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Nearly There... Interested to Receive Your Comments, and Also the Last Lap, the Home Straight, the Final Push – However You Describe It, We’Re Nearly There
Maths News 2013 [3]_Maths newsletter 1 23/05/2013 11:26 Page 2 Oxford Mathematical Institute Spring 2013, Number 11 Newsletter We hope that you enjoy receiving this annual Newsletter. We are Nearly there... interested to receive your comments, and also The last lap, the home straight, the final push – however you describe it, we’re nearly there. contributions for future The extraordinary transformation of a huge hole in the ground into a seven-floor Mathematical Newsletters. Institute is virtually complete. The Chairman of the Department is finalising the room plan; Please write to the editor: the events team is working on the official opening ceremony; meanwhile, the contractors have Robin Wilson completed the skin of the building and are fitting it out, from the basement car park to the MI Newsletter topmost office and the roof terraces. Mathematical Institute 24–29 St Giles Now that we can see the building itself, we Oxford OX1 3LB, realise what a fabulous space it will be. Each of or send e-mails to him, c/o the two stunning central atria features a 'crystal' [email protected] – a light-well into the below-ground teaching Design & production by Baseline Arts space – incorporating mathematics into its design. As you walk along Woodstock Road at night, you’ll see lights through the glass roofs of the atria and the office windows. The building is coming to life. We start to move in at the end of June, and by this year's alumni garden party, which will be held in September (please note the new time – see page 8), we shall be fully at work in our new home. -
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. -
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 -
![Arxiv:2007.09242V1 [Math.NT] 17 Jul 2020 References 13](https://docslib.b-cdn.net/cover/2574/arxiv-2007-09242v1-math-nt-17-jul-2020-references-13-7222574.webp)
Arxiv:2007.09242V1 [Math.NT] 17 Jul 2020 References 13
p-ADIC MODEL THEORY, p-ADIC INTEGRALS, EULER PRODUCTS, AND ZETA FUNCTIONS OF GROUPS JAMSHID DERAKHSHAN Abstract. We give a survey of Denef’s rationality theorem on p-adic integrals, its uniform in p versions, the relevant model theory, and a number of applica- tions to counting subgroups of finitely generated nilpotent groups and conjugacy classes in congruence quotients of Chevalley groups over rings of integers of local fields. We then state results on analytic properties of Euler products of such p-adic integrals over all p, and an application to counting conjugacy classes in congruence quotients of certain algebraic groups over the rationals. We then briefly discuss zeta functions arising from definable equivalence relations and p-adic elimination of imginaries, which have applications to counting represen- tations of groups. Contents 1. Introduction 2 2. Acknowledgments 3 3. p-adic numbers and measures 4 4. p-adic integration on analytic manifolds 4 5. Conjectures of Borevich-Shafarevich and Serre 5 6. Quantifier elimination for p-adic fields, and uniformity in p 6 arXiv:2007.09242v1 [math.NT] 17 Jul 2020 7. Denef’s rationality theorem and definability of the Serre series 8 8. Subgroup growth zeta functions of groups 10 9. Conjugacy class zeta functions of algebraic groups over local fields 11 10. Definability of the conjugacy class zeta function: Proof of Theorem 9.1(1) 13 11. From p-adic integrals to global zeta functions via Euler products 15 12. Global conjugacy class zeta function 17 13. Zeta functions arising from definable equivalence relations and p-adic elimination of imaginaries 18 References 19 1 2 J. -
Progress in Mathematics Volume 212
Progress in Mathematics Volume 212 Series Editors H. Bass 1. Oesterle A. Weinstein Alexander Lubotzky Dan Segal Subgroup Growth Birkhiiuser Verlag Basel· Boston· Berlin Authors: Alexander Lubotzky Dan Segal Institute of Mathematics Mathematical Institute Hebrew Un iversity All Soul s College Jerusalem 9 1904 Oxford OX I 4AL Israel UK e-mail: [email protected] e-mail : [email protected] 2000 Mathematics Subject Classification 20E07 A CIP cata logue record for this book is available from the Library of Congress, Washington D.C., USA Bibliographic infonnation published by Die Deutsche Bibliothek Die Deutsche Bibliothek tists this publication in the Deutsche Nationalbibliografie; detailed bihliographic data is available in the Internet at <hup:!/dnb.ddb.de>. ISBN-13: 918-3-0348-9846-1 e-ISBN -1 3: 918-3-0348-8%5-0 DOl: 10.1001/918-3-0348-8965-0 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustra tions, broadcasting, reproduction on microfilms or in other ways, and storage in data hanks. For any kind of use whatsoever, pennission from the copyright owner must be obtained. 0 2003 Birkhauser Verlag, P.O. Box 133, CH-40 10 Basel, Switzerland Softcover reprint of the hardcover 1st edition 2003 Member of the BertelsmannSpringer Publishing Group Printed on acid-free paper produced of chlorine-free pulp. rCF ..., 987654321 www.birkhauser.ch Ferran Sunyer i Balaguer (19121967) was a self taught Catalan mathematician who, in spite of a serious physical disability, was very active in research in classical mathematical analysis, an area in which he acquired international recognition. -
Applying the Classification of Finite Simple Groups a User’S Guide
Mathematical Surveys and Monographs Volume 230 Applying the Classification of Finite Simple Groups A User’s Guide Stephen D. Smith 10.1090/surv/230 Applying the Classification of Finite Simple Groups A User’s Guide Mathematical Surveys and Monographs Volume 230 Applying the Classification of Finite Simple Groups A User’s Guide Stephen D. Smith EDITORIAL COMMITTEE Robert Guralnick Benjamin Sudakov Michael A. Singer, Chair Constantin Teleman MichaelI.Weinstein 2010 Mathematics Subject Classification. Primary 20-02, 20D05, 20Bxx, 20Cxx, 20Exx, 20Gxx, 20Jxx. For additional information and updates on this book, visit www.ams.org/bookpages/surv-230 Library of Congress Cataloging-in-Publication Data Names: Smith, Stephen D., 1948– author. Title: Applying the classification of finite simple groups: A user’s guide / Stephen D. Smith. Other titles: Classification of finite simple groups Description: Providence, Rhode Island: American Mathematical Society, [2018] | Series: Mathe- matical surveys and monographs; volume 230 | Includes bibliographical references and index. Identifiers: LCCN 2017044767 | ISBN 9781470442910 (alk. paper) Subjects: LCSH: Finite simple groups. | Representations of groups. | AMS: Group theory and generalizations – Research exposition (monographs, survey articles). msc | Group theory and generalizations – Abstract finite groups – Finite simple groups and their classification. msc | Group theory and generalizations – Permutation groups – Permutation groups. msc | Group theory and generalizations – Representation theory of groups – Representation theory of groups. msc | Group theory and generalizations – Structure and classification of infinite or finite groups – Structure and classification of infinite or finite groups. msc | Group theory and generalizations – Linear algebraic groups and related topics – Linear algebraic groups and related topics. msc | Group theory and generalizations – Connections with homological algebra and category theory – Connections with homological algebra and category theory. -
Subgroup Growth, by Alexander Lubotzky and Dan Segal, Birkh¨Auser, Basel, 2003, 476 Pp., $148.00, ISBN 3-7643-6989-2
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 41, Number 2, Pages 253{256 S 0273-0979(03)01003-6 Article electronically published on December 16, 2003 Subgroup growth, by Alexander Lubotzky and Dan Segal, Birkh¨auser, Basel, 2003, 476 pp., $148.00, ISBN 3-7643-6989-2 The book under review is one of the first books on Asymptotic Group Theory|a new, quickly developing direction in modern mathematics which has links to many topics in Algebra, Analysis, Probability and Discrete Mathematics. Typically the subject of Asymptotic Group Theory is the study of the type of growth of various functions involving a natural parameter related to the group. Among the most important functions of this nature are the word growth and the subgroup growth functions, along with various modifications. While the word growth function γG(n) counts the number of elements of length no greater than n in the group, the subgroup growth function sG(n) counts the number of subgroups of index no greater than n in G. From a group-theoretical point of view, the natural questions are: 1. What are the general features of growth functions? 2. Which algebraic features of the group are reflected in the growth function? More broadly one might ask: 3. What are the applications of growth functions and what is their connection to other topics in mathematics and science? A number theorist might add to the above list: f g1 f g1 4. What are the arithmetic properties of the sequences sG(n) n=1, γG(n) n=1, or any other growth function associated to a group G? In addition, Logicians, Computer Scientists and Geometers might ask questions that relate the growth to their own areas.