DOCSLIB.ORG

October 2004

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 330 October 2004 Forthcoming LMS 2004 ELECTIONS SUBSCRIPTIONS Society AND OFFICERS AND PERIODICALS Meetings The ballot papers for the The annual subscription to the November elections to Council London Mathematical Society 2004 and Nominating Committee are for the 2004-05 session shall be: Friday 19 November being circulated with this copy Ordinary Members £33.00; London of the Newsletter. Nine candi- Reciprocity Members £16.50; Annual General dates for Members-at-Large of Associate Members £8.25. The Meeting Council were proposed by the prices of the Society’s periodi- D. Olive Nominating Committee. In cals to Ordinary, Reciprocity and P. Goddard addition, H.G. Dales was nomi- Associate Members for the (Presidential Address) nated directly by D. Salinger, 2004-05 session shall be: 1 [page 3] seconded by J.R. Partington, Proceedings £66; Journal J.K. Truss and R.B.J.T. Allenby, in £66.00; Bulletin £33.00; 2005 accordance with By-Law II.2. Nonlinearity £47.00; Journal of Friday 25 February Tony Scholl has completed his Computation and Mathematics London term as a Vice-President and Martin remains free. S. Lauritzen Bridson is nominated in his place. E. Thompson Please note that completed ANNUAL (Mary Cartwright ballot papers must be returned Lecture) by Thursday 11 November 2004. SUBSCRIPTION Norman Biggs The LMS annual subscription, Wednesday 18 May General Secretary including payment for publica- Birmingham tions, for the session Midlands Regional ANNUAL DINNER November 2004–October 2005 Meeting is due on 1 November 2004. The Annual Dinner will be held Together with this Newsletter after the Annual General is a renewal form to be com- Meeting on Friday 19 November pleted and returned with your at 7.30pm at the Bonnington remittance in the enclosed Hotel, London WC1. The cost is envelope. £35.00 per person and members No action is required if you may book places for guests. are already paying by direct The booking form, enclosed debit, and do not wish to with this Newsletter, should be change your choice of publica- returned together with pay- tions. Fully complete and return ment to the London the form if you are paying by Mathematical Society office by direct debit but wish to change Monday 15 November. your choice of publications or THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 330 October 2004 add/delete a subscription to the European library, common room or other public Mathematical Society. Bank accounts of room, and members paying by direct debit will be deb- (b) are accessible to other mathematicians ited with the appropriate amount on 17 (or to students) only with the mem- LONDON MATHEMATICAL SOCIETY January 2005. Other members should either ber's permission, given individually in enclose a cheque (£ sterling or US$) with each case. Annual General Meeting their form or, if they have a UK bank account Issues are the personal property of and wish to take advantage of this conven- members, who would be able, without Friday 19 November 2004 ient form of payment, request a direct debit negotiation with authorities, to take the mandate. Although the facility to pay by issues with them if they left their present University College London credit card is open to all members of the institution or to give them to another indi- Society, it is our preference that members vidual who is willing to abide by these continue to pay by direct debit. terms. 3.15 – 3.30 Annual General Meeting PUBLICATIONS PRICING ISAAC NEWTON INSTITUTE 3.30 – 4.30 Professor D.I. Olive (Swansea) Unified theories and the increasing synergy POLICY Sir John Kingman, the current Director of the between mathematics and physics The LMS has a pricing structure that allows Isaac Newton Institute, retires in 2006 and 2 individual members to purchase its journals, the University of Cambridge has started the 4.30 – 5.00 Tea 3 for personal use only, at a substantial dis- process of seeking a successor. Details are at count. In common with other mathematical www.newton.cam.ac.uk/director.html; appli- societies, the Society regards a subscription as cations should reach the Academic Secretary 5.00 – 6.00 Professor P. Goddard (IAS) for personal use only if: no later than 30 November 2004. Informal Presidential Address (a) issues are either destroyed or held on enquiries may be made to Peter Landshoff, Infinite dimensional symmetry a continuing basis among the mem- Chair of the Management Committee of the ber's personal belongings, and are Institute, (tel: +44 (0)1223 337880; email: not deposited even temporarily in a [email protected]). The meeting will be held in the Chemistry Auditorium, Christopher Ingold Building, University College London, 20 Gordon Street, London WC1. Please note early start. LMS Newsletter There are limited funds available to contribute in part to General Editor: Dr D.R.J. Chillingworth ([email protected]) the expenses of members of the Society or research students Reports Editor: Dr S.A. Huggett ([email protected]) to attend the meeting. Requests for support, including an Reviews Editor: Professor M.P.F. du Sautoy ([email protected]) Administrative Editor: Miss S.M. Oakes ([email protected]) estimate of expenses, may be addressed to the Programme Editorial office address: London Mathematical Society, De Morgan House, Secretary at the Society (web: www.lms.ac.uk; email: 57-58 Russell Square, London WC1B 4HS (tel: 020 7637 3686; fax: 020 7323 3655; [email protected]). email: [email protected], web: www.lms.ac.uk) Designed by CHP Design (tel: 020 7240 0466, email: [email protected], web:www.chpdesign.com) The meeting will be followed by the Annual Dinner. For Publication dates and deadlines: published monthly, except August. further details see the announcement in this Newsletter. Items and advertisements by first day of the month prior to publication. All enquiries may be addressed to Susan Oakes (tel: 020 Information in the Newsletter is free to be used elsewhere unless otherwise stated; attribution is requested when reproducing whole articles. The LMS cannot accept responsibility for the accuracy 7637 3686, e-mail: [email protected]). of information in the Newsletter. Views expressed do not necessarily represent the views or policy of the London Mathematical Society. Charity registration number: 252660. THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 330 October 2004 GENDER AND RESEARCH sciences as to lovers of Turner, the exhibition adds a new dimension to our appreciation of ACTIVITY IN THE 2001 RAE Britain’s greatest painter. The exhibition is at You may recall an item in the LMS Newsletter the Clore Watercolour Galleries, Tate Britain, a few months ago in which an analysis of the London until 7 November (www.tate.org.uk/ gender differences in the numbers of UK aca- home/news/vanishingpoint_ 23-04-04.htm) demics in mathematics and in those submitted to the 2001 RAE was carried out. The overall ERRATUM conclusion was that a smaller percentage of female mathematicians were submitted as In the notice of the Twistor String Theory research active than male mathematicians. Workshop in the last issue the name Jolliffe Interestingly, a similar analysis has now was spelt incorrectly. The email address been carried out by the AUT across all RAE should be [email protected] (and the Units of Assessment. The study found that web address is www.maths.ox.ac.uk/~lma- ‘across the sector, among academics engaged son/Tws.html). Our apologies. in both teaching and research activities, males were 1.6 times more likely than their IMU PRIZES female colleagues to be counted as research- 4 active and to have had their work submitted Nominations for the following 5 in the 2001 RAE.’ This ratio varies between International Mathematical Union prizes, subjects, and it turns out that in Mathematics which will be awarded at the opening cer- the ratio is almost exactly 1.6. We could com- emony of the ICM 2006 Congress, should fort ourselves with this – we are no worse be sent to the Chairs of the corresponding than many other disciplines – but overall the Prize Committees. The prizes being result is a disturbing one for UK research. awarded are Fields Medals, the Rolf The article may be found at Nevanlinna Prize and the Carl Friedrich www.aut.org.uk/ under News for July 2004. Gauss Prize. The relevant Committee Rachel Camina Chairs are as follows: Cathy Hobbs Fields Medals: Professor John Ball, Mathematical Institute, UP AND COMING 24-29 St Giles’, Oxford OX1 3LB, UK ([email protected]) Vanishing Point: The Perspective Drawings Rolf Nevanlinna Prize: of Turner Professor Margaret Wright, Computer As Professor of Perspective at the Royal Science Department, New York University, Academy for thirty years (1807-37), Turner Warren Weaver Hall, 251 Mercer Street, produced a number of remarkable drawings New York, NY 10012, USA demonstrating both the theory and practice ([email protected]) of linear and atmospheric perspective. Carl Friedrich Gauss Prize: Featuring about thirty-five of these rarely Professor Dr Martin Groetschel, Konrad- exhibited lecture diagrams, this special dis- Zuse-Zentrum für Informationstechnik play highlights the diagrams he used to illus- Berlin (ZIB), Takustr. 7, D-14195 Berlin- trate such subjects as colour theory, the Dahlem, Germany ([email protected]) nature of reflection and refraction, and the Nominations should ideally be sent by 15 basic theorems of standard perspective. Of December 2004. Winners of each prize are equal fascination to students of the arts and not eligible for the others. THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 330 October 2004 ICM2006 well as for young Spanish mathematicians.
Recommended publications
  • School Open Events 2021 Intake

    School Open Events 2021 Intake

    SCHOOL OPEN EVENTS 2021 INTAKE Religious Education Cooking Humanities Food Technology College Biology Gardening Celebrating Latin Football Qualifications University Sports Hall Pride PhysicsSCHOOLSSixth Form VIRTUAL TOURS Achievement Quality ApprenticeshipsEducation Progress Modern Languages Netball Life Theatre Technology Carers Consideration Teaching Physical Education Read Confidence Modern Languages Excellent Behaviour Rugby Mentor Drama Student Literature Graphics Specialist Rooms Learning Expressive ArtsTechnologySCHOOLS Art VIRTUAL TOURSDebating Assessment Courage BTECSCHOOLS ScienceNational Curriculum VIRTUAL TOURSBusiness Studies Pupil Teacher Textiles Clubs Enfield HomeworkEnglish Literature Form Values School Fun Proud Raising AspirationsSupportOutstanding French Aspirations Respectful Transition Nurtured Trust Athletics Design and PerformanceDiscipline Community Music Encouraged High Quality Teaching Maths Monitor Careers Orchestra Plan Chess Polite Chemistry Gymnasium Hockey Tennis Ofsted Aspirational Target Expressive Photography German Child Academy Trust Performance Media Studies Spanish Computer Science Parents Governing Body Development Applying for a Secondary School for September 2021 www.eadmissions.org.uk www.enfield.gov.uk/admissions SCHOOL OPEN EVENTS 2021 INTAKE Due to the current requirements in relation to social distancing, Enfield schools will not be able to hold their open evenings in the same way. Schools will, however, make sure that you have an opportunity to learn more about them, including opportunities
  • England LEA/School Code School Name Town 330/6092 Abbey

    England LEA/School Code School Name Town 330/6092 Abbey

    England LEA/School Code School Name Town 330/6092 Abbey College Birmingham 873/4603 Abbey College, Ramsey Ramsey 865/4000 Abbeyfield School Chippenham 803/4000 Abbeywood Community School Bristol 860/4500 Abbot Beyne School Burton-on-Trent 312/5409 Abbotsfield School Uxbridge 894/6906 Abraham Darby Academy Telford 202/4285 Acland Burghley School London 931/8004 Activate Learning Oxford 307/4035 Acton High School London 919/4029 Adeyfield School Hemel Hempstead 825/6015 Akeley Wood Senior School Buckingham 935/4059 Alde Valley School Leiston 919/6003 Aldenham School Borehamwood 891/4117 Alderman White School and Language College Nottingham 307/6905 Alec Reed Academy Northolt 830/4001 Alfreton Grange Arts College Alfreton 823/6905 All Saints Academy Dunstable Dunstable 916/6905 All Saints' Academy, Cheltenham Cheltenham 340/4615 All Saints Catholic High School Knowsley 341/4421 Alsop High School Technology & Applied Learning Specialist College Liverpool 358/4024 Altrincham College of Arts Altrincham 868/4506 Altwood CofE Secondary School Maidenhead 825/4095 Amersham School Amersham 380/6907 Appleton Academy Bradford 330/4804 Archbishop Ilsley Catholic School Birmingham 810/6905 Archbishop Sentamu Academy Hull 208/5403 Archbishop Tenison's School London 916/4032 Archway School Stroud 845/4003 ARK William Parker Academy Hastings 371/4021 Armthorpe Academy Doncaster 885/4008 Arrow Vale RSA Academy Redditch 937/5401 Ash Green School Coventry 371/4000 Ash Hill Academy Doncaster 891/4009 Ashfield Comprehensive School Nottingham 801/4030 Ashton
  • Case Study 2: Enfield Grammar School, Enfield, London Teacher: Verity Currie

    Case Study 2: Enfield Grammar School, Enfield, London Teacher: Verity Currie

    Extract from the evaluation report of the ACT/RFK ‘Speak Truth To Power’ Human Rights Curriculum pilot [July 2017] Case study 2: Enfield Grammar School, Enfield, London Teacher: Verity Currie Outcome: This is a short sequence of lessons for year 7 (11-12 year olds). It builds on an earlier project on human rights and looks “We’ve learned how important forward to a longer project on active citizenship. In this human rights are and how sequence students learn about a rights defender and start to they affect everyone.” plan a possible action they could undertake. This plan (Student) introduces students to the problems of deciding what would constitute an effective political action and raises problems to be picked up later. Sequence of learning: Additional resources: Lesson 1: The right to education and Malala Discuss what you want to achieve in life and the role of education in helping you. What would happen if you couldn’t attend school? How would your life prospects change? There are 32million fewer girls in primary school than boys, why might that be? What do we already know about Malala? Watch video (a) about Malala and think about how she (a) Malala's story - BBC News: defender. exemplifies being a rights https://youtu.be/FnloKzEAX7o Lesson 2: Planning action Discuss a human rights issue you feel strongly about and prepare to explain why to the class. Think about what a reasonable aim might be to tackle this issue. Then think about who the main decision-makers are, and who else could be influential? Brainstorm the kind of campaigning activities we have learned about previously.
  • IMS Bulletin July/August 2004

    IMS Bulletin July/August 2004

    Volume 33 Issue 4 IMS Bulletin July/August 2004 A Message from the (new) President Louis H Y Chen, Director of the Institute CONTENTS for Mathematical Sciences at the 2-3 Members’ News; National University of Singapore, is the Contacting the IMS IMS President for 2004–05. He says: hen I was approached by the 4 Profi le: C F Jeff Wu WCommittee on Nominations in 5 IMS Election Results: January 2003 and asked if I would be President-Elect and Council willing to be a possible nominee for IMS 7 UK Research Assessment; President-Elect, I felt that it was a great Tweedie Travel Award honor for me. However, I could not help 8 Mini-meeting Reports but think that the outcome of the nomi- nation process would most likely be a 10 Project Euclid & Google nominee who is based in the US, because, 11 Calls Roundup except for Willem van Zwet, Nancy Reid of probabilists and statisticians. 14 IMS Meetings and Bernard Silverman, all the 68 past Although IMS is US-based, its infl u- Presidents of IMS were US-based. When ence goes far beyond the US due to its 20 Other Meetings and I was fi nally chosen as the nominee for several fi rst-rate publications and many Announcements President-Elect, I was pleased, not so high quality meetings. Also, IMS has 23 Employment much because I was chosen, but because I reduced membership dues for individuals Opportunities took it as a sign that the outlook of IMS in developing countries to encourage 25 International Calendar of was becoming more international.
  • Rostislav Grigorchuk Texas A&M University

    Rostislav Grigorchuk Texas A&M University

    CLAREMONT CENTER for MATHEMATICAL SCIENCES CCMSCOLLOQUIUM On Gap Conjecture for group growth and related topics by Rostislav Grigorchuk Texas A&M University Abstract: In this talk we will present a survey of results around the Gap Conjecture which was formulated by thep speaker in 1989. The conjecture states that if growth of a finitely generated group is less than e n, then it is polynomial. If proved, it will be a far reaching improvement of the Gromov's remarkable theorem describing groups of polynomial growth as virtually nilpotent groups. Old and new results around conjecture and its weaker and stronger forms will be formulated and discussed. About the speaker: Professor Grigorchuk received his undergraduate degree in 1975 and Ph.D. in 1978, both from Moscow State University, and a habilitation (Doctor of Science) degree in 1985 at the Steklov Institute of Mathematics in Moscow. During the 1980s and 1990s, Rostislav Grigorchuk held positions in Moscow, and in 2002 joined the faculty of Texas A&M University, where he is now a Distinguished Professor of Mathematics. Grigorchuk is especially famous for his celebrated construction of the first example of a finitely generated group of intermediate growth, thus answering an important problem posed by John Milnor in 1968. This group is now known as the Grigorchuk group, and is one of the important objects studied in geometric group theory. Grigorchuk has written over 100 research papers and monographs, had a number of Ph.D. students and postdocs, and serves on editorial boards of eight journals. He has given numerous talks and presentations, including an invited address at the 1990 International Congress of Mathematicians in Kyoto, an AMS Invited Address at the March 2004 meeting of the AMS in Athens, Ohio, and a plenary talk at the 2004 Winter Meeting of the Canadian Mathematical Society.
  • Arxiv:1510.00545V4 [Math.GR] 29 Jun 2016 7

    Arxiv:1510.00545V4 [Math.GR] 29 Jun 2016 7

    SCHREIER GRAPHS OF GRIGORCHUK'S GROUP AND A SUBSHIFT ASSOCIATED TO A NON-PRIMITIVE SUBSTITUTION ROSTISLAV GRIGORCHUK, DANIEL LENZ, AND TATIANA NAGNIBEDA Abstract. There is a recently discovered connection between the spectral theory of Schr¨o- dinger operators whose potentials exhibit aperiodic order and that of Laplacians associated with actions of groups on regular rooted trees, as Grigorchuk's group of intermediate growth. We give an overview of corresponding results, such as different spectral types in the isotropic and anisotropic cases, including Cantor spectrum of Lebesgue measure zero and absence of eigenvalues. Moreover, we discuss the relevant background as well as the combinatorial and dynamical tools that allow one to establish the afore-mentioned connection. The main such tool is the subshift associated to a substitution over a finite alphabet that defines the group algebraically via a recursive presentation by generators and relators. Contents Introduction 2 1. Subshifts and aperiodic order in one dimension 3 2. Schr¨odingeroperators with aperiodic order 5 2.1. Constancy of the spectrum and the integrated density of states (IDS) 5 2.2. The spectrum as a set and the absolute continuity of spectral measures 9 2.3. Aperiodic order and discrete random Schr¨odingeroperators 10 3. The substitution τ, its finite words Subτ and its subshift (Ωτ ;T ) 11 3.1. The substitution τ and its subshift: basic features 11 3.2. The main ingredient for our further analysis: n-partition and n-decomposition 14 3.3. The maximal equicontinuous factor of the dynamical system (Ωτ ;T ) 15 3.4. Powers and the index (critical exponent) of Subτ 19 3.5.
  • What Is the Grigorchuk Group?

    What Is the Grigorchuk Group?

    WHAT IS THE GRIGORCHUK GROUP? JAKE HURYN Abstract. The Grigorchuk group was first constructed in 1980 by Rostislav Grigorchuk, defined as a set of measure-preserving maps on the unit interval. In this talk a simpler construction in terms of binary trees will be given, and some important properties of this group will be explored. In particular, we study it as a negative example to a variant of the Burnside problem posed in 1902, an example of a non-linear group, and the first discovered example of a group of intermediate growth. 1. The Infinite Binary Tree We will denote the infinite binary tree by T . The vertex set of T is all finite words in the alphabet f0; 1g, and two words have an edge between them if and only if deleting the rightmost letter of one of them yields the other: ? 0 1 00 01 10 11 . Figure 1. The infinite binary tree T . This will in fact be a rooted tree, with the root at the empty sequence, so that any automorphism of T must fix the empty sequence. Here are some exercises about Aut(T ), the group of automorphisms of T . In this paper, exercises are marked with either ∗ or ∗∗ based on difficulty. Most are taken from exercises or statements made in the referenced books. Exercise 1. Show that the group Aut(T ) is uncountable and has a subgroup iso- morphic to Aut(T ) × Aut(T ).∗ Exercise 2. Impose a topology on Aut(T ) to make it into a topological group home- omorphic to the Cantor set.∗∗ Exercise 3.
  • ENFIELD GRAMMAR SCHOOL (A Company Limited by Guarantee)

    ENFIELD GRAMMAR SCHOOL (A Company Limited by Guarantee)

    Registered number: 07697044 ENFIELD GRAMMAR SCHOOL (A Company Limited by Guarantee) TRUSTEES' REPORT AND FINANCIAL STATEMENTS FOR THE YEAR ENDED 31 AUGUST 2018 ENFIELD GRAMMAR SCHOOL (A Company Limited by Guarantee) CONTENTS Page Reference and Administrative Details 1 - 2 Trustees' Report 3 - 8 Governance Statement 9 - 12 Statement on Regularity, Propriety and Compliance 13 Statement of Trustees' Responsibilities 14 Independent Auditors' Report on the Financial Statements 15 - 17 Independent Reporting Accountant's Assurance Report on Regularity 18 - 19 Statement of Financial Activities Incorporating Income and Expenditure Account 20 Balance Sheet 21 Statement of Cash Flows 22 Notes to the Financial Statements 23 - 40 ENFIELD GRAMMAR SCHOOL (A Company Limited by Guarantee) REFERENCE AND ADMINISTRATIVE DETAILS OF THE ACADEMY, ITS MEMBERS, TRUSTEES AND ADVISERS FOR THE YEAR ENDED 31 AUGUST 2018 Members Mrs R Collis Mr P Collard Mrs A Williams Mr K Barnfield (resigned 31 August 2018) Ms R Stanley-McKenzie (resigned 31 August 2018) Rev Dr S Griffiths (appointed 21 September 2018) Mr C Hide (appointed 21 September 2018) Trustees Mr C Lamb, Headteacher Rev Dr S Griffiths Mr K Barnfield (resigned 20 July 2018) Mr P Collard Ms R Stanley-McKenzie (resigned 20 July 2018) Ms J Garrad (resigned 20 July 2018) Mr P Riddell Mrs A Williams Mr C Hide, Responsible Officer Mr K Altman Mrs R Collis, Chair of Governors Mrs J Woodward Mrs S Melandri Mrs J Jones (resigned 20 July 2018) Ms N Irish Mrs H Ashley-Fraser Mr A Ness (resigned 14 September 2017) Mr
  • Milnor's Problem on the Growth of Groups And

    Milnor's Problem on the Growth of Groups And

    Milnor’s Problem on the Growth of Groups and its Consequences R. Grigorchuk REPORT No. 6, 2011/2012, spring ISSN 1103-467X ISRN IML-R- -6-11/12- -SE+spring MILNOR’S PROBLEM ON THE GROWTH OF GROUPS AND ITS CONSEQUENCES ROSTISLAV GRIGORCHUK Dedicated to John Milnor on the occasion of his 80th birthday. Abstract. We present a survey of results related to Milnor’s problem on group growth. We discuss the cases of polynomial growth and exponential but not uniformly exponential growth; the main part of the article is devoted to the intermediate (between polynomial and exponential) growth case. A number of related topics (growth of manifolds, amenability, asymptotic behavior of random walks) are considered, and a number of open problems are suggested. 1. Introduction The notion of the growth of a finitely generated group was introduced by A.S. Schwarz (also spelled Schvarts and Svarc))ˇ [218] and independently by Milnor [171, 170]. Particu- lar studies of group growth and their use in various situations have appeared in the works of Krause [149], Adelson-Velskii and Shreider [1], Dixmier [67], Dye [68, 69], Arnold and Krylov [7], Kirillov [142], Avez [8], Guivarc’h [127, 128, 129], Hartley, Margulis, Tempelman and other researchers. The note of Schwarz did not attract a lot of attention in the mathe- matical community, and was essentially unknown to mathematicians both in the USSR and the West (the same happened with papers of Adelson-Velskii, Dixmier and of some other mathematicians). By contrast, the note of Milnor [170], and especially the problem raised by him in [171], initiated a lot of activity and opened new directions in group theory and areas of its applications.
  • Annual Report 2005

    Annual Report 2005

    DEPARTMENT OF MATHEMATICS ANNUAL REPORT 2005 PREAMBLE The Department of Mathematics comprises over 60 established and temporary staff, based on both the City and Tamaki campuses. The number of equivalent full-time students totalled about 851 in 2005. The Department is therefore one of the largest in the University of Auckland, and offers courses at all levels for students in several Faculties. Highlights for the Department in 2005 were: • Professor James Sneyd was elected as a Fellow of the Royal Society of New Zealand. • Professor James Sneyd was a joint winner of the NZ Mathematical Society 2005 Research Award. • Professor Boris Pavlov, Dr Colin Fox, and Dr Mike Meylan won funding for an NZIMA's thematic programme in 2006/07. • Marsden Grants were awarded in the 2005 round to both Professor David Gauld and Dr David Bryant. • Professor James Sneyd won a grant from the University of Massachusetts Medical Centre, and has had his NIH grant for an international project fully funded for the next five years • Dr Arkadii Slinko became a founding member of the ARC Economic Design Network which received $AU300,000 per year from the Australian Research Council for the next 5 years. • Dr Arkadii Slinko led the New Zealand International Mathematics Olympiad team to its best ever results in the competition in Mexico. One silver and two bronze medals put us in the top half of all teams, not far behind France. • The Department, jointly with DALSL, signed an agreement with Majlis Amanah Rakyat (MARA) in Malaysia to provide a 20-week course for 25 mathematics and science teachers.
  • THE GRIGORCHUK GROUP Contents Introduction 1 1. Preliminaries 2 2

    THE GRIGORCHUK GROUP Contents Introduction 1 1. Preliminaries 2 2

    THE GRIGORCHUK GROUP KATIE WADDLE Abstract. In this survey we will define the Grigorchuk group and prove some of its properties. We will show that the Grigorchuk group is finitely generated but infinite. We will also show that the Grigorchuk group is a 2-group, meaning that every element has finite order a power of two. This, along with Burnside's Theorem, gives that the Grigorchuk group is not linear. Contents Introduction 1 1. Preliminaries 2 2. The Definition of the Grigorchuk Group 5 3. The Grigorchuk Group is a 2-group 8 References 10 Introduction In a 1980 paper [2] Rostislav Grigorchuk constructed the Grigorchuk group, also known as the first Grigorchuk group. In 1984 [3] the group was proved by Grigorchuk to have intermediate word growth. This was the first finitely generated group proven to show such growth, answering the question posed by John Milnor [5] of whether such a group existed. The Grigorchuk group is one of the most important examples in geometric group theory as it exhibits a number of other interesting properties as well, including amenability and the characteristic of being just-infinite. In this paper I will prove some basic facts about the Grigorchuk group. The Grigorchuk group is a subgroup of the automorphism group of the binary tree T , which we will call Aut(T ). Section 1 will explore Aut(T ). The group Aut(T ) does not share all of its properties with the Grigorchuk group. For example we will prove: Proposition 0.1. Aut(T ) is uncountable. The Grigorchuk group, being finitely generated, cannot be uncountable.
  • Karen Vogtmann

    Karen Vogtmann

    CURRICULUM VITAE -KAREN VOGTMANN Mathematics Institute Office: C2.05 Zeeman Bldg. Phone: +44 (0) 2476 532739 University of Warwick Email: [email protected] Coventry CV4 7AL PRINCIPAL FIELDS OF INTEREST Geometric group theory, Low-dimensional topology, Cohomology of groups EDUCATION B.A. University of California, Berkeley 1971 Ph.D. University of California, Berkeley 1977 ACADEMIC POSITIONS University of Warwick, Professor, 9/13 to present Cornell University – Goldwin Smith Professor of Mathematics Emeritus, 7/15 to present – Goldwin Smith Professor of Mathematics, 7/11 to 7/15 – Professor, 1/94 to 7/11 – Associate Professor, 7/87 to 12/93 – Assistant Professor, 7/85 to 6/87 – Visiting Assistant Professor, 9/84 to 6/85 Columbia University, Assistant Professor, 7/79 to 6/86 Brandeis University, Visiting Assistant Professor, 9/78 to 12/78 University of Michigan, Visiting Assistant Professor, 9/77 to 6/78 and 1/79 to 6/79 RESEARCH AND SABBATICAL POSITIONS MSRI, Berkeley, CA 8/19 to 11/19 Newton Institute, Cambridge, Mass, 3/17 to 5/17 MSRI, Berkeley, CA 8/16 to 12/16 Research Professor, ICERM, Providence, RI, 9/13 to 12/13 Freie Universitat¨ Berlin, Berlin, Germany, 6/12 Mittag-Leffler Institute, Stockholm, Sweden, 3/12 to 5/12 Visiting Researcher, Oxford University, Oxford, England, 2/12 Professeur invite, Marseilles, France, 5/11 Hausdorff Institute for Mathematics, 9/09 to 12/09 and 5/10-8/10 Mathematical Sciences Research Institute, Berkeley, CA, 8/07-12/07 I.H.E.S., Bures-sur-Yvette, France 3/04 Professeur Invite,´ Marseilles, France, 3/00 Mathematical Sciences Research Institute, Berkeley, 1/95 to 7/95 I.H.E.S., Bures-sur-Yvette, France, 1/93-8/93 Chercheur, C.N.R.S., E.N.S.