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October 2013
LONDONLONDON MATHEMATICALMATHEMATICAL SOCIETYSOCIETY NEWSLETTER No. 429 October 2013 Society MeetingsSociety 2013 ELECTIONS voting the deadline for receipt of Meetings TO COUNCIL AND votes is 7 November 2013. and Events Members may like to note that and Events NOMINATING the LMS Election blog, moderated 2013 by the Scrutineers, can be found at: COMMITTEE http://discussions.lms.ac.uk/ Thursday 31 October The LMS 2013 elections will open on elections2013/. Good Practice Scheme 10th October 2013. LMS members Workshop, London will be contacted directly by the Future elections page 15 Electoral Reform Society (ERS), who Members are invited to make sug- Friday 15 November will send out the election material. gestions for nominees for future LMS Graduate Student In advance of this an email will be elections to Council. These should Meeting, London sent by the Society to all members be addressed to Dr Penny Davies 1 page 4 who are registered for electronic who is the Chair of the Nominat- communication informing them ing Committee (nominations@lms. Friday 15 November that they can expect to shortly re- ac.uk). Members may also make LMS AGM, London ceive some election correspondence direct nominations: details will be page 5 from the ERS. published in the April 2014 News- Monday 16 December Those not registered to receive letter or are available from Duncan SW & South Wales email correspondence will receive Turton at the LMS (duncan.turton@ Regional Meeting, all communications in paper for- lms.ac.uk). Swansea mat, both from the Society and 18-21 December from the ERS. Members should ANNUAL GENERAL LMS Prospects in check their post/email regularly in MEETING Mathematics, Durham October for communications re- page 11 garding the elections. -
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. -
William M. Goldman June 24, 2021 CURRICULUM VITÆ
William M. Goldman June 24, 2021 CURRICULUM VITÆ Professional Preparation: Princeton Univ. A. B. 1977 Univ. Cal. Berkeley Ph.D. 1980 Univ. Colorado NSF Postdoc. 1980{1981 M.I.T. C.L.E. Moore Inst. 1981{1983 Appointments: I.C.E.R.M. Member Sep. 2019 M.S.R.I. Member Oct.{Dec. 2019 Brown Univ. Distinguished Visiting Prof. Sep.{Dec. 2017 M.S.R.I. Member Jan.{May 2015 Institute for Advanced Study Member Spring 2008 Princeton University Visitor Spring 2008 M.S.R.I. Member Nov.{Dec. 2007 Univ. Maryland Assoc. Chair for Grad. Studies 1995{1998 Univ. Maryland Professor 1990{present Oxford Univ. Visiting Professor Spring 1989 Univ. Maryland Assoc. Professor 1986{1990 M.I.T. Assoc. Professor 1986 M.S.R.I. Member 1983{1984 Univ. Maryland Visiting Asst. Professor Fall 1983 M.I.T. Asst. Professor 1983 { 1986 1 2 W. GOLDMAN Publications (1) (with D. Fried and M. Hirsch) Affine manifolds and solvable groups, Bull. Amer. Math. Soc. 3 (1980), 1045{1047. (2) (with M. Hirsch) Flat bundles with solvable holonomy, Proc. Amer. Math. Soc. 82 (1981), 491{494. (3) (with M. Hirsch) Flat bundles with solvable holonomy II: Ob- struction theory, Proc. Amer. Math. Soc. 83 (1981), 175{178. (4) Two examples of affine manifolds, Pac. J. Math.94 (1981), 327{ 330. (5) (with M. Hirsch) A generalization of Bieberbach's theorem, Inv. Math. , 65 (1981), 1{11. (6) (with D. Fried and M. Hirsch) Affine manifolds with nilpotent holonomy, Comm. Math. Helv. 56 (1981), 487{523. (7) Characteristic classes and representations of discrete subgroups of Lie groups, Bull. -
Obituary Notices Ronald Drayton Brown
Obituary notices Ronald Drayton Brown Died 31 October 2008, elected to Fellowship 1965 Ronald Drayton (Ron) Brown was born in Melbourne on 14 October 1927. He grew up as an only child in modest suburban circumstances in Prahran and did not come from a scientific or academic background. His father had achieved some distinction in amateur athletics. His secondary education was at Wesley College, to which he had won a scholarship. He excelled in mathematics and physics and was an interested reader of astronomy books. He was dux of the school in his final year and was awarded an exhibition in physics in the Victorian matriculation examinations. In his first undergraduate year at the University of Melbourne, he majored in physics and chemistry. In second year he dropped Ron Brown physics, despite scoring better results than in chemistry. While completing a chemistry major he also informally attended the lectures in third year physics and mathematics, without completing the examinations, ending up with an effective triple major for his BSc in 1946. In the days before it was possible to do a PhD anywhere in Australia, Ron began his research career as an MSc student in the Department of Chemistry at the University of Melbourne with Dr Francis Lahey as supervisor. His thesis topic was alkaloid products from Australian plants, particularly Acronychia baueri. He had chosen this project because it would involve some organic chemistry and some spectroscopy. He was attracted by the relationships between the structure of organic compounds and their spectra, and the use of these ideas in deducing the structure of newly isolated compounds. -
CSIRO Annual Report 2016-17
Annual Report 2016–17 Australia’s innovation catalyst CSIRO, in partnership with Deakin University, launched Australia’s first carbon fibre production facility. Carbon fibre is a low weight product with high rigidity, tensile strength and chemical resistance that is used in aerospace, civil engineering, cars, health and the military. Successful collaborations like this demonstrate how the Australian research sector can accelerate research, lead innovation and expand job opportunities in the country. About this report This annual report is a summary of CSIRO’s activities and financial position for the 12-month period ended 30 June 2017. In this report, unless otherwise stated, references to the ‘organisation’, ‘we’, ‘us’ and ‘our’ refer to CSIRO as a whole. In this report, references to a year are to the financial year ended 30 June 2017, unless otherwise stated. It is also available at: www.csiro.au/annualreport2017. COVER: Nanomaterials, like the carbon nanotubes illustrustrated on the front cover, are extremely small chemicals, millionths of a millimetre in size. They come in many forms each with unique mechanical, electronic and optical properties. Through the development of new products and processes, nanotechnology will potentially contribute solutions to major challenges facing Australia in the electronic, energy and environmental sectors. Image: Amanda Barnard, Data61 i www.csiro.au CSIRO Head Office Clunies Ross Street, Acton ACT 2601 GPO Box 1700, Canberra ACT 2601 Australia T (02) 6276 6000 • ABN 41 687 119 230 1 September 2017 The Hon Arthur Sinodinos AO Minister for Industry, Innovation and Science Parliament House CANBERRA ACT 2600 Australia’s national science agency took strides forward on its Strategy 2020 through the year ending 30 June 2017. -
Arxiv:1502.01692V2 [Math.DG]
LIMITING CONFIGURATIONS FOR SOLUTIONS OF HITCHIN’S EQUATION RAFE MAZZEO, JAN SWOBODA, HARTMUT WEISS, AND FREDERIK WITT Abstract. We review recent work on the compactification of the mod- uli space of Hitchin’s self-duality equation. We study the degeneration behavior near the ends of this moduli space in a set of generic directions by showing how limiting configurations can be desingularized. Following ideas of Hitchin, we can relate the top boundary stratum of this space of limiting configurations to a Prym variety. A key rˆole is played by the family of rotationally symmetric solutions to the self-duality equation on C, which we discuss in detail here. Contents 1. Introduction 1 2. Holomorphic bundles with Higgs fields 3 2.1. Stable bundles 3 2.2. Higgs bundles 5 2.3. Parabolic Higgs bundles 7 2.4. Spectral curves 8 3. Limiting configurations 9 3.1. Motivation 9 3.2. The fiducial solution 9 3.3. Construction of limiting configurations 13 4. Desingularization by gluing 16 5. The hyperk¨ahler metric 19 5.1. Moment maps 19 arXiv:1502.01692v2 [math.DG] 2 Jul 2015 5.2. The semi-flat metric 20 References 21 1. Introduction The moduli space of Higgs bundles, introduced by Hitchin [Hi87] and Simpson [Si88], is a well investigated object in algebraic geometry and topol- ogy. We wish here to study it from the viewpoint of Riemannian geometry. Hitchin showed that there exists a natural hyperk¨ahler metric on the smooth Date: July 17, 2021. RM supported by NSF Grant DMS-1105050, JS supported by DFG Grant Sw 161/1-1. -
Annual Report 2003
ANNUAL REPORT 2003 Published by the Marketing and Communications Division The Australian National University Published by The Marketing and Communications Division The Australian National University Produced by ANU Publications Unit Marketing and Communications Division The Australian National University Printed by University Printing Service The Australian National University ISSN 1327-7227 April 2004 Contents Council and University Office rs 7 Review of 2003 10 Council and Council Committee Meetings 20 University Statistics 22 Cooperation with Government and other Public Institutions 30 Joint Research Projects undertaken with Universities, CSIRO and other Institutions 76 Principal Grants and Donations 147 University Public Lectures 168 Freedom of Information Act 1982 Statement 172 Auditor-General’s Report 175 Financial Statements 179 University Organisational Structure 222 Academic Structure 223 ANU Acronyms 224 Index 225 Further information about ANU Detailed information about the achievements of ANU in 2003, especially research and teaching outcomes, is contained in the annual reports of the University’s Research Schools, Faculties, Centres and Administrative Divisions. For course and other academic information, contact: Director Student and Academic Services The Australian National University Canberra ACT 0200 T: 02 6125 3339 F: 02 6125 0751 For general information, contact: Director Marketing and Communications Division The Australian National University Canberra ACT 0200 T: 02 6125 2229 F: 02 6125 5568 The Council and University -
Differential Geometry and the Quaternions
DIFFERENTIAL GEOMETRY AND THE QUATERNIONS Nigel Hitchin (Oxford) The Chern Lectures Berkeley April 9th-18th 2013 3 26th December 1843 • 16th October 1843 2 3 RIEMANNIAN MANIFOLDS OF FOUR DIMENSIONS 965 We call a frame an ordered set of four mutually perpendicular unit vectors eo, Ci, C2, 63. There exists one and only one rotation carrying 3 one frame to another. The coordinates Xof X\, &2, Xz of a point ï&S with respect to the frame eo, ei, C2, e3 are defined by the equation (2) % = XQCO + Xtfi + X2t2 + Xst3. Let eo*, ei*, e2*, e3* be a frame related to eo, ei, e2, e3 by means of the rela- tions 3 (3) e«* = ]F) daftp, a = 0, 1, 2, 3, OwherN RIEMANNIAe (aap) is a propeN MANIFOLDr orthogonaSl OmatrixF FOU, anR d DIMENSIONSlet #0*, #1*, #2*1 , #3* be the coordinates of the same point x with respect to the frame SHIING-SHEN CHERN eo*, ei*, e2*, e3*. Then we have Introduction. It is well known that3 in three-dimensional elliptic or spherica(3a) l geometry the so-callex*d Clifford'= X) a<*p%p,s parallelis m or parataxot = 0,y 1ha, 2s, 3. locallymany interestinµ = µ ωg properties+ µ ω .+ Aµ group-theoretiω c reason for the most • 1 1 2 2 3 3 importanThe propertiet of thess oef propertiespherical sgeometr is the facy art etha thost the ewhich universa, whel ncoverin expresseg d grouin pterm of ths eo fprope coordinater orthogonas withl grourespecp itn tfouo ar framevariable, remais is thn e invariandirect t ifproducµunde= 0tr chango distinguishedf thee universaof the framel almostcoverin. -
BIRS 2010 Scientific Report
Banff International Research Station for Mathematical Innovation and Discovery 2010 Scientific Report 5-Day Workshops 2010 Jan 10 Jan 15 Mathematics and Physics of Polymer Entanglement Jan 17 Jan 22 Multi-Scale Stochastic Modeling of Cell Dynamics Jan 24 Jan 29 Sparse Random Structures: Analysis and Computation Jan 31 Feb 5 Theory and Applications of Matrices Described by Patterns Jan 31 Feb 5 Branching Random Walks and Searching in Trees Feb 7 Feb 12 Small-scale Hydrodynamics: Microfluidics and Thin Films Feb 14 Feb 19 Convex Algebraic Geometry Feb 21 Feb 26 Some Mathematical Problems of Material Science Feb 28 Mar 5 Randomization, Relaxation and Complexity Mar 7 Mar 12 Quasi-Isometric Rigidity in Low-Dimensional Topology Mar 7 Mar 12 (0,2) Mirror Symmetry and Heterotic Gromov-Witten Invariants Mar 14 Mar 19 Geometric Scattering Theory and Applications Mar 21 Mar 26 Deterministic and Stochastic Front Propagation Mar 28 Apr 2 Volume Inequalities Apr 4 Apr 9 Coordinated Mathematical Modeling of Internal Waves Apr 11 Apr 16 Generalized Complex and Holomorphic Poisson Geometry Apr 18 Apr 23 Optimal Transportation and Applications Apr 25 Apr 30 Character Varieties in the Geometry and Topology of Low-Dimensional Manifolds May 2 May 7 Functional Data Analysis: Future Directions May 2 May 7 Creative Writing in Mathematics and Science May 9 May 14 Nonlinear Diffusions and Entropy Dissipation: From Geometry to Biology May 16 May 21 Inverse Transport Theory and Tomography May 23 May 28 Self-assembly of Block Copolymers: Theoretical Models and Mathematical -
String-Math 2012
Volume 90 String-Math 2012 July 16–21, 2012 Universitat¨ Bonn, Bonn, Germany Ron Donagi Sheldon Katz Albrecht Klemm David R. Morrison Editors Volume 90 String-Math 2012 July 16–21, 2012 Universitat¨ Bonn, Bonn, Germany Ron Donagi Sheldon Katz Albrecht Klemm David R. Morrison Editors Volume 90 String-Math 2012 July 16–21, 2012 Universitat¨ Bonn, Bonn, Germany Ron Donagi Sheldon Katz Albrecht Klemm David R. Morrison Editors 2010 Mathematics Subject Classification. Primary 11G55, 14D21, 14F05, 14J28, 14M30, 32G15, 53D18, 57M27, 81T40. 83E30. Library of Congress Cataloging-in-Publication Data String-Math (Conference) (2012 : Bonn, Germany) String-Math 2012 : July 16-21, 2012, Universit¨at Bonn, Bonn, Germany/Ron Donagi, Sheldon Katz, Albrecht Klemm, David R. Morrison, editors. pages cm. – (Proceedings of symposia in pure mathematics; volume 90) Includes bibliographical references. ISBN 978-0-8218-9495-8 (alk. paper) 1. Geometry, Algebraic–Congresses. 2. Quantum theory– Mathematics–Congresses. I. Donagi, Ron, editor. II. Katz, Sheldon, 1956- editor. III. Klemm, Albrecht, 1960- editor. IV. Morrison, David R., 1955- editor. V. Title. QA564.S77 2012 516.35–dc23 2015017523 DOI: http://dx.doi.org/10.1090/pspum/090 Color graphic policy. Any graphics created in color will be rendered in grayscale for the printed version unless color printing is authorized by the Publisher. In general, color graphics will appear in color in the online version. Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. -
NEWSLETTER No
NEWSLETTER No. 458 May 2016 NEXT DIRECTOR OF THE ISAAC NEWTON INSTITUTE In October 2016 David Abrahams will succeed John Toland as Director of the Isaac Newton Institute for Mathematical Sciences and NM Rothschild and Sons Professor of Mathematics in Cambridge. David, who is a Royal Society Wolfson Research Merit Award holder, has been Beyer Professor of Applied Mathematics at the University of Man- chester since 1998. From 2014-16 he was Scientific Director of the International Centre for Math- ematical Sciences in Edinburgh and was President of the Institute of Mathematics and its Applica- tions from 2007-2009. David’s research has been in the broad area of applied mathematics, mainly focused on the theoretical understanding of wave processes including scattering, diffraction, localisation and homogenisation. In recent years his research has broadened somewhat, to now cover topics as diverse as mathematical finance, nonlinear vis- He has also been involved in a range of public coelasticity and glaciology. He has close links with engagement activities over the years. He a number of industrial partners. regularly offers mathematics talks of interest David plays an active role within the internation- to school students and the general public, al mathematics community, having served on over and ran the annual Meet the Mathematicians 30 national and international working parties, outreach events for sixth form students with panels and committees over the past decade. Chris Howls (Southampton). With Chris Budd This has included as a Member of the Applied (Bath) he has organised a training conference Mathematics sub-panel for the 2008 Research As- in 2010 on How to Talk Maths in Public, and in sessment Exercise and Deputy Chair for the Math- 2014 co-chaired the inaugural Festival of Math- ematics sub-panel in the 2014 Research Excellence ematics and its Applications. -
Generators for the Cohomology Ring of the Moduli Space of Rank 2 Higgs
Generators for the cohomology ring of the moduli space of rank 2 Higgs bundles Tam´as Hausel Department of Mathematics, University of California, Berkeley, Calif. 94720 Michael Thaddeus Department of Mathematics, Columbia University, New York, N.Y. 10027 A central object of study in gauge theory is the moduli space of unitary flat connections on a compact surface. Thanks to the efforts of many people, a great deal is understood about the ring structure of its cohomology. In particular, the ring is known to be generated by the so-called universal classes [2, 36], and, in rank 2, all the relations between these classes are also known [3, 27, 40, 52]. If instead of just unitary connections one allows all flat connections, one obtains larger moduli spaces of equal importance and interest. However, these spaces are not compact and so very little was known about the ring structure of their cohomology. This paper will show that, in the rank 2 case, the cohomology ring of this noncompact space is again generated by universal classes. A companion paper [23] gives a complete set of explicit relations between these generators. The noncompact spaces studied here have significance extending well beyond gauge the- ory. They play an important role in 3-manifold topology: see for example Culler-Shalen [10]. And they are the setting for much of the geometric Langlands program: see for example Beilinson-Drinfeld [5]. But they have received perhaps the most attention from algebraic geometers, in the guise of moduli spaces of Higgs bundles. A Higgs bundle is a holomor- phic object, related to a flat connection by a correspondence theorem similar to that of Narasimhan-Seshadri in the unitary case.