LMS Elections 2018 Candidate Biographies
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Generalised Noncommutative Geometry on Finite Groups and Hopf
J. Noncommut. Geom. 13 (2019), 1055–1116 Journal of Noncommutative Geometry DOI 10.4171/JNCG/345 © European Mathematical Society Generalised noncommutative geometry on finite groups and Hopf quivers Shahn Majid and Wen-Qing Tao Abstract. We explore the differential geometry of finite sets where the differential structure is given by a quiver rather than as more usual by a graph. In the finite group case we show that the data for such a differential calculus is described by certain Hopf quiver data as familiar in the context of path algebras. We explore a duality between geometry on the function algebra vs geometry on the group algebra, i.e. on the dual Hopf algebra, illustrated by the noncommutative Riemannian geometry of the group algebra of S3. We show how quiver geometries arise naturally in the context of quantum principal bundles. We provide a formulation of bimodule Riemannian geometry for quantum metrics on a quiver, with a fully worked example on 2 points; in the quiver case, metric data assigns matrices not real numbers to the edges of a graph. The paper builds on the general theory in our previous work [19]. Mathematics Subject Classification (2010). 81R50, 58B32, 16G20. Keywords. Hopf algebra, nonsurjective calculus, quiver, duality, finite group, bimodule connection. 1. Introduction Noncommutative differential geometry is an extension of geometry to the case where the coordinate algebra A may be noncommutative or “quantum.” The starting point is a “differential structure” on A defined as a pair .1; d/ where the space of “1-forms” 1 is an A-A-bimodule (so one can multiply by the algebra from the left or the right) and d A 1 obeys the Leibniz rule. -
Public Request to Take Stronger Measures of Social Distancing Across the UK with Immediate Effect 14Th March 2020
Public request to take stronger measures of social distancing across the UK with immediate effect 14th March 2020 (last update: 15th March 2020, 18:25) As scientists living and working in the UK, we would like to express our concern about the course of action announced by the Government on 12th March 2020 regarding the Coronavirus outbreak. In particular, we are deeply preoccupied by the timeline of the proposed plan, which aims at delaying social distancing measures even further. The current data about the number of infections in the UK is in line with the growth curves already observed in other countries, including Italy, Spain, France, and Germany [1]. The same data suggests that the number of infected will be in the order of dozens of thousands within a few days. Under unconstrained growth, this outbreak will affect millions of people in the next few weeks. This will most probably put the NHS at serious risk of not being able to cope with the flow of patients needing intensive care, as the number of ICU beds in the UK is not larger than that available in other neighbouring countries with a similar population [2]. Going for \herd immunity" at this point does not seem a viable option, as this will put NHS at an even stronger level of stress, risking many more lives than necessary. By putting in place social distancing measures now, the growth can be slowed down dramatically, and thousands of lives can be spared. We consider the social distancing measures taken as of today as insufficient, and we believe that addi- tional and more restrictive measures should be taken immediately, as it is already happening in other countries across the world. -
4Th International Conference on New Frontiers in Physics, ICNFP2015, from 23 to 30 August 2015, Kolymbari, Crete, Greece
4th International Conference on New Frontiers in Physics, ICNFP2015, from 23 to 30 August 2015, Kolymbari, Crete, Greece From 23 to 24 August, Lectures From 24 to 30 August, Main Conference http://indico.cern.ch/e/icnfp2015 Yiota Foka on behalf of the ICNFP2015 Organizing Committee: Larissa Bravina, University of Oslo (Norway) (co-chair) Yiota Foka, GSI (Germany) (co-chair) Sonia Kabana, University of Nantes and Subatech (France) (co-chair) Evgeny Andronov, SPbSU (Russia) Panagiotis Charitos, CERN (Switzerland) Laszlo Csernai, University of Bergen (Norway) Nikos Kallithrakas, Technical University of Chania (Greece) Alisa Katanaeva, SPbSU (Russia) Elias Kiritsis, APC and University of Crete (Greece) Adam Kisiel, WUT (Poland) Vladimir Kovalenko, SPbSU (Russia) Emanuela Larentzakis, OAC, Kolymbari (Greece) Patricia Mage-Granados, CERN (Switzerland) Anton Makarov, SPbSU (Russia) Dmitrii Neverov, SPbSU (Russia) Ahmed Rebai, Completude Ac. Nantes (France) Andrey Seryakov, SPbSU (Russia) Daria Shukhobodskaia, SPbSU (Russia) Inna Shustina, (Ukraine) Abstract We apply for financial aid to support the participation of graduate students and postdoctoral research associates at the 4th International Conference on New Frontiers in Physics, to be held in Kolymbari, Crete, Greece, from 23 to 30 Au- gust 2015. The conference series \New Frontiers in Physics" aims to promote interdisciplinarity and cross-fertilization of ideas between different disciplines addressing fundamental physics. 1 Introduction While different fields each face a distinct set of field-specific challenges in the coming decade, a significant set of commonalities has emerged in the technical nature of some of these challenges, or are underlying the fundamental concepts involved. A Grand Unified Theory should in principle reveal this underlying relationship. -
Lms Elections to Council and Nominating Committee 2017: Candidate Biographies
LMS ELECTIONS TO COUNCIL AND NOMINATING COMMITTEE 2017: CANDIDATE BIOGRAPHIES Candidate for election as President (1 vacancy) Caroline Series Candidates for election as Vice-President (2 vacancies) John Greenlees Catherine Hobbs Candidate for election as Treasurer (1 vacancy) Robert Curtis Candidate for election as General Secretary (1 vacancy) Stephen Huggett Candidate for election as Publications Secretary (1 vacancy) John Hunton Candidate for election as Programme Secretary (1 vacancy) Iain A Stewart Candidates for election as Education Secretary (1 vacancy) Tony Gardiner Kevin Houston Candidate for election as Librarian (Member-at-Large) (1 vacancy) June Barrow-Green Candidates for election as Member-at-Large of Council (6 x 2-year terms vacant) Mark AJ Chaplain Stephen J. Cowley Andrew Dancer Tony Gardiner Evgenios Kakariadis Katrin Leschke Brita Nucinkis Ronald Reid-Edwards Gwyneth Stallard Alina Vdovina Candidates for election to Nominating Committee (2 vacancies) H. Dugald Macpherson Martin Mathieu Andrew Treglown 1 CANDIDATE FOR ELECTION AS PRESIDENT (1 VACANCY) Caroline Series FRS, Professor of Mathematics (Emeritus), University of Warwick Email address: [email protected] Home page: http://www.maths.warwick.ac.uk/~cms/ PhD: Harvard University 1976 Previous appointments: Warwick University (Lecturer/Reader/Professor)1978-2014; EPSRC Senior Research Fellow 1999- 2004; Research Fellow, Newnham College, Cambridge 1977-8; Lecturer, Berkeley 1976-77. Research interests: Hyperbolic Geometry, Kleinian Groups, Dynamical Systems, Ergodic Theory. LMS service: Council 1989-91; Nominations Committee 1999- 2001, 2007-9, Chair 2009-12; LMS Student Texts Chief Editor 1990-2002; LMS representative to various other bodies. LMS Popular Lecturer 1999; Mary Cartwright Lecture 2000; Forder Lecturer 2003. -
Matched Pairs of Lie Groups Associated to Solutions of the Yang-Baxter Equations
Pacific Journal of Mathematics MATCHED PAIRS OF LIE GROUPS ASSOCIATED TO SOLUTIONS OF THE YANG-BAXTER EQUATIONS SHAHN MAJID Vol. 141, No. 2 December 1990 PACIFIC JOURNAL OF MATHEMATICS Vol. 141, No. 2, 1990 MATCHED PAIRS OF LIE GROUPS ASSOCIATED TO SOLUTIONS OF THE YANG-BAXTER EQUATIONS SHAHN MAJID Two groups G, H are said to be a matched pair if they act on each other and these actions, (a, /?), obey a certain compatibility condition. In such a situation one may form a bicrossproduct group, denoted Gβ cχiQ H. Also in this situation one may form a bicrossproduct Hopf, Hopf-von Neumann or Kac algebra obtained by simultaneous cross product and cross coproduct. We show that every compact semi-simple simply-connected Lie group G is a member of a matched pair, denoted (G, G*)9 in a natural way. As an example we construct the matched pair in detail in the case (SU(2), SU(2)*) where SU(2)* = is the simply-connected group of a Lie algebra su(2)*. Here su(2)* is defined with respect to a standard canonical solution of the CYBE on the complexification of su(2). 1. Introduction and preliminaries. The notion of a matched pair of groups was studied in [18] and more recently in [12]. Two groups G, H are a matched pair if they act on each other and these actions α, β obey the condition (*) \/x,y e G, &,* e Hy ax-χ{e) = e, β<?-ι(e) = e, where e denotes the relevant group identity. We have chosen here conventions in which the natural objects are right actions αri, β&-ι. -
Quantum Riemannian Geometry of Phase Space and Nonassociativity
Demonstr. Math. 2017; 50: 83–93 Demonstratio Mathematica Open Access Research Article Edwin J. Beggs and Shahn Majid* Quantum Riemannian geometry of phase space and nonassociativity DOI 10.1515/dema-2017-0009 Received August 3, 2016; accepted September 5, 2016. Abstract: Noncommutative or ‘quantum’ differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics) but also differential forms, bundles and Riemannian structures at this level. The data for the algebra quantisation is a classical Poisson bracket while the data for quantum differential forms is a Poisson-compatible connection. We give an introduction to our recent result whereby further classical data such as classical bundles, metrics etc. all become quantised in a canonical ‘functorial’ way at least to 1st order in deformation theory. The theory imposes compatibility conditions between the classical Riemannian and Poisson structures as well as new physics such as n typical nonassociativity of the differential structure at 2nd order. We develop in detail the case of CP where the i j commutation relations have the canonical form [w , w¯ ] = iλδij similar to the proposal of Penrose for quantum twistor space. Our work provides a canonical but ultimately nonassociative differential calculus on this algebra and quantises the metric and Levi-Civita connection at lowest order in λ. Keywords: Noncommutative geometry, Quantum gravity, Poisson geometry, Riemannian geometry, Quantum mechanics MSC: 81R50, 58B32, 83C57 In honour of Michał Heller on his 80th birthday. 1 Introduction There are today lots of reasons to think that spacetime itself is better modelled as ‘quantum’ due to Planck-scale corrections. -
Quantum Geometry, Logic and Probability
Quantum geometry, logic and probability Shahn Majid School of Mathematics, Queen Mary University of London Abstract Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. How- ever, these ‘lattice spacing’ weights do not have to be independent of the direction of the arrow. We use this greater freedom to give a quantum geometric interpretation of discrete Markov processes with transition probabilities as arrow weights, namely taking the diffusion form @ f = ( ∆θ + q p)f for the graph Laplacian ∆θ, potential + − − functions q; p built from the probabilities, and finite difference @+ in the time direction. Motivated by this new point of view, we intro- duce a ‘discrete Schrödinger process’ as @ = {( ∆ + V ) for the + − Laplacian associated to a bimodule connection such that the discrete evolution is unitary. We solve this explicitly for the 2-state graph, finding a 1-parameter family of such connections and an induced ‘gen- eralised Markov process’ for f = 2 in which there is an additional j j source current built from . We also mention our recent work on the CC-BY-NC-ND 4.0 quantum geometry of logic in ‘digital’ form over the field F2 = 0; 1 , • f g including de Morgan duality and its possible generalisations. Keywords logic, noncommutative geometry, digital geometry, quantum gravity, duality, power set, Heyting algebra. Philosophical Problems in Science (Zagadnienia FilozoficzneNo w Nauce) 69 (2020), pp. 191–236 192 Shahn Majid 1. Introduction hese are notes growing out of a conference in Kraków with Tthe wonderful question “Is logic physics?”. -
Philosophy of Space and Time - Shahn Majid
FUNDAMENTALS OF PHYSICS - Philosophy of Space And Time - Shahn Majid PHILOSOPHY OF SPACE AND TIME Shahn Majid Queen Mary, University of London, London, UK. Keywords: Born-reciprocity, relativity, quantum theory, momentum space, spacetime continuum, Planck scale, quantum gravity, quantum spacetime, quantum group, noncommutative geometry, relative realism, nature of time Contents 1. Introduction 2. Prehistory of Space and Time 3. Spacetime Continuum 4. Failure of the Spacetime Continuum 5. Quantum Geometry 6. Quantum Spacetime and Experiment 7. Time, Matter and Dark Energy 8. Philosophical Perspective 9. Conclusions Glossary Bibliography Biographical Sketch Summary It is easy to think that our notions of space and time have barely changed since the ancient Greeks. With the proviso of certain relativistic effects, we more or less take them for granted as the backdrop in which all other Sciences take place. But is this correct? We will see in this chapter that since the 1950s it has been clear that the assumption of a spacetime continuum is actually unjustified and could well be wrong. Only in the 1980s, however, were serious alternatives developed by mathematicians and since then a growing confluence of philosophical ideology, mathematical innovation and the possibility of experimental test has led to the emergence of a new science of space and time. UNESCO-EOLSS In principle thereSAMPLE are as many approaches toCHAPTERS spacetime as there are to the unsolved problem of a unified theory of quantum gravity. However, we will explain how a coherent new science has emerged in spite of that, based on the idea of „quantum spacetime‟ as a common framework. -
NEWSLETTER Issue: 481 - March 2019
i “NLMS_481” — 2019/2/13 — 11:04 — page 1 — #1 i i i NEWSLETTER Issue: 481 - March 2019 HILBERT’S FRACTALS CHANGING SIXTH AND A-LEVEL PROBLEM GEOMETRY STANDARDS i i i i i “NLMS_481” — 2019/2/13 — 11:04 — page 2 — #2 i i i EDITOR-IN-CHIEF COPYRIGHT NOTICE Iain Moatt (Royal Holloway, University of London) News items and notices in the Newsletter may [email protected] be freely used elsewhere unless otherwise stated, although attribution is requested when reproducing whole articles. Contributions to EDITORIAL BOARD the Newsletter are made under a non-exclusive June Barrow-Green (Open University) licence; please contact the author or photog- Tomasz Brzezinski (Swansea University) rapher for the rights to reproduce. The LMS Lucia Di Vizio (CNRS) cannot accept responsibility for the accuracy of Jonathan Fraser (University of St Andrews) information in the Newsletter. Views expressed Jelena Grbic´ (University of Southampton) do not necessarily represent the views or policy Thomas Hudson (University of Warwick) of the Editorial Team or London Mathematical Stephen Huggett (University of Plymouth) Society. Adam Johansen (University of Warwick) Bill Lionheart (University of Manchester) ISSN: 2516-3841 (Print) Mark McCartney (Ulster University) ISSN: 2516-385X (Online) Kitty Meeks (University of Glasgow) DOI: 10.1112/NLMS Vicky Neale (University of Oxford) Susan Oakes (London Mathematical Society) David Singerman (University of Southampton) Andrew Wade (Durham University) NEWSLETTER WEBSITE The Newsletter is freely available electronically Early Career Content Editor: Vicky Neale at lms.ac.uk/publications/lms-newsletter. News Editor: Susan Oakes Reviews Editor: Mark McCartney MEMBERSHIP CORRESPONDENTS AND STAFF Joining the LMS is a straightforward process. -
LMS Elections 2018 Candidate Biographies
LMS ELECTIONS TO COUNCIL AND NOMINATING COMMITTEE 2020: CANDIDATE BIOGRAPHIES Candidate for election as President (1 vacancy) Jon Keating Candidates for election as Vice-President (2 vacancies) Iain Gordon Catherine Hobbs Candidate for election as Treasurer (1 vacancy) Simon Salamon Candidate for election as General Secretary (1 vacancy) Robb McDonald Candidate for election as Publications Secretary (1 vacancy) John Hunton Candidate for election as Programme Secretary (1 vacancy) Chris Parker Candidates for election as Education Secretary (1 vacancy) Kevin Houston Candidate for election as Librarian (Member-at-Large) (1 x 1-year vacancy) Mark McCartney Candidates for election as Member-at-Large of Council (6 x 2-year terms) Peter Ashwin Anne-Christine Davis Christopher John Howls Minhyong Kim Niall MacKay Shahn Majid Mariya Ptashnyk Anne Taormina Amanda Turner Candidates for election to Nominating Committee (2 x 3-year terms vacant) Chris Budd Rachel Camina John Parker Gwyneth Stallard 1 CANDIDATE FOR ELECTION AS PRESIDENT (1 VACANCY) Jonathan Peter Keating FRS, Sedleian Professor of Natural Philosophy, University of Oxford Email: [email protected] Homepage: https://www.maths.ox.ac.uk/people/jon.keating PhD: University of Bristol, 1989 Previous appointments: Royal Society Research Assistant, University of Bristol, 1989–1991; Lecturer in Applied Mathematics, University of Manchester, 1991-1995; Reader in Applied Mathematics, University of Bristol, 1995- 1997; BRIMS Research Fellow, Hewlett-Packard Laboratories, Bristol, 1995-2001; Professor of Mathematical Physics, University of Bristol, 1997-2012; Head of Department of Mathematics, University of Bristol, 2001-2004; EPSRC Senior Research Fellow, 2004-2009; Dean of Science, University of Bristol, 2009-2013; Henry Overton Wills Professor of Mathematics, University of Bristol, 2012-2019; Chair of the Heilbronn Institute for Mathematical Research, 2015-2020. -
NEWSLETTER Issue: 492 - January 2021
i “NLMS_492” — 2020/12/21 — 10:40 — page 1 — #1 i i i NEWSLETTER Issue: 492 - January 2021 RUBEL’S MATHEMATICS FOUR PROBLEM AND DECADES INDEPENDENCE ON i i i i i “NLMS_492” — 2020/12/21 — 10:40 — page 2 — #2 i i i EDITOR-IN-CHIEF COPYRIGHT NOTICE Eleanor Lingham (Sheeld Hallam University) News items and notices in the Newsletter may [email protected] be freely used elsewhere unless otherwise stated, although attribution is requested when EDITORIAL BOARD reproducing whole articles. Contributions to the Newsletter are made under a non-exclusive June Barrow-Green (Open University) licence; please contact the author or David Chillingworth (University of Southampton) photographer for the rights to reproduce. Jessica Enright (University of Glasgow) The LMS cannot accept responsibility for the Jonathan Fraser (University of St Andrews) accuracy of information in the Newsletter. Views Jelena Grbic´ (University of Southampton) expressed do not necessarily represent the Cathy Hobbs (UWE) views or policy of the Editorial Team or London Christopher Hollings (Oxford) Mathematical Society. Robb McDonald (University College London) Adam Johansen (University of Warwick) Susan Oakes (London Mathematical Society) ISSN: 2516-3841 (Print) Andrew Wade (Durham University) ISSN: 2516-385X (Online) Mike Whittaker (University of Glasgow) DOI: 10.1112/NLMS Andrew Wilson (University of Glasgow) Early Career Content Editor: Jelena Grbic´ NEWSLETTER WEBSITE News Editor: Susan Oakes Reviews Editor: Christopher Hollings The Newsletter is freely available electronically at lms.ac.uk/publications/lms-newsletter. CORRESPONDENTS AND STAFF LMS/EMS Correspondent: David Chillingworth MEMBERSHIP Policy Digest: John Johnston Joining the LMS is a straightforward process. For Production: Katherine Wright membership details see lms.ac.uk/membership. -
Brief Biographies of Candidates
London Mathematical Society Elections 2017 Brief Biographies of Candidates H2624_P2 Please read carefully before casting your vote. Contents Page Number Biographies of Candidates 3 Nomination Information 14 Officer Roles 14 Members-at-Large of Council 14 Member-at-Large (Librarian) 15 Nominating Committee 15 Single Transferable Vote 16 Candidate for election as President (1 vacancy) Caroline Series FRS, Professor of Mathematics (Emeritus), University of Warwick Email address: [email protected] Home page: http://www.maths.warwick.ac.uk/~cms/ PhD: Harvard University 1976. Previous appointments: Warwick University (Lecturer/Reader/Professor)1978-2014; EPSRC Senior Research Fellow 1999- 2004; Research Fellow, Newnham College, Cambridge 1977-8; Lecturer, Berkeley 1976-77. Research interests: Hyperbolic Geometry, Kleinian Groups, Dynamical Systems, Ergodic Theory. LMS service: Council 1989-91; Nominations Committee 1999- 2001, 2007-9, Chair 2009-12; LMS Student Texts Chief Editor 1990-2002; LMS representative to various other bodies; LMS Popular Lecturer 1999; Mary Cartwright Lecture 2000; Forder Lecturer 2003. Additional information. FIMA, FAMS, Hon. Fellow Somerville College, Oxford; Junior Whitehead Prize 1987; Senior Anne Bennett Prize 2014; British Science Association President 2011; Maths subpanel member RAE 2008, REF 2014; EPSRC Mathematics College 1998 - 2010 and various EPSRC panels; IMU Committee for Women in Mathematics Vice Chair 2015-18. Candidates for election as Vice-Presidents (2 vacancies) John Greenlees, School of Mathematics and Statistics, University of Sheffield. Email: [email protected] Home page: http://greenlees.staff.shef.ac.uk/ PhD: University of Cambridge 1986. Previous appointments: Lecturer, National University of Singapore 1986–89: Visiting Assistant Professor, University of Chicago 1989-90; Nuffield Foundation Science Research Fellowship 1995-96; Visiting Associate Professor, University of Chicago 1994; INI Programme Organizer, Cambridge 2002; Head of School 2010-13; Research Professor MSRI, 2014.