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Arxiv:1009.0785V3 [Math.NT] 7 Sep 2015 Ersnaininstead
THE CONJECTURAL CONNECTIONS BETWEEN AUTOMORPHIC REPRESENTATIONS AND GALOIS REPRESENTATIONS KEVIN BUZZARD AND TOBY GEE Abstract. We state conjectures on the relationships between automorphic representations and Galois representations, and give evidence for them. Contents 1. Introduction. 1 2. L-groups and local definitions. 4 3. Global definitions, and the first conjectures. 16 4. The case of tori. 22 5. Twisting and Gross’ η. 27 6. Functoriality. 34 7. Reality checks. 35 8. Relationship with theorems/conjectures in the literature. 37 References 41 1. Introduction. 1.1. Given an algebraic Hecke character for a number field F , a classical con- struction of Weil produces a compatible system of 1-dimensional ℓ-adic representa- tions of Gal(F /F ). In the late 1950s, Taniyama’s work [Tan57] on L-functions of abelian varieties with complex multiplications led him to consider certain higher- dimensional compatible systems of Galois representations, and by the 1960s it was realised by Serre and others that Weil’s construction might well be the tip of a arXiv:1009.0785v3 [math.NT] 7 Sep 2015 very large iceberg. Serre conjectured the existence of 2-dimensional ℓ-adic repre- sentations of Gal(Q/Q) attached to classical modular eigenforms for the group GL2 over Q, and their existence was established by Deligne not long afterwards. More- over, Langlands observed that one way to attack Artin’s conjecture on the analytic continuation of Artin L-functions might be via first proving that any non-trivial n-dimensional irreducible complex representation of the absolute Galois group of a number field F came (in some precise sense) from an automorphic representation for GLn /F , and then analytically continuing the L-function of this automorphic representation instead. -
National Life Stories an Oral History of British Science
NATIONAL LIFE STORIES AN ORAL HISTORY OF BRITISH SCIENCE Professor Michael McIntyre Interviewed by Paul Merchant C1379/72 Please refer to the Oral History curators at the British Library prior to any publication or broadcast from this document. Oral History The British Library 96 Euston Road London NW1 2DB United Kingdom +44 (0)20 7412 7404 [email protected] Every effort is made to ensure the accuracy of this transcript, however no transcript is an exact translation of the spoken word, and this document is intended to be a guide to the original recording, not replace it. Should you find any errors please inform the Oral History curators The British Library National Life Stories Interview Summary Sheet Title Page Ref no: C1379/72 Collection title: An Oral History of British Science Interviewee’s surname: McIntyre Title: Professor Interviewee’s forename: Michael Sex: Male Occupation: Applied Date and place of birth: 28/7/1941, Sydney, mathematician Australia Mother’s occupation: / Father’s occupation: Neurophysiologist Dates of recording, tracks (from – to): 28/03/12 (track 1-3), 29/03/12 (track 4-6), 30/03/12 (track 7-8) Location of interview: Department of Applied Mathematics and Theoretical Physics, University of Cambridge Name of interviewer: Dr Paul Merchant Type of recorder: Marantz PMD661 Recording format : WAV 24 bit 48kHz Total no. of tracks: 8 Mono/Stereo: Stereo Total Duration: 9:03:31 Additional material: The interview transcripts for McIntyre’s mother, Anne, father, Archibald Keverall and aunt, Anne Edgeworth are available for public access. Please contact the oral history section for more details. -
De Morgan Newsletter 2008
UCL DEPARTMENT OF MATHEMATICS DDee MMoorrggaann AAssssoocciiaattiioonn NNeewwsslleetttteerr from the Department of Mathematics UCL Issue - 16 - 2008 Editor - Michael O'Neill De Morgan Association Dinner Wednesday 4 June 2008 The venue for the Annual Dinner of the De Morgan Association was again the Jeremy Bentham Room at UCL. Over the years it has been known by other names – most of us will remember it as the Upper Hall, one of the refectories. Its relatively new name was particularly fitting since our Guest of Honour was Dr Andew Murrison MP, who spoke on some of the work of Jeremy Bentham as a social reformer. Dr Murrison is currently Shadow Minister of Defence, having previously been Shadow Minister of Health. His political career mirrors his earlier career in the medical branch of the Royal Navy, when research into neurological decompression illness led to the award of an MD and the Gilbert Blane Medal. This year marked the 10th Anniversary of the death of Sir James Lighthill on 17 July 1998. Sir James was one of Britain’s great mathematicians and a former Provost of UCL and, on his retirement, a member of the Department of Mathematics. He died tragically while engaging in one of his hobbies of long distance swimming. In this issue of the Newsletter, Professor Julian Hunt, who was the founding Dr Andrew Murrison speaking at the Director of the Lighthill Institute of Mathematical Sciences, De Morgan Association Dinner assesses Lighthill’s legacy to the mathematical sciences some 10 years after his untimely death. The year also marked the retirement of two distinguished members of the Department – Professor John Jayne and Dr Kalvis Jansons – and the arrival of one new member of the academic staff, Professor Alexey Zaikin. -
Prizes and Awards Session
PRIZES AND AWARDS SESSION Wednesday, July 12, 2021 9:00 AM EDT 2021 SIAM Annual Meeting July 19 – 23, 2021 Held in Virtual Format 1 Table of Contents AWM-SIAM Sonia Kovalevsky Lecture ................................................................................................... 3 George B. Dantzig Prize ............................................................................................................................. 5 George Pólya Prize for Mathematical Exposition .................................................................................... 7 George Pólya Prize in Applied Combinatorics ......................................................................................... 8 I.E. Block Community Lecture .................................................................................................................. 9 John von Neumann Prize ......................................................................................................................... 11 Lagrange Prize in Continuous Optimization .......................................................................................... 13 Ralph E. Kleinman Prize .......................................................................................................................... 15 SIAM Prize for Distinguished Service to the Profession ....................................................................... 17 SIAM Student Paper Prizes .................................................................................................................... -
De Morgan Newsletter 2017
UCL DEPARTMENT OF MATHEMATICS NEWSLETTER 2017/18 De Morgan Association NEWSLETTER UCL Mathematics Department The Department’s commitment to research and teaching of core mathematics, along with our willingness to embrace and collaborate with Professor Robb McDonald researchers in other disciplines, of which there Head Of Mathematics Department are many at UCL, is something we are keen to build on. I am delighted that this ambition has A glance through this year’s De Morgan now been recognised formally by the University. newsletter reveals a busy year with much In September 2017 UCL’s Provost and President, success to celebrate. We were pleased to Professor Michael Arthur, announced a small welcome four new Lecturers: Roger Casals, Ed number of ‘ideas’ key to UCL’s evolution which Segal, Iain Smears and Ewelina Zatorska. We (i) demonstrate genuine, grassroots academic are especially grateful to the estate of Howard enthusiasm, (ii) come from areas that have Davies, a former long-serving colleague, whose the potential to become world-leading and (iii) generous donation helped make one of these be deeply cross-disciplinary. Among these appointments. elite ideas is the ambition to co-locate UCL’s Departments of Mathematics and Statistical The department’s sustained recruitment of Science to form an Institute of Mathematical and outstanding staff such as Ed, Ewelina, Iain, and Statistical Sciences (IMSS). Professor Arthur Roger, along with excellent undergraduate and writes of Mathematics, Statistical Science and postgraduate students clearly demonstrates IMSS: the health of our subject. Mathematics is, of course, a fundamental discipline, and one which ‘Research quality and student experience are is finding ever-increasing applications, often already excellent in these subjects, but they lack in surprising areas. -
Memorial Tributes: Volume 15
THE NATIONAL ACADEMIES PRESS This PDF is available at http://nap.edu/13160 SHARE Memorial Tributes: Volume 15 DETAILS 444 pages | 6 x 9 | HARDBACK ISBN 978-0-309-21306-6 | DOI 10.17226/13160 CONTRIBUTORS GET THIS BOOK National Academy of Engineering FIND RELATED TITLES Visit the National Academies Press at NAP.edu and login or register to get: – Access to free PDF downloads of thousands of scientific reports – 10% off the price of print titles – Email or social media notifications of new titles related to your interests – Special offers and discounts Distribution, posting, or copying of this PDF is strictly prohibited without written permission of the National Academies Press. (Request Permission) Unless otherwise indicated, all materials in this PDF are copyrighted by the National Academy of Sciences. Copyright © National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 15 Memorial Tributes NATIONAL ACADEMY OF ENGINEERING Copyright National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 15 Copyright National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 15 NATIONAL ACADEMY OF ENGINEERING OF THE UNITED STATES OF AMERICA Memorial Tributes Volume 15 THE NATIONAL ACADEMIES PRESS Washington, D.C. 2011 Copyright National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 15 International Standard Book Number-13: 978-0-309-21306-6 International Standard Book Number-10: 0-309-21306-1 Additional copies of this publication are available from: The National Academies Press 500 Fifth Street, N.W. Lockbox 285 Washington, D.C. 20055 800–624–6242 or 202–334–3313 (in the Washington metropolitan area) http://www.nap.edu Copyright 2011 by the National Academy of Sciences. -
James Lighthill (1924–98)
news and views Obituary and go on studying them!” And so he did. James Lighthill (1924–98) It was through this total immersion that a new realm of scientific endeavour was Applied mathematician defined, explored and revealed to the fluid dynamics community. ORIAL and fluid dynamicist In biofluiddynamics, Lighthill ICT Fluid dynamics developed and has contributed equally to our understanding continued to thrive through its of the flight of birds and of insects, topics UNIVERSAL P applicability to fields of great practical for which his mastery of aerodynamics8 was importance. Dominant among these, well adapted. His appointment as provost during the first half of this century, was of University College London (1979–89) aerodynamics, which grew from an did nothing to diminish his formidable embryonic understanding of boundary- research output. Again, his interaction layer theory, flow instability, and subsonic with zoologists was of key importance. and supersonic flow. Since about 1960, the One such collaboration stands out — that dynamics of ocean and atmosphere, with with Torkel Weis-Fogh, a successor of its intricate interplay of wave-motion and James Gray at Cambridge — which led to turbulence, has emerged as a field of elucidation of the mechanism of lift- comparable vitality. And since about 1970, production in small hovering insects. This the fluid dynamics of biological systems is the clap–fling–sweep sequence by which has developed as a field of immense circulation round each wing, and so lift, is challenge now ripe for rapid growth. generated by an essentially inviscid James Lighthill’s meteoric career was mechanism. Thus does the chalcid wasp characterized by pioneering contributions Encarsia formosa achieve a lift coefficient in each of these areas. -
Philip Leverhulme Prize Winners 2012
Philip Leverhulme CLassiCs Professor Patrick Finglass Department of Classics, University of Nottingham Prize Winners 2012 In nine years since the award of his DPhil, Professor Patrick Finglass has established himself as one of the world’s leading scholars of Greek lyric and tragic poetry. His monumental commentaries on Sophoclean Philip Leverhulme Prizes, with a value of £70,000 each, are awarded tragedy (Electra, 2007; Ajax, 2011) are already standard works of to outstanding scholars who have made a substantial and recognised reference, a remarkable achievement for a scholar of his age; yet Finglass contribution to their particular field of study, recognised at an has produced not only these, but also a third major commentary (on international level, and where the expectation is that their greatest Pindar’s Pythian 11, 2007) and a substantial number of magisterial achievement is yet to come. articles, especially on the text and interpretation of Sophocles. His work The Prizes commemorate the contribution to the work of the Trust to date is characterized by an extraordinary combination of the energy made by Philip Leverhulme, the Third Viscount Leverhulme and and ambition of youth and the erudition and judgement that normally grandson of the Founder. come only with a lifetime’s experience. Commentaries on the remaining plays of Sophocles and on the fragments of the lyric poet, Stesichorus, The broad fields of research covered by this year’s awards were: are eagerly awaited; these will further cement what is already a towering • Classics international reputation. • Earth, Ocean and Atmospheric Sciences www.nottingham.ac.uk/classics/people/patrick.finglass • History of Art • Law Professor Miriam Leonard • Mathematics and Statistics Department of Greek and Latin, University College London • Medieval, Early Modern and Modern History. -
Explicit Serre Weights for Two-Dimensional Galois Representations
Explicit Serre weights for two-dimensional Galois representations Misja Frederik Alban Steinmetz Supervisor: Prof. Fred Irvin Diamond Second Supervisor: Prof. Kevin Mark Buzzard Submitted for the degree of Doctor of Philosophy Department of Mathematics King's College London August 2019 1 2 Abstract Let F be a totally real field and p a prime number. Given a Galois representation ρ : GF Ñ GL2pFpq, we have precise conjectures (see [BLGG13]) in terms of non-explicit p-adic Hodge theory giving the sets of weights of Hilbert modular forms such that the reduction of the associated Galois representation is isomorphic to ρ. Under the assumption that p is unramified in F an alternative explicit formulation of these sets of weights was proposed in the paper [DDR16] replacing the p-adic Hodge theory by local class field theory. Subsequently, the equivalence of the reformulated conjecture to the original conjecture was proved in [CEGM17]. In this thesis we generalise the conjecture of [DDR16] and the proof of equivalence of the two conjectures of [CEGM17] to hold for any totally real field F . Thereby, we give an equivalent explicit version of the conjectures on the modularity of two-dimensional Galois representations over totally real fields. The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without proper acknowledgement. Contents Chapter 1. Introduction 5 1.1. Notation 8 1.2. Conventions in p-adic Hodge theory 9 1.3. Acknowledgements 10 Chapter 2. The weight in Serre's conjecture 13 2.1. Historical notes on Serre's conjecture 13 2.2. -
Curriculum Vitae Í
Rebecca Bellovin B [email protected] Curriculum vitae Í https://rmbellovin.github.io Employment 2019–present Distributed systems engineer, Ably Realtime. 2018–2019 EPSRC postdoc, Imperial College London. 2015–2018 Junior Research Fellow, Imperial College London. 2014–2015 NSF postdoctoral fellow, University of California, Berkeley. 2013–2014 ERC postdoc, Imperial College London. Education 2013 Ph. D., Stanford University. Advisor: Brian Conrad Thesis: p-adic Hodge theory in rigid analytic families 2008 B.A., Columbia University. Summa cum laude, with honors in mathematics Preprints and Publications [1] R. Bellovin. “Cohomology of (ϕ, Γ)-modules over pseudorigid spaces”. Submitted. 2021. url: https://arxiv.org/abs/2102.04820. [2] R. Bellovin. “Modularity of trianguline representations”. Preprint. 2021. url: https: //arxiv.org/abs/2108.02823. [3] R. Bellovin. “Galois representations over pseudorigid spaces”. Submitted. 2020. url: https://arxiv.org/abs/2002.06687. [4] R. Bellovin and T. Gee. “G-valued local deformation rings and global lifts”. In: Algebra Number Theory 13.2 (2019), pp. 333–378. [5] R. Bellovin and O. Venjakob. “Wach modules, regulator maps, and ε-isomorphisms in families”. In: Int. Math. Res. Not. 16 (2019), pp. 5127–5204. [6] R. Bellovin. “Generic smoothness for G-valued potentially semi-stable deformation rings”. In: Ann. Inst. Fourier (Grenoble) 66.6 (2016), pp. 2565–2620. [7] R. Bellovin. “p-adic Hodge theory in rigid analytic families”. In: Algebra Number Theory 9.2 (2015), pp. 371–433. [8] R. Bellovin et al. “Newton polygons for a variant of the Kloosterman family”. In: Women in numbers 2: research directions in number theory. Vol. 606. -
Brandon William Allen Levin University of Arizona [email protected] Department of Mathematics 617 N
Brandon William Allen Levin University of Arizona [email protected] Department of Mathematics www.math.arizona.edu/~bwlevin 617 N. Santa Rita Avenue, P.O. Box 210089 Tucson, Arizona 85721 EDUCATION 2013 Ph.D. in Mathematics, Stanford University Dissertation: “G-valued flat deformations and local models of Shimura varieties” Advisor: Brian Conrad 2008 Certificate of Advanced Study in Pure Mathematics, University of Cambridge 2007 B.S. in Mathematics, summa cum laude, Duke University EMPLOYMENT 2017- Assistant Professor, University of Arizona, Department of Mathematics 2014-2017 L.E. Dickson Instructor, University of Chicago, Department of Mathematics 2013-2014 Invited Member, Institute for Advanced Study, Princeton, NJ, School of Mathematics PUBLICATIONS 1. “Reductions of some two-dimensional crystalline representations via Kisin modules,” joint with J. Bergdall, to appear in IMRN (2020). 2. “A Harder-Narasimhan theory for Kisin modules,” joint with C. Wang Erickson, Algebraic Geometry 7 (2020), no. 6, 645-695. 3. “Serre weights and Breuil’s lattice conjecture in dimension three,” joint with D. Le, B. V. Le Hung and S. Morra, Forum of Math, Pi, 8 (2020), e5, 135p. 4. “Weight elimination in Serre-type conjectures,” joint with D. Le and B. V. Le Hung, Duke Math. J. 168 (2019), no. 13, pp. 2433-2506. 5. “Compatible systems of Galois representations associated to the exceptional group E6,” joint with G. Boxer, F. Calegari, M. Emerton, K. Madapusi Pera, and S. Patrikis, Forum of Math, Sigma, 7 (2019), e4, 29p. 6. “Potentially crystalline deformation rings and Serre weight conjectures: Shapes and shadows,” joint with D. Le, B. V. Le Hung and S. -
NEWSLETTER Issue: 483 - July 2019
i “NLMS_483” — 2019/6/21 — 14:12 — page 1 — #1 i i i NEWSLETTER Issue: 483 - July 2019 50 YEARS OF MATHEMATICS EXACT AND THERMODYNAMIC AND MINE APPROXIMATE FORMALISM DETECTION COMPUTATIONS i i i i i “NLMS_483” — 2019/6/21 — 14:12 — 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) Andrew Wade (Durham University) NEWSLETTER WEBSITE Early Career Content Editor: Vicky Neale The Newsletter is freely available electronically News Editor: Susan Oakes at lms.ac.uk/publications/lms-newsletter. Reviews Editor: Mark McCartney MEMBERSHIP CORRESPONDENTS AND STAFF Joining the LMS is a straightforward process.