastic partners in the Center and its activities contributing their time, effort, and institutional funds and resources. • These are outstanding scholars whose commitment ensures the success of the Center. The research programs of these personnel are intrinsically and deeply inter-connected forming a natural base for their collaborative research. • The expected advances and milestones detailed in our joint research mission will constitute major progress in our mathematical understanding of the world around us and the forces which govern it. – Further unexpected practical spin-off to the protein folding problem in Biology and Quantum Computing in Computer Science/Physics are under development. • The scientific strength and visibility of the team and their existing collaborations with one another and around the globe warrant the success of the Center in achieving its ambitious intellectual goals, in attracting the highest level international collaborators and affiliates, and in educating and stimulating the next generation of Danish mathematicians and mathematical physicists. • The Human Ressource Mission includes the opportunity for Danish students and post docs to participate at the apex of this exciting field and take part in breakthroughs among this elite team. Center for Quantum Geometry of Moduli Spaces Proposal for the Danish National Research Foundation The proposed center director • Jørgen Ellegaard Andersen born 16’th of June 1965. • D.Phil in Mathematics from Oxford University in 1992. • C.B. Morrey Jr. Assistant Professor at Department of Mathematics at U. C. Berkeley, where he participated in and co-directed several NSF grants during 1992 to 1997. • Associate Professor of Mathematics at Aarhus University in 1997. • The Danish Bank Scholarship Prize in 2000 was spent at the Mathematical Sciences Research Institute in Berkeley. • Clay Professor at UC Berkeley funded by the Clay Mathematics Institute 2001 to 2002. • Returned to Aarhus University in 2002 and in 2007 he was appointed professor of mathematics. • International leader in the field of quantization of moduli spaces, Hitchin's connection and its relation to Toeplitz operators and the Reshetikhin-Turaev quantum field theories, where he has produced a number of breakthrough results written up in 34 research papers published in international journals. The main research results include: – The asymptotic faithfulness of the Reshetikhin-Turaev quantum field theory representations of the mapping class groups. – Resolution of the Property T question for mapping class groups using quantum geometry of moduli spaces, a long-standing problem in geometric group theory. – The Reshtikhin-Turaev quantum field theory determines the unknot. • He currently directs: – CTQM, initiated in 2006 based on a grant from FNU; – The Niels Bohr Professorship (Nicolai Reshetikhin) funded by Danish National Research Foundation; – GEOMAPS, a PhD-school coordinating Danish research groups on the interface of geometry and theoretical physics; – ITGP, a European Science Foundation network which involves the top 170 researcher within the area of Interactions of Low-Dimensional Topology and Geometry with Mathematical Physics from 21 countries. • Editor of two top international mathematics journals. • Supervisor of 9 PhD-students, five of whom currently work on Quantum Geometry of Moduli Spaces. • Plenary speaker at numerous international conferences, master classes and distinguished lecture series. Center for Quantum Geometry of Moduli Spaces Proposal for the Danish National Research Foundation The Principal Researchers: Professor Jørgen Ellegaard Andersen Professor Henning Haahr Andersen Assoc. professor Alexei Venkov Assoc. Professor Anna Beliakova Aarhus University Aarhus University Aarhus University Aarhus University Niels Bohr Professor Nicolai Reshetikhin Professor Robert Penner Professor Vladimir Fock Recurring visitor from U.C. Berkeley Recurring visitor from U. Southern California Recurring visitor from Strasbourg University Professor Maxim Kontsevich, Fieldsmedalist Savilian Professor Nigel Hitchin Institut des Hautes Études Scientifiques Oxford University.
Load more

Recommended publications
  • CURRICULUM VITAE David Gabai EDUCATION Ph.D. Mathematics
    CURRICULUM VITAE David Gabai EDUCATION Ph.D. Mathematics, Princeton University, Princeton, NJ June 1980 M.A. Mathematics, Princeton University, Princeton, NJ June 1977 B.S. Mathematics, M.I.T., Cambridge, MA June 1976 Ph.D. Advisor William P. Thurston POSITIONS 1980-1981 NSF Postdoctoral Fellow, Harvard University 1981-1983 Benjamin Pierce Assistant Professor, Harvard University 1983-1986 Assistant Professor, University of Pennsylvania 1986-1988 Associate Professor, California Institute of Technology 1988-2001 Professor of Mathematics, California Institute of Technology 2001- Professor of Mathematics, Princeton University 2012-2019 Chair, Department of Mathematics, Princeton University 2009- Hughes-Rogers Professor of Mathematics, Princeton University VISITING POSITIONS 1982-1983 Member, Institute for Advanced Study, Princeton, NJ 1984-1985 Postdoctoral Fellow, Mathematical Sciences Research Institute, Berkeley, CA 1985-1986 Member, IHES, France Fall 1989 Member, Institute for Advanced Study, Princeton, NJ Spring 1993 Visiting Fellow, Mathematics Institute University of Warwick, Warwick England June 1994 Professor Invité, Université Paul Sabatier, Toulouse France 1996-1997 Research Professor, MSRI, Berkeley, CA August 1998 Member, Morningside Research Center, Beijing China Spring 2004 Visitor, Institute for Advanced Study, Princeton, NJ Spring 2007 Member, Institute for Advanced Study, Princeton, NJ 2015-2016 Member, Institute for Advanced Study, Princeton, NJ Fall 2019 Visitor, Mathematical Institute, University of Oxford Spring 2020
    [Show full text]
  • New Trends in Teichmüller Theory and Mapping Class Groups
    Mathematisches Forschungsinstitut Oberwolfach Report No. 40/2018 DOI: 10.4171/OWR/2018/40 New Trends in Teichm¨uller Theory and Mapping Class Groups Organised by Ken’ichi Ohshika, Osaka Athanase Papadopoulos, Strasbourg Robert C. Penner, Bures-sur-Yvette Anna Wienhard, Heidelberg 2 September – 8 September 2018 Abstract. In this workshop, various topics in Teichm¨uller theory and map- ping class groups were discussed. Twenty-three talks dealing with classical topics and new directions in this field were given. A problem session was organised on Thursday, and we compiled in this report the problems posed there. Mathematics Subject Classification (2010): Primary: 32G15, 30F60, 30F20, 30F45; Secondary: 57N16, 30C62, 20G05, 53A35, 30F45, 14H45, 20F65 IMU Classification: 4 (Geometry); 5 (Topology). Introduction by the Organisers The workshop New Trends in Teichm¨uller Theory and Mapping Class Groups, organised by Ken’ichi Ohshika (Osaka), Athanase Papadopoulos (Strasbourg), Robert Penner (Bures-sur-Yvette) and Anna Wienhard (Heidelberg) was attended by 50 participants, including a number of young researchers, with broad geo- graphic representation from Europe, Asia and the USA. During the five days of the workshop, 23 talks were given, and on Thursday evening, a problem session was organised. Teichm¨uller theory originates in the work of Teichm¨uller on quasi-conformal maps in the 1930s, and the study of mapping class groups was started by Dehn and Nielsen in the 1920s. The subjects are closely interrelated, since the mapping class group is the
    [Show full text]
  • Trustees, Administration, Faculty
    Section Six Trustees, Administration, Faculty 546 Trustees, Administration, Faculty OFFICERS Robert B. Chess (2006) Chairman Nektar Therapeutics Kent Kresa, C hairman Lounette M. Dyer (1998) David L. Lee, V ice Chairman Gilad I. Elbaz (2008) Founder Jean-Lou Chameau, President Factual Inc. Edward M. Stolper, Provost William T. Gross (1994) C hairman and Founder Dean W. Currie Idealab V ice President for Business and Frederick J. Hameetman (2006) Finance Chairman Charles Elachi Cal American Vice President and Director, Jet R obert T. Jenkins (2005) Propulsion Laboratory Peter D. Kaufman (2008) Peter D. Hero Chairman and CEO Vice President for Glenair, Inc. Development and Institute Jon Faiz Kayyem (2006) Relations CEO Sharon E. Patterson Osmetech PLC Associate Vice President for Louise Kirkbride (1995) Finance and Treasurer Board Member Scott Richland State of California Contractors Chief Investment Officer State License Board Anneila I. Sargent Jon B. Kutler (2005) Vice President for Student Chairman and CEO Affairs Admiralty Partners, Inc. Victoria D. Stratman Louis J. Lavigne Jr. (2009) General Counsel Management Consultant Mary L. Webster Lavigne Group Secretary David Li Lee (2000) Managing General Partner Clarity Partners, L.P. BOARD OF TRUSTEES York Liao (1997) Managing Director Winbridge Company Ltd. Trustees Alexander Lidow (1998) (with date of first election) CEO EPC Corporation Robert C. Bonner (2008) Ronald K. Linde (1989) Senior Partner Independent Investor Sentinel HS Group, L.L.C. Chair, The Ronald and Maxine Brigitte M. Bren (2009) Linde Foundation John E. Bryson (2005) Founder/Former CEO Chairman and CEO (Retired) Envirodyne Industries, Inc. Edison International Shirley M. Malcom (1999) Jean-Lou Chameau (2006) Director, Education and Human President Resources Programs California Institute of Technology American Association for the Milton Chang (2005) Advancement of Science Managing Director Deborah McWhinney (2007) President Incubic Venture Capital 547 John S.
    [Show full text]
  • Chern-Simons Gauge Theory: 20 Years After
    %17-4 7XYHMIWMR Advanced 1EXLIQEXMGW S.-T. Yau, 7IVMIW Editor Chern-Simons Gauge Theory: 20 Years After Jørgen E. Andersen Hans U. Boden Atle Hahn Benjamin Himpel Editors %QIVMGER1EXLIQEXMGEP7SGMIX]-RXIVREXMSREP4VIWW Chern-Simons Gauge Theory: 20 Years After https://doi.org/10.1090/amsip/050 AMS/IP Studies in Advanced Mathematics Volume 50 Chern-Simons Gauge Theory: 20 Years After Jørgen E. Andersen Hans U. Boden Atle Hahn Benjamin Himpel Editors American Mathematical Society • International Press Shing-Tung Yau, General Editor 2000 Mathematics Subject Classification. Primary 11F23, 14E20, 16S10, 19L10, 20C20, 20F99, 20L05, 30F60, 32G15, 46E25, 53C50, 53D20, 53D99, 54C40, 55R80, 57M25, 57M27, 57M60, 57M50, 57N05, 57N10, 57R56, 58D27, 58D30, 58E09, 58J28, 58J30, 58J52, 58Z05, 70S15, 81T08, 81T13, 81T25, 81T30, 81T45, 83C80. Library of Congress Cataloging-in-Publication Data Chern-Simons gauge theory: 20 years after / Jørgen E. Andersen ...[et al.], editors. p. cm. (AMS/IP studies in advanced mathematics ; v. 50) Proceedings of a workshop held at the Max Planck Institute for Mathematics in Bonn, Aug. 3–7, 2009. Includes bibliographical references. ISBN 978-0-8218-5353-5 (alk. paper) 1. Number theory—Congresses. 2. Algebraic topology—Congresses. 3. Associative rings— Congresses. 4. K-theory—Congresses. 5. Group theory—Congresses. I. Andersen, Jørgen E. 1965– QA241.C6355 2010 514.74—dc22 2011012166 Copying and reprinting. Material in this book may be reproduced by any means for edu- cational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledg- ment of the source is given.
    [Show full text]
  • LETTERS to the EDITOR Responses to ”A Word From… Abigail Thompson”
    LETTERS TO THE EDITOR Responses to ”A Word from… Abigail Thompson” Thank you to all those who have written letters to the editor about “A Word from… Abigail Thompson” in the Decem- ber 2019 Notices. I appreciate your sharing your thoughts on this important topic with the community. This section contains letters received through December 31, 2019, posted in the order in which they were received. We are no longer updating this page with letters in response to “A Word from… Abigail Thompson.” —Erica Flapan, Editor in Chief Re: Letter by Abigail Thompson Sincerely, Dear Editor, Blake Winter I am writing regarding the article in Vol. 66, No. 11, of Assistant Professor of Mathematics, Medaille College the Notices of the AMS, written by Abigail Thompson. As a mathematics professor, I am very concerned about en- (Received November 20, 2019) suring that the intellectual community of mathematicians Letter to the Editor is focused on rigor and rational thought. I believe that discrimination is antithetical to this ideal: to paraphrase I am writing in support of Abigail Thompson’s opinion the Greek geometer, there is no royal road to mathematics, piece (AMS Notices, 66(2019), 1778–1779). We should all because before matters of pure reason, we are all on an be grateful to her for such a thoughtful argument against equal footing. In my own pursuit of this goal, I work to mandatory “Diversity Statements” for job applicants. As mentor mathematics students from diverse and disadvan- she so eloquently stated, “The idea of using a political test taged backgrounds, including volunteering to help tutor as a screen for job applicants should send a shiver down students at other institutions.
    [Show full text]
  • Moduli Spaces and Macromolecules
    BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 53, Number 2, April 2016, Pages 217–268 http://dx.doi.org/10.1090/bull/1524 Article electronically published on February 3, 2016 MODULI SPACES AND MACROMOLECULES R. C. PENNER Abstract. Techniques from moduli spaces are applied to biological macro- molecules. The first main result provides new a priori constraints on protein geometry discovered empirically and confirmed computationally. The second main result identifies up to homotopy the natural moduli space of several in- teracting RNA molecules with the Riemann moduli space of a surface with several boundary components in each fixed genus. Applications to RNA fold- ing prediction are discussed. The mathematical and biological frameworks are surveyed and presented from first principles. Contents Introduction 218 1. Moduli spaces 220 1.1. Conformal quadrilaterals 221 1.2. Triangles in neutral geometries 222 1.3. Elliptic curves 224 1.4. Riemann moduli space 226 1.5. Fatgraphs 229 1.6. Graph connections 233 2. Protein 235 2.1. Chemistry and geometry 235 2.2. Protein folding 237 2.3. Fatgraph model 239 2.4. SO(3)-graph connections 240 2.5. Further remarks on protein 244 3. Sugar 245 4. RNA 247 4.1. Chemistry and topology 247 4.2. RNA Folding 250 4.3. Chord diagrams, seeds, and shapes 253 4.4. Further remarks on RNA 257 Appendix. Matrix models 260 Acknowledgments 262 About the author 262 References 262 Received by the editors August 24, 2015. 2010 Mathematics Subject Classification. Primary 92-02, 92C40, 92C05, 30F60, 32G15, 53C05. Key words and phrases.
    [Show full text]
  • Institut Des Hautes Ét Udes Scientifiques Rapport Annuel 2018
    RAPPORT ANNUEL 2018 INSTITUT 60 ANS DES HAUTES ÉT U D E S SCIENTIFIQUES Fondation Reconnue d’Utilité Publique depuis 1981 IHES Rapport annuel 2018 | 1 TABLE DES MATIÈRES TABLE OF CONTENTS Message du Président P.3 A Word from the Chairman L’IHES en bref P.4 IHES in a nutshell Recherche et événements P.7 Research and Events Prix et disti ncti ons scienti fi ques P.8 Scienti fi c Awards Vie scienti fi que P.9 Scienti fi c Acti vity Professeurs P.19 Professors Professeurs permanents P.19 Permanent Professors Chercheurs CNRS à l’IHES P.26 CNRS Researchers at IHES Directeur P.30 Director Membres émérites P.31 Emeritus Members Chercheurs invités P.34 Invited Researchers Stati sti ques P.34 Stati sti cs Professeurs associés P.38 Associate Professors Programme général d’invitati ons P.46 General Invitati on Programme Post-doctorants P.52 Postdocs Événements P.54 Events Cours de l’IHES P.54 Cours de l’IHES Conférences et séminaires P.55 Conferences and Seminars Administrati on P.63 Management Gouvernance P.64 Governance Conseil scienti fi que P.64 Scienti fi c Council Conseil d’administrati on P.65 Board of Directors Souti ens insti tuti onnels P.66 Partners Situati on fi nancière P.67 Financial Report Rapport du commissaire aux comptes P.67 Statutory Auditor’s Report Bilan et compte de résultat P.70 Balance Sheets and Statements of Financial Acti viti es Note fi nancière P.72 Financial Notes Développement et communicati on P.74 Development and Communicati on Donateurs P.78 Donors Les Amis de l’IHES P.82 Les Amis de l’IHES Aperçu 2019 P.84 2019 Preview
    [Show full text]
  • Publications 1. (With AA Boni)
    Publications 1. (with A. A. Boni) “Sensitivity analysis of a mechanism for methane oxidation kinetics”, Combustion Science and Technology 15 (1977), 99-106. 2. “The action of the mapping class group on isotopy classes of curves and arcs in surfaces”, thesis, Massachusetts Institute of Technology (1982), 180 pages. 3. “The action of the mapping class group on curves in surfaces”, proceedings of the Sexta Escuela Latino Americana de Matematicas, Oaxtepec, Mexico (1982), 59-82. 4. “The action of the mapping class group on curves in surfaces”, L’Enseignement Mathematique 30 (1984), 39-55. 5. “The theory of surface homeomorphisms”, Institut Mittag-Leffler, Report number 1 (1984). 6. “An introduction to train tracks”, Low-dimensional Topology and Kleinian Groups, London Math. Soc. Lecture Notes 112 (1986), 77-90. 7. “Extremal length on Denjoy domains”, Transactions of the American Math Society 102 (1988), 641-645. 8. (with D. B. A. Epstein) “Euclidean decompositions of non-compact hyperbolic manifolds”, Journal of Differential Geometry 27 (1988), 67-80. 9. “The moduli space of a punctured surface and perturbative series”, Bulletin of the American Math Society 15 (1986), 73-77. 10. (with A. Papadopoulos) “A characterization of pseudo-Anosov foliations”, Pacific Journal of Mathematics 130 (1987), 359-377. 11. “The moduli space of punctured surfaces”, Proceedings of Mathematical Aspects of String Theory, Advanced Series in Mathematics Physics 1 (1987), World Scientific, 313-340. 12. “Perturbative series and the moduli space of Riemann surfaces”, Journal of Dif- ferential Geometry 27 (1988), 35-53. 13. “The decorated Teichm¨uller space of punctured surfaces”, Communications in Mathematical Physics 113 (1987), 299-339.
    [Show full text]
  • Trustees, Administration, Faculty
    Section Six Trustees, Administration, Faculty 628 Trustees, Administration, Faculty OFFICERS Peggy L. Cherng (2012) Co-Chairman Panda Restaurant Group David L. Lee, Chairman Robert B. Chess (2006) Ronald K. Linde, Vice Chairman Chairman Nektar Therapeutics Thomas F. Rosenbaum, President David Dreier (2013) Edward M. Stolper, Provost Lounette M. Dyer (1998) Joshua S. Friedman (2012) Matthew Brewer Co-founder, Co-Chairman and Controller Co-Chief Executive Officer Dean W. Currie Canyon Partners, LLC Vice President for Business and William T. Gross (1994) Finance Founder and Chief Executive Officer Charles Elachi Idealab Vice President and Director, Jet Narenda K. Gupta (2011) Propulsion Laboratory Co-Founder and Managing Director Diana Jergovic Nexus Venture Partners Vice President for Maria D. Hummer-Tuttle (2012) Strategic Implementation President Brian K. Lee Hummer Tuttle Foundation Vice President for Robert T. Jenkins (2005) Development and Institute G. Bradford Jones (2014) Relations Founding Partner Sharon E. Patterson Redpoint Ventures Associate Vice President for Peter D. Kaufman (2008) Finance and Treasurer Chairman and Chief Executive Officer Scott Richland Glenair, Inc. Chief Investment Officer Louise Kirkbride (1995) Joseph E. Shepherd Board Member Vice President for Student State of California Contractors Affairs State License Board Victoria D. Stratman Walter G. Kortschak (2012) General Counsel Senior Advisor and Former Managing Mary L. Webster Partner Secretary Summit Partners, L.P. Jon B. Kutler (2005) Chairman and Chief Executive Officer BOARD OF TRUSTEES Admiralty Partners, Inc. David Li Lee (2000) Trustees Managing General Partner (with date of first election) Clarity Partners, L.P. York Liao (1997) Sean Bailey (2015) Managing Director President Winbridge Company Ltd.
    [Show full text]
  • Trustees, Administration, Faculty
    Section Six Trustees, Administration, Faculty 616 Trustees, Administration, Faculty OFFICERS Peggy L. Cherng (2012) Co-Chairman Panda Restaurant Group David L. Lee, C hairman Robert B. Chess (2006) Ronald K. Linde, V ice Chairman C hairman Nektar Therapeutics Edward M. Stolper, Interim President and David Dreier (2013) Provost Lounette M. Dyer (1998) Joshua S. Friedman (2012) Matthew Brewer Co-founder, Co-Chairman and Controller Co-Chief Executive Officer D ean W. Currie Canyon Partners, LLC Vice President for Business and W illiam T. Gross (1994) Finance Founder and CEO Charles Elachi Idealab Vice President and Director, Jet Narenda K. Gupta (2011) Propulsion Laboratory Co-Founder and Managing Director Brian K. Lee Nexus Venture Partners Vice President for B. Kipling Hagopian (2012) Development and Institute Managing Partner Relations Apple Oaks Partners, LLC Sharon E. Patterson Maria Hummer-Tuttle (2012) Associate Vice President for President Finance and Treasurer Hummer Tuttle Foundation Scott Richland Rober t T. Jenkins (2005) Chief Investment Officer Peter D. Kaufman (2008) Anneila I. Sargent Chairman and CEO Vice President for Student Glenair, Inc. Affairs Louise Kirkbride (1995) Victoria D. Stratman Board Member General Counsel State of California Contractors Mary L. Webster State License Board Secretary Walter G. Kortschak (2012) Senior Advisor and Former Managing Partner BOARD OF TRUSTEES Summit Partners, L.P. Jon B. Kutler (2005) Chairman and CEO Trustees Admiralty Partners, Inc. (with date of first election) David Li Lee (2000) Managing General Partner Robert C. Bonner (2008) Clarity Partners, L.P. Senior Partner York Liao (1997) Sentinel HS Group, L.L.C. Managing Director Brigitte M.
    [Show full text]
  • Cluster Algebras: an Introduction
    CLUSTER ALGEBRAS: AN INTRODUCTION LAUREN K. WILLIAMS Dedicated to Andrei Zelevinsky on the occasion of his 60th birthday Abstract. Cluster algebras are commutative rings with a set of distinguished generators having a remarkable combinatorial structure. They were introduced by Fomin and Zelevinsky in 2000 in the context of Lie theory, but have since appeared in many other contexts, from Poisson geometry to triangulations of surfaces and Teichm¨uller theory. In this expository paper we give an introduc- tion to cluster algebras, and illustrate how this framework naturally arises in Teichm¨uller theory. We then sketch how the theory of cluster algebras led to a proof of the Zamolodchikov periodicity conjecture in mathematical physics. Contents 1. Introduction 1 2. What is a cluster algebra? 3 3. Cluster algebras in Teichm¨uller theory 12 4. Cluster algebras and the Zamolodchikov periodicity conjecture 18 References 24 1. Introduction Cluster algebras were conceived by Fomin and Zelevinsky [13] in the spring of 2000 as a tool for studying total positivity and dual canonical bases in Lie theory. However, the theory of cluster algebras has since taken on a life of its own, as connections and applications have been discovered to diverse areas of mathematics including quiver representations, Teichm¨uller theory, tropical geometry, integrable systems, and Poisson geometry. In brief, a cluster algebra A of rank n is a subring of an ambient field F of rational functions in n variables. Unlike “most” commutative rings, a cluster algebra is not presented at the outset via a complete set of generators and relations. Instead, from the initial data of a seed – which includes n distinguished generators called cluster variables plus an exchange matrix – one uses an iterative procedure called mutation to produce the rest of the cluster variables.
    [Show full text]
  • To Mark the Completion of the Ipmus Research Building, a Ceremony And
    Murayama and President Hamada, (ination) just after its birth, and then News please refer to http///www.ipmu.jp/ turned into a very hot reball. ja/node/643). Following the speeches, distinguished guests, Mr.Shigeo Okaya Keiichi Maeda Received Young (Director of the Strategic Programs Astronomer Award Division, S&T Policy Bureau, MEXT) On January 23, 2010, the and Prof. Toshio Kuroki (WPI Program Astronomical Society of Japan (ASJ) Director and Deputy Director of the announced that Keiichi Maeda, an Research Center for Scientic Systems, assistant professor at IPMU, had been JSPS) offered words of congratulation. selected as a recipient of the ASJ Young Then, Prof. Hidetoshi Ohno of the Astronomer Award for his contribution University of Tokyo Graduate School to the“ theoretical and observational , Inauguration Ceremony of IPMU’s of Frontier Sciences the architect study on the structure of supernova Research Building on February who designed the building, explained explosions.” Prof. Maeda developed a 23rd the concept he used to design the new method to theoretically calculate To mark the completion of the IPMU’s new building, as“ a place having the emissions from supernovae, and he also Research Building, a ceremony and capability” to create communication discovered new aspects of supernova reception were held on February 23, among researchers. explosions through observations by the 2010, with about 150 people (guests, At the reception, the IPMU Chamber Subaru and other telescopes. The award University of Tokyo researchers, and Orchestra, consisting of IPMU’s ceremony took place on March 25, 2010 administrative staff) in attendance. researchers, administrative staff, and at the annual meeting of the ASJ.
    [Show full text]