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Universitext Universitext Series editors Sheldon Axler San Francisco State University Carles Casacuberta Universitat de Barcelona Angus MacIntyre Queen Mary University of London Kenneth Ribet University of California, Berkeley Claude Sabbah École polytechnique, CNRS, Université Paris-Saclay, Palaiseau Endre Süli University of Oxford Wojbor A. Woyczyński Case Western Reserve University Universitext is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well class-tested by their author, may have an informal, personal even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, into very polished texts. Thus as research topics trickle down into graduate-level teaching, first textbooks written for new, cutting-edge courses may make their way into Universitext. More information about this series at http://www.springer.com/series/223 W. Frank Moore • Mark Rogers Sean Sather-Wagstaff Monomial Ideals and Their Decompositions 123 W. Frank Moore Sean Sather-Wagstaff Department of Mathematics School of Mathematical and Statistical Wake Forest University Sciences Winston-Salem, NC, USA Clemson University Clemson, SC, USA Mark Rogers Department of Mathematics Missouri State University Springfield, MO, USA ISSN 0172-5939 ISSN 2191-6675 (electronic) Universitext ISBN 978-3-319-96874-2 ISBN 978-3-319-96876-6 (eBook) https://doi.org/10.1007/978-3-319-96876-6 Library of Congress Control Number: 2018948828 Mathematics Subject Classification (2010): 13-01, 05E40, 13-04, 13F20, 13F55 © Springer Nature Switzerland AG 2018 This work is subject to copyright. -
MATH FILE -Mathematical Reviews Online
Notices of the American Mathematical Society November 1984, Issue 237 Volume 31 , Number 7, Pages 737- 840 Providence, Rhode Island ·USA JSSN 0002-9920 Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the o(fice of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab· stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions. -
Branch Groups Laurent Bartholdi Rostislav I. Grigorchuk Zoranšunik
Branch Groups Laurent Bartholdi Rostislav I. Grigorchuk Zoran Suniˇ k´ Section de Mathematiques,´ Universite´ de Geneve,` CP 240, 1211 Geneve` 24, Switzer- land E-mail address: [email protected] Department of Ordinary Differential Equations, Steklov Mathematical Insti- tute, Gubkina Street 8, Moscow 119991, Russia E-mail address: [email protected] Department of Mathematics, Cornell University, 431 Malott Hall, Ithaca, NY 14853, USA E-mail address: [email protected] Contents Introduction 5 0.1. Just-infinite groups 6 0.2. Algorithmic aspects 7 0.3. Group presentations 7 0.4. Burnside groups 8 0.5. Subgroups of branch groups 9 0.6. Lie algebras 10 0.7. Growth 10 0.8. Acknowledgments 11 0.9. Some notation 11 Part 1. Basic Definitions and Examples 13 Chapter 1. Branch Groups and Spherically Homogeneous Trees 14 1.1. Algebraic definition of a branch group 14 1.2. Spherically homogeneous rooted trees 15 1.3. Geometric definition of a branch group 21 1.4. Portraits and branch portraits 23 1.5. Groups of finite automata and recursively defined automorphisms 23 1.6. Examples of branch groups 26 Chapter 2. Spinal Groups 32 2.1. Construction, basic tools and properties 32 2.2. G groups 38 2.3. GGS groups 41 Part 2. Algorithmic Aspects 45 Chapter 3. Word and Conjugacy Problem 46 3.1. The word problem 46 3.2. The conjugacy problem in G 47 Chapter 4. Presentations and endomorphic presentations of branch groups 50 4.1. Non-finite presentability 50 4.2. Endomorphic presentations of branch groups 52 4.3. -
Notices of the American Mathematical Society ABCD Springer.Com
ISSN 0002-9920 Notices of the American Mathematical Society ABCD springer.com Visit Springer at the of the American Mathematical Society 2010 Joint Mathematics December 2009 Volume 56, Number 11 Remembering John Stallings Meeting! page 1410 The Quest for Universal Spaces in Dimension Theory page 1418 A Trio of Institutes page 1426 7 Stop by the Springer booths and browse over 200 print books and over 1,000 ebooks! Our new touch-screen technology lets you browse titles with a single touch. It not only lets you view an entire book online, it also lets you order it as well. It’s as easy as 1-2-3. Volume 56, Number 11, Pages 1401–1520, December 2009 7 Sign up for 6 weeks free trial access to any of our over 100 journals, and enter to win a Kindle! 7 Find out about our new, revolutionary LaTeX product. Curious? Stop by to find out more. 2010 JMM 014494x Adrien-Marie Legendre and Joseph Fourier (see page 1455) Trim: 8.25" x 10.75" 120 pages on 40 lb Velocity • Spine: 1/8" • Print Cover on 9pt Carolina ,!4%8 ,!4%8 ,!4%8 AMERICAN MATHEMATICAL SOCIETY For the Avid Reader 1001 Problems in Mathematics under the Classical Number Theory Microscope Jean-Marie De Koninck, Université Notes on Cognitive Aspects of Laval, Quebec, QC, Canada, and Mathematical Practice Armel Mercier, Université du Québec à Chicoutimi, QC, Canada Alexandre V. Borovik, University of Manchester, United Kingdom 2007; 336 pages; Hardcover; ISBN: 978-0- 2010; approximately 331 pages; Hardcover; ISBN: 8218-4224-9; List US$49; AMS members 978-0-8218-4761-9; List US$59; AMS members US$47; Order US$39; Order code PINT code MBK/71 Bourbaki Making TEXTBOOK A Secret Society of Mathematics Mathematicians Come to Life Maurice Mashaal, Pour la Science, Paris, France A Guide for Teachers and Students 2006; 168 pages; Softcover; ISBN: 978-0- O. -
Uniform Theory of Multiplicative Valued Difference Fields By
Uniform Theory of Multiplicative Valued Difference Fields by Koushik Pal A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Logic and the Methodology of Science in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Thomas W. Scanlon, Chair Professor Leo A. Harrington Professor Theodore A. Slaman Professor W. Hugh Woodin Professor Lam Tsit-Yuen Spring 2011 Uniform Theory of Multiplicative Valued Difference Fields Copyright 2011 by Koushik Pal 1 Abstract Uniform Theory of Multiplicative Valued Difference Fields by Koushik Pal Doctor of Philosophy in Logic and the Methodology of Science University of California, Berkeley Professor Thomas W. Scanlon, Chair The first part of the thesis concerns the existence of model companions of certain unstable theories with automorphisms. Let T be a first-order theory with the strict order property. According to Kikyo and Shelah's theorem, the theory of models of T with a generic auto- morphism does not have a model companion. However, existence can be restored with some restriction on the automorphism. We show the existence of model companions of the theory of linear orders with increasing automorphisms and the theory of ordered abelian groups with multiplicative automorphisms. Both these theories have the strict order property. The second part of the thesis uses these results from the first part in the context of valued difference fields, which are valued fields with an automorphism on them. Understanding the theory of such structures requires one to specify how the valuation function interacts with the automorphism. Two special cases have been worked out before. -
February 2010
THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 389 February 2010 Society INTERNATIONAL REVIEW OF Meetings MATHEMATICAL SCIENCES 2010 and Events Invitation to nominate potential members of the International Panel 2010 Friday 26 February EPSRC are organising an Interna- EPSRC now invite nominations Mary Cartwright tional Review of Mathematical of potential members of the Inter- Lecture, Durham Sciences which will take place in De- national Panel. Nominations should [page 3] cember 200. The review, which will be made via an online form at www. be chaired by Professor Margaret survey.bris.ac.uk/epsrc/msir-panom Wednesday 14 April H. Wright, New York University, will: which will remain open until 5 Northern Regional • assess and compare the quality February 2010. In order to obtain Meeting, Newcastle of the UK research base in the an independent view, EPSRC seek [page 6] Mathematical Sciences with the individuals working outside the UK. Monday 21 June rest of the world Nominees must be highly regarded SW & South Wales • assess the impact of the research- by their peers, not only for the depth Regional Meeting base activities in the Mathematical and breadth of their scientific knowl- Cardiff Sciences internationally and on edge, but also for their personal in- other disciplines nationally, on tegrity and sound judgement. They Friday 2 July wealth creation and quality of life should normally be active in their Hardy Lecture • comment on progress since the field and it is likely that they hold or London 2004 International Review. have recently held senior positions; Monday 13 September The International Review will they should also be highly effective Midlands Regional cover the breadth and quality of all in team-working situations. -
A Year of Achievement to Receive Your Comments, and Also Contributions for Future Newsletters
Maths News 2010 (4a):Maths newsletter 1 10/5/10 08:40 Page 2 Oxford Mathematical Institute Spring 2010, Number 8 Newsletter We hope that you enjoy receiving this annual Newsletter. We are interested A year of achievement to receive your comments, and also contributions for future Newsletters. Please write to the editor: Robin Wilson MI Newsletter Mathematical Institute 24–29 St Giles Oxford OX1 3LB, or send e-mails to him, c/o [email protected] Design & production by Baseline Arts Photo by Rob Judges Rob by Photo University) (Princeton Applewhite Denise by Photo Three mathematical knights: Sir John Ball, Sir Martin Taylor and Sir Andrew Wiles Although Oxford mathematicians regularly receive national and international recognition for their wide-ranging achievements, this past year has been particularly successful. Among those most worthy of note are the following. I Two distinguished number theorists are I Raphaël Rouquier, Waynflete Professor of Pure returning to Oxford, both to Merton College: Mathematics, has been awarded the Elie Cartan Sir Martin Taylor, FRS, Vice-President of the Prize by the French Academy of Sciences. Royal Society, has been appointed Warden of Merton from October 2010, and Sir Andrew I Sir Roger Penrose, former Rouse Ball Professor Raphaël Rouquier Wiles has been appointed as a Royal Society of Applied Mathematics, shared this year’s 2010 Anniversary Research Professor at the Trotter Prize at Texas A&M University, USA. Mathematical Institute from July 2011. I Endre Süli, Professor of Numerical Analysis, I The Royal Society has awarded its prestigious has been elected a Foreign Member of the Sylvester Medal to Sir John Ball, Oxford’s Serbian Academy of Sciences and Arts. -
2014 Annual Report
CLAY MATHEMATICS INSTITUTE www.claymath.org ANNUAL REPORT 2014 1 2 CMI ANNUAL REPORT 2014 CLAY MATHEMATICS INSTITUTE LETTER FROM THE PRESIDENT Nicholas Woodhouse, President 2 contents ANNUAL MEETING Clay Research Conference 3 The Schanuel Paradigm 3 Chinese Dragons and Mating Trees 4 Steenrod Squares and Symplectic Fixed Points 4 Higher Order Fourier Analysis and Applications 5 Clay Research Conference Workshops 6 Advances in Probability: Integrability, Universality and Beyond 6 Analytic Number Theory 7 Functional Transcendence around Ax–Schanuel 8 Symplectic Topology 9 RECOGNIZING ACHIEVEMENT Clay Research Award 10 Highlights of Peter Scholze’s contributions by Michael Rapoport 11 PROFILE Interview with Ivan Corwin, Clay Research Fellow 14 PROGRAM OVERVIEW Summary of 2014 Research Activities 16 Clay Research Fellows 17 CMI Workshops 18 Geometry and Fluids 18 Extremal and Probabilistic Combinatorics 19 CMI Summer School 20 Periods and Motives: Feynman Amplitudes in the 21st Century 20 LMS/CMI Research Schools 23 Automorphic Forms and Related Topics 23 An Invitation to Geometry and Topology via G2 24 Algebraic Lie Theory and Representation Theory 24 Bounded Gaps between Primes 25 Enhancement and Partnership 26 PUBLICATIONS Selected Articles by Research Fellows 29 Books 30 Digital Library 35 NOMINATIONS, PROPOSALS AND APPLICATIONS 36 ACTIVITIES 2015 Institute Calendar 38 1 ach year, the CMI appoints two or three Clay Research Fellows. All are recent PhDs, and Emost are selected as they complete their theses. Their fellowships provide a gener- ous stipend, research funds, and the freedom to carry on research for up to five years anywhere in the world and without the distraction of teaching and administrative duties. -
November 2009
THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 386 November 2009 Society 2009 ELECTIONS for the 200 elections was also in- Meetings cluded. Members are also able to TO COUNCIL AND make direct nominations; details and Events NOMINATING will be given in the April and May Newsletters next year. 2009 COMMITTEE Friday 20 November The ballot papers for the November ANNUAL GENERAL AGM, London elections to Council and Nominat- MEETING [pages , 3] ing Committee were circulated with the October Newsletter. Nominat- The Annual General Meeting of 4–6 December ing Committee has put forward the Society will be held at 3.00 Joint meeting names for each Officer post; in pm on Friday 20 November 2009 with the Belgian addition members have proposed at the Institute of Education, Mathematical Society, candidates for two posts: General London. The business shall be: Leuven Secretary and Education Secre- (i) the adoption of the Annual tary. A total of 5 candidates have Report for 2008/09 2010 been proposed (9 by Nominating (ii) the report of the Treasurer Friday 26 February Committee, 6 by members) for (iii) appointment of Auditors Mary Cartwright the 7 vacancies in Members-at- (iv) elections to Council and Lecture, Durham Large of Council. Four names have Nominating Committee been proposed (all by Nominating (v) presentation of certificates Friday 2 July Committee) for 2 vacancies in the to Prize winners Hardy Lecture membership of the Nominating I hope that as many members as London Committee. possible will be able to attend. Monday 13 September Please note that completed bal- Peter Cooper Midlands Regional lot papers must be returned by Executive Secretary Meeting, Nottingham Thursday 12 November 2009. -
Scientific Report for 2008
The Erwin Schr¨odingerInternational Boltzmanngasse 9/2 ESI Institute for Mathematical Physics A-1090 Vienna, Austria Scientific Report for 2008 Impressum: Eigent¨umer,Verleger, Herausgeber: The Erwin Schr¨odingerInternational Institute for Mathematical Physics, Boltzmanngasse 9, A-1090 Vienna. Redaktion: Joachim Schwermer, Jakob Yngvason Supported by the Austrian Federal Ministry of Science and Research (BMWF). Contents Preface 3 The ESI in 2008 . 5 Scientific Reports 7 Main Research Programmes . 7 Combinatorics and Statistical Physics . 7 Metastability and Rare Events in Complex Systems . 11 Hyperbolic Dynamical Systems . 17 Operator Algebras and Conformal Field Theory . 22 Workshops Organized Outside the Main Programmes . 25 Winter School in Geometry and Physics . 25 Tensor Network Methods and Entanglement in Quantum Many-Body Systems . 25 Intermetallics . 27 ESI - 15th Anniversary Celebration . 28 Frontiers in Mathematical Biology . 28 Summer School on \Combinatorics and Statistical Mechanics" . 30 Summer School on \Current Topics in Mathematical Physics" . 31 Mathematical General Relativity . 33 Mathematical Challenges in String Phenomenology . 34 Structural Probability . 37 5th Vienna Central European Seminar on Particle Physics and Quantum Field Theory: \Highlights in Computational Quantum Field Theory" . 41 Supersymmetry and Noncommutative QFT: In Memoriam Julius Wess . 42 Profinite Groups . 43 Junior Research Fellows Programme . 47 Senior Research Fellows Programme . 49 Christos N. Likos: Introduction to Theoretical Soft Matter Physics . 49 Radoslav Rashkov: Dualities between gauge theories and strings . 50 Goran Mui´c:Selected Topics in the Theory of Automorphic Forms for Reductive Groups . 51 Herbert Kurke, Denis Osipov, Alexander Zheglov . 53 Werner Ballmann . 55 Roberto Longo . 55 Seminars and Colloquia 57 ESI Preprints 67 ESI Preprints in 2008 . 67 ESI Preprints until end of February 2009 . -
ON SOME PRO-P GROUPS from INFINITE-DIMENSIONAL LIE
ONSOMEPRO-p GROUPS FROM INFINITE-DIMENSIONAL LIE THEORY INNA CAPDEBOSCQ AND BERTRAND RÉMY April 3, 2013 Abstract: We initiate the study of some pro-p-groups arising from infinite-dimensional Lie theory. These groups are completions of some subgroups of incomplete Kac-Moody groups over finite fields, with respect to various filtrations of algebraic or geometric origin. We show topological finite generation for the pro-p Sylow subgroups in many complete Kac-Moody groups. This implies abstract simplicity of the latter groups. We also discuss with the question of (non-)linearity of these pro-p groups. Keywords: Kac-Moody theory, infinite root systems, pro-p groups, abstract simplicity, rigidity, non-linearity. AMS classification (2000): 17B22, 17B67, 20E32, 20E42, 20F20, 20G44, 51E24. 2 Contents INTRODUCTION........................................................... 3 1. ALGEBRAIC COMPLETIONS OF KAC-MOODY GROUPS..................... 4 1.1. Kac-Moody Lie algebras. 4 1.2. Minimal Kac-Moody groups. 5 1.3. Complete Kac-Moody groups. 5 2. FRATTINI SUBGROUPS OF p-SYLOW SUBGROUPS......................... 6 2.1. Some facts from pro-p groups. 6 2.2. Finite generation. 7 2.3. Related questions. 9 3. ABSTRACT SIMPLICITY FOR COMPLETE KAC-MOODY GROUPS ............ 9 3.1. Tits systems. 10 3.2. Abstract simplicity. 10 3.3. Related questions. 11 4. NON-LINEARITY STATEMENTS AND CONJECTURES........................ 11 4.1. Further material on profinite groups. 12 4.2. Non-linearities. 12 4.3. Related questions. 14 REFERENCES............................................................. 14 3 INTRODUCTION The general theme of this paper is a connection between infinite-dimensional Lie theory and pro-p groups. More precisely, we are interested in Kac-Moody groups over finite fields: in various complete versions of these groups, we obtain locally compact, totally disconnected groups admitting a useful action on an explicit building. -
Annualreport 2010 2011
C CENTRE R DERECHERCHES M MATHÉMATIQUES AnnualReport 2010 2011 . i C ii C CENTRE R DERECHERCHES M MATHÉMATIQUES AnnualReport 2010 2011 . iii Centre de recherches mathématiques Université de Montréal C.P. 6128, succ. Centre-ville Montréal, QC H3C 3J7 Canada [email protected] Also available on the CRM website http://crm.math.ca/docs/docRap_an.shtml. © Centre de recherches mathématiques Université de Montréal, 2012 ISBN 978-2-921120-49-4 C Presenting the Annual Report 2010 – 2011 1 ematic Program 4 ematic Programs of the Year 2010 – 2011: “Geometric, Combinatorial and Computational Group e- ory” and “Statistics” ............................................ 5 Aisenstadt Chairholders in 2010 – 2011: Yuri Gurevich, Angus Macintyre, Alexander Razborov, and James Robins ................................................ 6 Activities of the ematic Semesters ...................................... 9 Past ematic Programs ............................................. 21 General Program 23 CRM activities .................................................. 24 Colloquium Series ................................................ 36 Multidisciplinary and Industrial Program 39 Activities of the Climate Change and Sustainability Program ........................ 40 Activities of the Multidisciplinary and Industrial Program .......................... 41 CRM Prizes 47 CRM – Fields – PIMS Prize 2011 Awarded to Mark Lewis ........................... 48 André-Aisenstadt Prize 2011 Awarded to Joel Kamnitzer ........................... 48 CAP – CRM Prize 2011 Awarded