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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 STEEN MARKVORSEN Department of Mathematics Technical University of Denmark Building 303 NEWSLETTER No. 36 DK-2800 Kgs. Lyngby, Denmark e-mail: [email protected] KRZYSZTOF CIESIELSKI June 2000 Mathematics Institute Jagiellonian University Reymonta 4 30-059 Kraków, Poland EMS News : Agenda, Editorial, 3ecm, Bedlewo Meeting, Limes Project ........... 2 e-mail: [email protected] KATHLEEN QUINN Open University [address as above] Catalan Mathematical Society ........................................................................... 3 e-mail: [email protected] SPECIALIST EDITORS The Hilbert Problems ....................................................................................... 10 INTERVIEWS Steen Markvorsen [address as above] SOCIETIES Interview with Peter Deuflhard ....................................................................... 14 Krzysztof Ciesielski [address as above] EDUCATION Vinicio Villani Interview with Jaroslav Kurzweil ..................................................................... 16 Dipartimento di Matematica Via Bounarotti, 2 56127 Pisa, Italy A Major Challenge for Mathematicians ........................................................... 20 e-mail: [email protected] MATHEMATICAL PROBLEMS Paul Jainta EMS Position Paper: Towards a European Research Area ............................. 24 Werkvolkstr. 10 D-91126 Schwabach, Germany e-mail: [email protected] Forthcoming Conferences ................................................................................. 28 ANNIVERSARIES June Barrow-Green and Jeremy Gray Open University [address as above] Recent Books ..................................................................................................... 34 e-mail: [email protected] and [email protected] and Personal Column .............................................................................................. 42 CONFERENCES Kathleen Quinn [address as above] RECENT BOOKS Ivan Netuka and Vladimir Sou³ek Designed and printed by Armstrong Press Limited Mathematical Institute Unit 3 Crosshouse Road, Southampton, Hampshire SO14 5GZ, UK Charles University phone: (+44) 23 8033 3132; fax: (+44) 23 8033 3134 Sokolovská 83 18600 Prague, Czech Republic Published by European Mathematical Society e-mail: [email protected] ISSN 1027 - 488X and [email protected] ADVERTISING OFFICER NOTICE FOR MATHEMATICAL SOCIETIES Vivette Girault Labels for the next issue will be prepared during the second half of August 2000. Laboratoire d’Analyse Numérique Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Department of Mathematics, Boite Courrier 187, Université Pierre P.O. Box 4, FIN-00014 University of Helsinki, Finland; e-mail: [email protected] et Marie Curie, 4 Place Jussieu 75252 Paris Cedex 05, France INSTITUTIONAL SUBSCRIPTIONS FOR THE EMS NEWSLETTER Institutes and libraries can order the EMS Newsletter by mail from the EMS Secretariat, e-mail: [email protected] Department of Mathematics, P. O. Box 4, FI-00014 University of Helsinki, Finland, or by e-mail: OPEN UNIVERSITY Please include the name and full address (with postal code), telephone and fax number (with coun- PRODUCTION TEAM try code) and e-mail address. The annual subscription fee (including mailing) is 60 euros; an Liz Scarna, Barbara Maenhaut invoice will be sent with a sample copy of the Newsletter. EMS June 2000 1 EMS NEWS EMS News: Committee and Agenda EXECUTIVE COMMITTEE EMS Agenda PRESIDENT (1999–2002) 2000 Prof. ROLF JELTSCH 13-16 June Seminar for Applied Mathematics EMS Lectures by Prof. Dr. George Papanicolaou (Stanford, USA). ETH, CH-8092 Zürich, Switzerland ETH, Zürich (Switzerland): Financial Mathematics e-mail: [email protected] Contact: David Brannan, e-mail: [email protected] VICE-PRESIDENTS 17-22 June Prof. ANDRZEJ PELCZAR (1997–2000) EURESCO Conference in Mathematical Analysis at Castelvecchio Pascoli (Italy): Institute of Mathematics Partial Differential Equations and their Applications to Geometry and Physics Jagellonian University Organiser: J. Eichhorn, Greifswald (Germany), e-mail: [email protected] Raymonta 4 [This series of conferences is financed by the ESF.] PL-30-059 Krakow, Poland 3-7 July e-mail: [email protected] ALHAMBRA 2000: a joint mathematical European-Arabic conference in Granada (Spain), Prof. LUC LEMAIRE (1999–2002) promoted by the EMS and the Spanish Royal Mathematical Society Department of Mathematics Contact: Ceferino Ruiz, e-mail: [email protected] website: www.ugr.es/~alhambra2000 Université Libre de Bruxelles 6 July C.P. 218 – Campus Plaine Executive Committee Meeting in Barcelona (Spain) Bld du Triomphe 7-8 July B-1050 Bruxelles, Belgium EMS Council Meeting at Institut d’Estudis Catalans, Carrer del Carme 47, E-08001 Barcelona e-mail: [email protected] (Spain), starting at 10 a.m. SECRETARY (1999–2002) Contact: EMS Secretariat, e-mail: [email protected] Prof. DAVID BRANNAN 10-14 July Department of Pure Mathematics Third European Congress of Mathematics (3ecm) in Barcelona (Spain) The Open University e-mail: [email protected] website: www.iec.es/3ecm/ Walton Hall 24 July-3 August Milton Keynes MK7 6AA, UK EMS Summer School, in Edinburgh (Scotland): e-mail: [email protected] New analytic and geometric methods in inverse problems TREASURER (1999–2002) Organiser: Erkki Somersalo, Otaniemi (Finland), e-mail: [email protected] Prof. OLLI MARTIO 15 August Department of Mathematics Deadline for submission of material for the September issue of the EMS Newsletter P.O. Box 4 Contact: Robin Wilson, e-mail: [email protected] FIN-00014 University of Helsinki 17 August-2 September Finland EMS Summer School at Saint-Flour, Cantal (France): Probability theory e-mail: [email protected] Organiser: Pierre Bernard, Clermont-Ferrand (France), e-mail: [email protected] ORDINARY MEMBERS 28-30 August Prof. BODIL BRANNER (1997–2000) EMS Lectures by Prof. Dr. George Papanicolaou (Stanford, USA). Department of Maathematics University of Crete, Heraklion, Crete (Greece): Time Reversed Acoustics Technical University of Denmark Contact: David Brannan, e-mail: [email protected] Building 303 Autumn DK-2800 Kgs. Lyngby, Denmark Fifth Diderot Mathematical Forum on Mathematics and Telecommunications e-mail: [email protected] Date and programme to be announced. Prof. DOINA CIORANESCU (1999–2002) Contact: Jean-Pierre Bourguignon, e-mail: [email protected] Laboratoire d’Analyse Numérique 22-27 September EURESCO Conference at Obernai, near Strasbourg (France): Université Paris VI Number theory and Arithmetical Geometry: Motives and Arithmetic 4 Place Jussieu Organiser: U. Jannsen, Regensburg (Germany), e-mail: [email protected] 75252 Paris Cedex 05, France EURESCO Conference at San Feliu de Guixols (Spain): e-mail: [email protected] Geometry, Analysis and Mathematical Physics: Analysis and Spectral Theory Prof. RENZO PICCININI (1999–2002) Organiser: J. Sjöstrand, Palaiseau (France), e-mail: [email protected] Dipto di Matem. F. Enriques 30 September Universit à di Milano Deadline for proposals for 2001 EMS Lectures Via C. Saldini 50 Contact: David Brannan, e-mail: [email protected] I-20133 Milano, Italy Deadline for proposals for 2002 EMS Summer Schools e-mail: [email protected] Contact: Renzo Piccinini, e-mail: [email protected] Prof. MARTA SANZ-SOLÉ (1997–2000) 11-12 November Facultat de Matematiques Executive Committee Meeting in London (UK), at the invitation of the London Mathematical Universitat de Barcelona Society. Gran Via 585 15 November E-08007 Barcelona, Spain Deadline for submission of material for the December issue of the EMS Newsletter e-mail: [email protected] Contact: Robin Wilson, e-mail: [email protected] Prof. ANATOLY VERSHIK (1997–2000) P.O.M.I., Fontanka 27 2001 191011 St Petersburg, Russia 15 February e-mail: [email protected] Deadline for submission of material for the March issue of the EMS Newsletter EMS SECRETARIAT Contact: Robin Wilson, e-mail: [email protected] Ms. T. MÄKELÄINEN 10-11 March Department of Mathematics Executive Committee Meeting in Kaiserslautern (Germany), at the invitation of the Fraunhofer- P.O. Box 4 Institut für Techno- und Wirtschafts Mathematik. FIN-00014 University of Helsinki 9-21 July Finland EMS Summer School at the Euler Institute, St Petersburg (Russia): tel: (+358)-9-1912-2883 Asymptotic combinatorics and applications to mathematical physics and representation theory fax: (+358)-9-1912-3213 Organiser: Anatoly Vershik, e-mail: [email protected] telex: 124690 3-6 September e-mail: [email protected] 1st EMS-SIAM conference, Berlin website: http://www.emis.de Organiser: Peter Deuflhard, e-mail: [email protected] 2 EMS June 2000 SOCIETIES TheThe CatalanCatalan MathematicalMathematical SocietySociety Sebastià Xambó-Descamps One of the 25 societies of the Institute of tiques and René Descartes’ La Geometria. Cangur and awarded special prizes to the Catalan Studies (IEC), the Catalan Among high school teachers, the Recull twelve best winners of the joint three com- Mathematical Society (SCM) today faces Cangur has a growing popularity; this book munities; the award ceremony for this year important challenges. Some of these stem is a collection of Cangur problems, updated will be in Barcelona in July, after the 3ecm. from its local
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  • Many-Body Entanglement in Classical & Quantum Simulators

    Many-Body Entanglement in Classical & Quantum Simulators

    Many-Body Entanglement in Classical & Quantum Simulators Johnnie Gray A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy of University College London. Department of Physics & Astronomy University College London January 15, 2019 2 3 I, Johnnie Gray, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the work. Abstract Entanglement is not only the key resource for many quantum technologies, but es- sential in understanding the structure of many-body quantum matter. At the interface of these two crucial areas are simulators, controlled systems capable of mimick- ing physical models that might escape analytical tractability. Traditionally, these simulations have been performed classically, where recent advancements such as tensor-networks have made explicit the limitation entanglement places on scalability. Increasingly however, analog quantum simulators are expected to yield deep insight into complex systems. This thesis advances the field in across various interconnected fronts. Firstly, we introduce schemes for verifying and distributing entanglement in a quantum dot simulator, tailored to specific experimental constraints. We then confirm that quantum dot simulators would be natural candidates for simulating many-body localization (MBL) - a recently emerged phenomenon that seems to evade traditional statistical mechanics. Following on from that, we investigate MBL from an entanglement perspective, shedding new light on the nature of the transi- tion to it from a ergodic regime. As part of that investigation we make use of the logarithmic negativity, an entanglement measure applicable to many-body mixed states.