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Experiments on Growth Series of Braid Groups Jean Fromentin
Experiments on growth series of braid groups Jean Fromentin To cite this version: Jean Fromentin. Experiments on growth series of braid groups. 2021. hal-02929264v3 HAL Id: hal-02929264 https://hal.archives-ouvertes.fr/hal-02929264v3 Preprint submitted on 14 Apr 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. EXPERIMENTS ON GROWTH SERIES OF BRAID GROUPS JEAN FROMENTIN In memory of Patrick Dehornoy, a great mentor. Abstract. We introduce an algorithmic framework to investigate spherical and geodesic growth series of braid groups relatively to the Artin’s or Birman– Ko–Lee’s generators. We present our experimentations in the case of three and four strands and conjecture rational expressions for the spherical growth series with respect to the Birman–Ko–Lee’s generators. 1. Introduction Originally introduced as the group of isotopy classes of n-strands geometric braids, the braid group Bn admits many finite presentations by generators and relations. From each finite semigroup generating set S of Bn we can define at least two growth series. The spherical growth series counts elements of Bn by their dis- tance from the identity in the Cayley graph Cay(Bn,S) of Bn with respect to S. -
LMS – EPSRC Durham Symposium
LMS – EPSRC Durham Symposium Anthony Byrne Grants and Membership Administrator 12th July 2016, Durham The work of the LMS for mathematics The charitable aims of the Society: Funding the advancement of mathematical knowledge Encouraging mathematical research and collaboration ’, George Legendre Celebrating mathematical 30 Pieces achievements Publishing and disseminating mathematical knowledge Advancing and promoting mathematics The attendees of the Young Researchers in Mathematics Conference 2015, held at Oxford Historical Moments of the London Mathematical Society 1865 Foundation of LMS at University College London George Campbell De Morgan organised the first meeting, and his father, Augustus De Morgan became the 1st President 1865 First minute book list of the 27 original members 1866 LMS moves to Old Burlington House, Piccadilly J.J. Sylvester, 2nd President of the Society. 1866 Julius Plûcker Thomas Hirst Plûcker Collection of boxwood models of quartic surfaces given to Thomas Archer Hirst, Vice- President of LMS, and donated to the Society 1870 Move to Asiatic Society, 22 Albemarle Street William Spottiswoode, President 1874 Donation of £1,000 from John William Strutt (Lord Rayleigh) Generous donation enabled the Society to publish volumes of the Proceedings of the London Mathematical Society. J.W. Strutt (Lord Rayleigh), LMS President 1876-78 1881 First women members Charlotte Angas Scott and Christine Ladd 1884 First De Morgan medal awarded to Arthur Cayley 1885 Sophie Bryant First woman to have a paper published in LMS Proceedings 1916 Return to Burlington House the home of LMS until 1998 1937 ACE ’s Automatic Turing LMS Proceedings, 1937 Computing Engine, published Alan Turing’s first paper 1950 On Computable Numbers 1947 Death of G.H. -
ORDERING BRAIDS: in MEMORY of PATRICK DEHORNOY with the Untimely Passing of Patrick Dehornoy in September 2019, the World Of
ORDERING BRAIDS: IN MEMORY OF PATRICK DEHORNOY DALE ROLFSEN With the untimely passing of Patrick Dehornoy in September 2019, the world of mathematics lost a brilliant scholar who made profound contributions to set theory, algebra, topology, and even computer science and cryptography. And I lost a dear friend and a strong influence in the direction of my own research in mathematics. In this article I will concentrate on his remarkable discovery that the braid groups are left-orderable, and its consequences, and its strong influence on my own research. I'll begin by describing how I learned of his work. 1. When I met Patrick In the late 1990's I had been working on a conjecture of Joan Birman [1] regarding the braid groups Bn and the (larger) monoids SBn of singular braids. I remind the reader that Bn has the presentation with generators σ1; : : : ; σn−1 and relations σiσj = σjσi if ji − jj > 1 and σiσjσi = σjσiσj when ji − jj = 1. Figure 1: The Artin generator σi In addition to the usual Artin generators σi in which the i-th strand passes below the next strand, SBn has elements τi in which those strands intersect each other. In the study of SBn and influenced by Vassiliev theory, Birman proposed the following mapping: σi −! σi −1 τi −! σi − σi For this to make sense, the target needs to be not just Bn, but rather the group ring ZBn. She conjectured that this map SBn ! ZBn is injective. Investigating this problem with a student at the time, Jun Zhu, we were making calculations in ZBn, including cancellations such as ab = ac =) b = c. -
EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics the Open University Milton Keynes MK7 6AA, UK E-Mail: [email protected]
CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics The Open University Milton Keynes MK7 6AA, UK e-mail: [email protected] ASSOCIATE EDITORS VASILE BERINDE Department of Mathematics, University of Baia Mare, Romania e-mail: [email protected] NEWSLETTER No. 47 KRZYSZTOF CIESIELSKI Mathematics Institute March 2003 Jagiellonian University Reymonta 4 EMS Agenda ................................................................................................. 2 30-059 Kraków, Poland e-mail: [email protected] Editorial by Sir John Kingman .................................................................... 3 STEEN MARKVORSEN Department of Mathematics Executive Committee Meeting ....................................................................... 4 Technical University of Denmark Building 303 Introducing the Committee ............................................................................ 7 DK-2800 Kgs. Lyngby, Denmark e-mail: [email protected] An Answer to the Growth of Mathematical Knowledge? ............................... 9 SPECIALIST EDITORS Interview with Vagn Lundsgaard Hansen .................................................. 15 INTERVIEWS Steen Markvorsen [address as above] Interview with D V Anosov .......................................................................... 20 SOCIETIES Krzysztof Ciesielski [address as above] Israel Mathematical Union ......................................................................... 25 EDUCATION Tony Gardiner -
“Alexandroff Readings”
Lomonosov Moscow State University INTERNATIONAL TOPOLOGICAL CONFERENCE “ALEXANDROFF READINGS” Moscow, May 21-25, 2012 ABSTRACTS Supported by Russian Foundation Bogolyubov Laboratory of for Basic Geometrical Methods of Research Mathematical Physics Contents S. Ageev: Universal G-spaces in the sense of R. Palais . 7 P.Akhmet'ev, O.Frolkina: On non-immersibility of RP 10 to R15 7 A. Akimova, S. Matveev: Classification of low complexity knots in the thickened torus . 8 A.V. Akopyan (joint work with R.N. Karasev): Cutting the same fraction of several measures . 8 Al-Bayati Jalal Hatem: On simply-paracompact space . 9 D.V. Artamonov: The Schlesinger system and isomonodromic deformations of bundles with connections on Riemann sufraces 10 S. Avvakumov: A counterexample to the Lando conjecture on intersection of spheres in 3-space . 11 A.A. Ayzenberg: Algebraic properties of spherical nerve-complexes 11 E. Bastrykov: On points of compactifications of discrete spaces 12 R.B. Beshimov, M.N. Mamadaliyev: The weakly density of su- perextension . 13 A. Bogatyy, I. Bogatyy: Combinatorial types of polyhedra and Rakov conjecture . 14 Vladimir Bondarenko: Random polytopes with (0-1)-vertices . 15 A. Buryak: Nakajima's quiver varieties and combinatorial identities 15 V.Chatyrko: The (dis)connectedness of products in the box topol- ogy . 16 D. Crowley, A. Skopenkov: A classification of embeddings of non- simply connected 4-manifolds in 7-space . 17 Giuseppe Di Maio: A link between Italian and Russian mathe- matical schools: Arzel`aand Alexandroff convergences . 17 G.F. Djabbarov: Local τ-density of exponential spaces . 18 M.A. Dobrynina: On generalizations of Fedorchuk's Normal Func- tor Theorem in category P . -
C 2010 KENDALL NICOLE MAURER ALL RIGHTS RESERVED
c 2010 KENDALL NICOLE MAURER ALL RIGHTS RESERVED MINIMALLY SIMPLE GROUPS AND BURNSIDE’S THEOREM A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Kendall Nicole Maurer May, 2010 MINIMALLY SIMPLE GROUPS AND BURNSIDE’S THEOREM Kendall Nicole Maurer Thesis Approved: Accepted: Advisor Dean of the College Dr. James P. Cossey Dr. Chand K. Midha Faculty Reader Dean of the Graduate School Dr. Jeffrey Riedl Dr. George R. Newkome Faculty Reader Date Dr. Antonio Quesada Department Chair Dr. Joseph Wilder ii ABSTRACT William Burnside’s paqb theorem is a very important result in group theory, which states that any group G of order paqb is solvable. An interesting fact about this the- orem is that it was originally proven using techniques from character theory, another branch of algebra. In fact, it was about seventy years before a group-theoretic proof of Burnside’s theorem was developed through the work of Goldschmidt, Matsuyama, Bender, and other mathematicians. Their approach to proving the theorem was to show that, in essence, minimally simple groups of size paqb do not exist. Our purpose here is to use various techniques from the group-theoretic proof of Burnside’s theorem to establish and prove similar results about minimally simple groups G of arbitrary order. iii ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my wonderful family and friends, especially my mother and father; my sisters, Michelle and Staci; and Grandma Mikey. You always inspire me and give so much of yourselves. -
Lives in Parma, Italy • Professor of Mathematics (Professore Ordinario) at the University of Parma Since 2006 • Degree (1994) and Ph.D
GIUSEPPE MINGIONE, CV 1. Vita • Giuseppe Mingione, born in 1972 in Caserta (Italy), Italian citizen; lives in Parma, Italy • Professor of Mathematics (Professore Ordinario) at the University of Parma since 2006 • Degree (1994) and Ph.D. (1998) in Mathematics, Universit`adi Napoli \Fed- erico II" • Formerly research associate (1996-2000) and associate professor (2001-2005) at the University of Parma 2. Distinctions • Amerio Prize 2016 • Invited speaker, 7th European Congress of Mathematics, Berlin, 2016 • Nachdiplom Lecturer, ETH Z¨urich, 2015 • Highly cited researcher (Thomson Reuters-Clarivate, in 2014, 15 and 16) • Plenary address, Italian Mathematical Society conference, 2011 • Caccioppoli Prize 2010 • Plenary address, German Mathematical Society conference, 2008 • European Research Council Grant, 2007 • Stampacchia Medal 2006 • Bartolozzi Prize 2005 • Otto Haupt Chair, University of Erlangen-Nuremberg, 2004 3. Mentoring • 4 Postdocs at the University of Parma • 1 PhD student (defended) at the Scuola Normale Superiore, Pisa 4. Editorial boards • Communications in Contemporary Mathematics (2016-) • Analysis in Theory and Applications (2015-) • Advances in Differential Equations (2015-) • Book Series on OA Measure Theory - De Gruyter Verlag (2014-) • UMI Lecture Notes - Springer Verlag (2013-) • Advances in Nonlinear Analysis (2011-) • Nonlinear Analysis (2011-) • Advances in Calculus of Variations (2008-) • manuscripta mathematica (2007-2015) 5. Bibliometrics • H-Index = 32 (Scopus), 30 (WoS) • Highly cited researcher (Thomson Reuters-Clarivate -
Existentially Closed Groups, by Graham Higman and Elizabeth Scott
242 BOOK REVIEWS 7. R. Howe, On the role of the Heisenberg group in harmonic analysis, Bull. Amer. Math. Soc. 3 (1980), 254-845. 8. K. Nishiwada, Huygens' principle for a wave equation and the asymptotic behavior of solutions along geodesies, in Hyperbolic equations and related topics (S. Mizohata, éd.), Academic Press, 1986. 9. R. Seeley, Complex powers of an elliptic operator, Proc. Symp. Pure Appl. Math. 10(1976), 288-307. 10. I. E. Segal, Mathematical Cosmology and Extragalactic Astronomy, Aca demic Press, New York, 1976. BENT 0RSTED ODENSE UNIVERSITY BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 23, Number 1, July 1990 ©1990 American Mathematical Society 0273-0979/90 $1.00+ $.25 per page Existentially closed groups, by Graham Higman and Elizabeth Scott. London Mathematical Society Monographs, New Series, vol. 3., Clarenden Press, Oxford, 1988, xiv + 156 pp., $49.95. ISBN 0-19-853543-0 SUMMARY This volume grew out of lectures given by Higman at Oxford in 1983 and 1984 as recorded and amended by Scott. It is not a comprehensive work on e.c. groups but rather contains an am ple selection of topics written at an easily accessible graduate level. Both algebraic and model-theoretic aspects of e.c. groups are high lighted. Thus, Chapter 2 gives two very diferent group-theoretic proofs that the normalizer of a finite characteristically simple sub group of an e.c. group G is a maximal subgroup of G, as well as related results, and has considrable technical interest. [For exten sions of one of these methods, see the reviewer's "A.c. -
Victor M. Buchstaber
Victor M. Buchstaber Corresponding Member of the Russian Academy of Sciences Professor PERSONAL Born: 1 April 1943, Tashkent, USSR Citizen of Russian Federation Married with two children, born 1967 and 1972 EDUCATION 1960-1964 Tashkent State University, Mechanical Mathematical Department 1964-1966 Moscow State University, Mechanical Mathematical Department 1966-1969 Postgraduate study at Moscow State University. QUALIFICATION 1967 Diploma in Mathematics, Moscow State University Thesis: "On the J-functor of cell complexes" Advisors: Professors S.P.Novikov and D.B.Fuks. 1970 Ph.D. in Mathematics Thesis: "Cohomology operations in generalized cohomology theories" Advisors: Professors S.P.Novikov and D.B.Fuks. 1984 Dr. Sc. in Mathematics. Thesis: "Two-valued formal groups. Algebraic theory and topological applications." 2006 Corresponding Member of the Russian Academy of Sciences APPOINTMENTS 1969-1979 VNIIFTRI (National Scientific and Research Institute for Physical- Technical and Radiotechnical Measurements), Research scientific positions 1979 - present VNIIFTRI, Head of the Mathematical Modeling Laboratory (now part-time position) 1993 - present The Chair of Higher Geometry and Topology, Department of Mathematics of Moscow State University, Professor (part-time position) 1996 - 2006 The Geometry and Topology Division of Steklov Mathematical Institute, Russian Academy of Sciences, Research Leader 2005 - 2010 The School of Mathematics, University of Manchester, Professor (part-time position) 2010 - present The School of Mathematics, University -
Victor Enolski (1945–2019) Emma Previato
Victor Enolski (1945–2019) Emma Previato Our friend and coauthor Victor Enolski passed away in Ukraine, on April 26, 1945. His father, Eugene (Zelik) 0 June 2019, after a brief but valiant struggle with pancre- Ènol ski˘ı, was a major in the Soviet Army during WWII atic cancer. Victor’s profound and multipronged contribu- and afterwards Professor of History in Kiev State Univer- tion to the mathematical sciences flew under the radar, to sity; his mother, Elizabeth Enolskaya (n´eeVainrub), served some extent; “Victor’s modesty is legend” says one of the in hospitals during the war as a senior lieutenant; after the pieces below, and indeed he was self-effacing to a fault, war she was a medical doctor in child psychiatry. Victor promoting instead others’ work, creating interdisciplinary earned an MSc from Kiev State University under the super- collaborations among scientists of diverse backgrounds, re- vision of Professor D. Ya. Petrina, National Academy of discovering classical work with childlike enthusiasm and Sciences of Ukraine (NASU), with a Master’s thesis Differ- breathing new life into it. We write this homage to his ential Equations for Feynman Integrals. Another part of his life with the hope of bringing his contribution to the at- MSc research, on the Mandelstam hypothesis in elemen- tention of the larger mathematical community, particu- tary particle physics, is the topic of his earliest MathSciNet larly because the subjects of his main focus, the special entry [15]. At NASU, Victor earned a PhD in Theoretical functions of classical -
Document of Work
SEVENTH FRAMEWORK PROGRAMME “Ideas” Specific programme European Research Council Grant agreement for Advanced Grant Annex I - “Description of Work” Project acronym: QuaDynEvoPro Project full title: Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture Grant agreement no.: 290888 Duration: 60 months Date of preparation of Annex I: November 22, 2011 Principal Investigator: Gianni Dal Maso Host Institution: Scuola Internazionale Superiore di Studi Avanzati QuaDynEvoPro Proposal Number: 290888 November 22, 2011 ERC Advanced Grant 2011 - Proposal Number: 290888 Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture QuaDynEvoPro Description of Work Principal Investigator: Gianni Dal Maso Host Institution: Scuola Internazionale Superiore di Studi Avanzati (SISSA) Proposal Title: Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture Proposal Acronym: QuaDynEvoPro Proposal Duration: 60 Months Summary This research project deals with nonlinear evolution problems that arise in the study of the inelastic be- haviour of solids, in particular in plasticity and fracture. The project will focus on selected problems, grouped into three main topics, namely: 1. Plasticity with hardening and softening, 2. Quasistatic crack growth, 3. Dynamic fracture mechanics. The analysis of the models of these mechanical problems leads to deep mathematical questions originated by two common features: the energies are not convex and the solutions exhibit discontinuities both with respect to space and time. In addition, plasticity problems often lead to concentration of the strains, whose mathe- matical description requires singular measures. Most of these problems have a variational structure and are governed by partial differential equations. Therefore, the construction of consistent models and their analysis need advanced mathematical tools from the calculus of variations, from measure theory and geometric measure theory, and also from the theory of nonlinear elliptic and parabolic partial differential equations. -
GARSIDE GROUPS and GEOMETRY – in MEMORY of PATRICK DEHORNOY 3 the Curve Graph – See E.G
GARSIDE GROUPS AND GEOMETRY BERT WIEST Abstract. This article in memory of Patrick Dehornoy (1952 – 2019) is an in- vitation to Garside theory for mainstream geometric group theorists interested in mapping class groups, curve complexes, and the geometry of Artin–Tits groups. 1. Meeting Patrick When I remember Patrick Dehornoy, the first thing that comes to my mind is his humour – he was one of the people who knew how to do serious work and have serious discussions with a smile and even a laugh, always in a way that advanced the work. And his work! His energy and his efficiency at everything he touched were downright scary to me. He was clearly the driving force behind the two book projects [23, 24] he had with me (together with Ivan Dynnikov and Dale Rolfsen). Each time, his plans for these books grew more and more ambitious even during the writing process, and it must have been terribly frustrating to him that his co-authors had trouble following his rhythm. His unbelievable productiveness and efficiency concerned not only his mathematical work, but also his administrative work (as head of his department, but also in French national scientific administration), and his private projects (constructing his house and his garden, and creating humorous little movies, for instance). I remember Patrick’s sometimes startling openness when discussing his private life. I remember his kindness and generosity, in particular with younger mathe- maticians, taking time and sharing his ideas. I remember his patience with less efficient people. When I told him quite frankly that the book on the foundations of Garside theory was too long and abstract for me, he listened patiently and promised to write something short and enjoyable that would at least give a glimpse of the arXiv:2008.08802v1 [math.GR] 20 Aug 2020 book.