Msc Mathematics and the Foundations of Computer Science HANDBOOK

Total Page:16

File Type:pdf, Size:1020Kb

Msc Mathematics and the Foundations of Computer Science HANDBOOK MSc Mathematics and the Foundations of Computer Science HANDBOOK ISSUED OCTOBER 2014 Handbook for the MSc Mathematics and the Foundations of Computer Science Mathematical Institute 2014 Contents 1 Sources of Information 5 1.1 The Grey Book . 5 1.2 The Proctors' and Assessor's Memorandum . 5 1.3 Statements of Provision for MFoCS Students . 5 1.4 The Mathematical, Physical and Life Sciences Division Graduate Handbook . 6 2 Useful Contacts 6 3 Finding Your Way Around 7 3.1 The Mathematical Institute . 7 3.1.1 The Andrew Wiles Building . 7 3.2 The Department of Computer Science . 7 3.3 The Lecture List . 7 3.4 Libraries . 8 4 Terminology 9 5 The University and You 10 5.1 Joint Consultative Committee with Graduates . 10 5.2 University Gazette and Oxford Blueprint . 10 5.3 University Club . 10 6 Guidance on Regulations 11 7 Reading Courses 12 8 Presentation of Miniprojects and Dissertations 13 8.1 Miniprojects . 13 8.2 Dissertations . 13 8.2.1 Wording permission for 3rd party material . 14 1 9 Regulations 15 10 Guidance on Examination Conventions 16 11 Role of the Supervisors 19 11.1 \General" supervisor . 19 11.2 \Dissertation" supervisor . 20 12 COURSES OFFERED IN 2014/2015 21 13 SECTION A: MATHEMATICAL FOUNDATIONS 23 13.1 Schedule I . 23 13.2 Algebraic Number Theory | Prof. Flynn | 16 HT . 23 13.3 Algebraic Topology | Prof. Douglas | 16MT . 25 13.4 Analytic Number Theory |Prof. Heath-Brown|16MT . 25 13.5 Analytic Topology | Dr Suabedissen | 16MT . 27 13.6 Commutative Algebra | Prof. Segal | 16HT . 27 13.7 G¨odel'sIncompleteness Theorems | Dr Isaacson | 16HT . 28 13.8 Introduction to Representation Theory | Prof Nikolov | 16 MT . 29 13.9 Lambda Calculus and Types | Dr Vicary | 16 lectures HT . 30 13.10Lie Algebras | Prof. Ciubotaru | 16MT . 32 13.11Model Theory | Prof. Zilber | 16MT . 32 13.12Modular Forms | Prof Lauder | 16MT . 33 13.13Topology and Groups | Prof. Dancer | 16 MT . 35 13.14Schedule II . 36 13.15Algebraic Geometry | Dr Berczi | 16MT . 36 13.16Axiomatic Set Theory | Dr Suabedissen | 16HT . 37 13.17Homological Algebra | Prof. Kremnitzer | 16MT . 37 13.18Infinite Groups | Prof. Nikolov | 16HT . 38 13.19Non-Commutative Rings | Prof. Ardakov | 16HT . 38 13.20Geometric Group Theory | Prof Papazoglou | 16MT . 39 14 SECTION B: APPLICABLE THEORIES 41 14.1 Schedule I . 41 14.2 Applied Probability | Dept. of Statistics to allocate | 16 MT . 41 14.3 Categories, Proofs and Processes | Prof Abramsky | 20 lectures + extra reading MT 42 14.4 Communication Theory | Dr Griffiths | 16 MT . 44 14.5 Computer-Aided Formal Verification | Dr Abate |16MT . 45 14.6 Concurrency | Dr Gibson-Robson | 16 lectures + extra reading HT . 47 14.7 Foundations of Computer Science | Prof P Goldberg | 16 lectures MT . 49 14.8 Graph Theory | Prof. Riordan | 16HT . 51 2 14.9 Quantum Computer Science|Prof Bob Coecke |24 Lectures MT . 52 14.10Schedule II . 54 14.11Automata, Logic and Games | Dr M Vanden Boom |16 lectures + reading MT . 54 14.12Categorical Quantum Mechanics|Dr Heunen and Dr Vicary|16 Lectures HT . 56 14.13Combinatorics | Prof. Scott | 16MT . 58 14.14Computational Algebraic Topology | Prof Tillmann & Prof Abramsky 14HT . 59 14.15Computational Learning Theory | Prof. Worrell | 16MT . 61 15 Computational Number Theory | Prof R Heath-Brown | Reading course TT 62 15.1 Distributional Models of Meaning | Prof B Coecke| Reading course HT . 63 15.2 Elliptic Curves | Prof. Kim | 16HT . 65 15.3 Finite Dimensional Normed Spaces | Dr Sanders | 16TT . 67 15.4 Machine Learning - Prof Nando de Freitas - 24HT . 69 15.5 Networks | Prof. Porter | 16HT . 70 15.6 Probabilistic Combinatorics | Prof. McDiarmid | 16HT . 72 16 Theory of Data and Knowledge Bases| Prof T Lukasiewicz | 16 lectures HT 73 .1 Safety Information . 74 .2 Action in Case of Emergency . 74 .3 Statement of Safety Policy . 74 .4 Statement of Health and Safety Organisation . 74 .5 Departmental Health and Safety Committee . 74 .6 Code of Practice-Harassment . 74 .7 Smoking . 75 .8 Electricity . 75 .9 Equipment rooms - Department of Computer Science . 75 .10 Lighting - Department of Computer Science . 75 .11 Other Safety Information . 75 A University's Policy on Plagiarism 76 A.1 What is plagiarism? . 76 A.2 Why does plagiarism matter? . 76 A.3 What forms can plagiarism take? . 76 A.4 Not just printed text! . 77 B Electronic Resources for Mathematics 78 C Applying for Computer Resources 82 C.1 University Policy on Intellectual Property . 83 C.2 Regulations Relating to the Use of Information Technology Facilities and University Policy on Data Protection and Computer Misuse . 83 3 C.3 Equal Opportunities . 83 4 1 Sources of Information This handbook is designed as a guide for students on the Mathematics and Foundations of Computer Science course in the Mathematical Institute (MFoCS). It does not replace the official regulations relating to your degree, which you will find in the Examination Regulations, but it is a less formal and more easily understood guide to being a student in the Mathematical Institute. It also contains general information about the Department, people, facilities and safety. There is an edition of this handbook on the Mathematical Institute's website at: http://www.maths.ox.ac.uk/members/students/postgraduate-courses In addition to this handbook there are some important sources of information that you should make sure you are familiar with. 1.1 The Grey Book The Examination Regulations, usually known for obvious reasons as the "Grey Book", is the author- atitive document on the regulations for the University degrees and examinations. You should receive a free copy of the relevant part of this book through your College at the beginning of your first term. The Grey Book defines the rules for admission to and progression through the programmes of study and the syllabus for examinations. The regulations are available online at: http://www.admin.ox.ac.uk/examregs/contents.shtml 1.2 The Proctors' and Assessor's Memorandum The University has two Proctors, the Senior Proctor and the Junior Proctor, who are responsible for making sure that the University operates according to its statutes. As well as being members of key decision-making committees, they deal with • University (as distinct from college) student discipline • complaints about University matters • the running of University examinations They also carry out ceremonial duties, e.g. at degree ceremonies. The Assessor is the third senior officer, responsible particularly for student welfare and finance. The Proctors' and Assessor's Memorandum is the document relating to the rules and the statutes of the University which you are expected to follow. This can be found at: http://www.admin.ox.ac.uk/proctors/info/pam/ 1.3 Statements of Provision for MFoCS Students These detail the provisions that have been made for you by the University and the Colleges. The statement that is applicable to you is written by the Mathematical Institute; this can be found at: http://www.maths.ox.ac.uk/members/students/postgraduate-courses/msc-mfocs 5 1.4 The Mathematical, Physical and Life Sciences Division Graduate Handbook The division also produce a graduate handbook, which you should make sure you are familiar with. This can be found at: http://www.mpls.ox.ac.uk/intranet/teachingandlearning/graduateprog.html 2 Useful Contacts Course Director Prof Samson Abrambsky 83558 [email protected] Course Administrator and Exam Coordinator Monica Kundan Finlayson 15206 fi[email protected] Room SO.16, Mathematical Institute IT Support [email protected] http://www.maths.ox.ac.uk/help/support Academic Administrator - Maths Charlotte Turner-Smith 15203 [email protected] Academic Administrator - Computing Leanne Carveth 73863 [email protected] Undergraduate/Graduate Studies Librarian: Whitehead Library Cathy Hunt 73559 [email protected] Receptionist Mathematical Institute 73525 [email protected] Confidential Harassment Advisors Dr Sarah Waters 80141 [email protected] Prof Alain Goriely 15169 [email protected] Disability Contact The Academic Administrator 15203 [email protected] Safety Officer - Maths Keith Gillow 80605 safety-offi[email protected] Safety Officer - Computing Andy Simpson 83515 [email protected] Facilities Management Team [email protected] 6 3 Finding Your Way Around Your academic life in Oxford will involve two intimately connected but distinct institutions. You are a member both of a College and of the University; your supervisor is a member of the Mathematical Institute or the Department of Computer Science and probably a member of a different college. Your college will also allocate a college advisor to you. 3.1 The Mathematical Institute The Mathematical Institute occupies a brand new building, the Andrew Wiles Building, in the Radcliffe Observatory Quarter. An entry card system (using your University Card) controls access to the building. You will be provided with information on how to activate your card at the Graduate Induction Day. Should your card not work then please report the problem to [email protected] and include in the email the details from the card: Name. Category/Type/Status (e.g. Congregation, Student, Staff etc), Card Number, Card Expiry Date/Valid Until Date Rules governing access to the Mathematical Institute are as follows: 1. Cards are issued on a personal basis and must not be loaned or passed on to another person. 2. No-one should allow access to another person. 3. When a card is used to gain access to the building, the system keeps a record of that use for a period of approximately six months. 3.1.1 The Andrew Wiles Building The Andrew Wiles Building houses lecture theatres and seminar rooms in which most of the uni- versity lectures in Mathematics take place.
Recommended publications
  • Samson Abramsky and Bob Coecke. an Integrated Diagrammatic Universe for Knowledge, Language and Artificial Reasoning. John
    An integrated diagrammatic universe for knowledge, language and artificial reasoning Samson Abramsky and Bob Coecke October 5, 2015 Introduction In many different areas of scientific investigation, purely diagrammatic expressions have begun to be used as mathematical substitutes for the traditional symbolic expressions. These new languages reflect clear operational concepts such as ‘systems’ and ‘processes’, and ‘wires’ are used to represent information flow. Composition is built-in, as the act of connecting wires together. These diagrams are more intuitive, and easier to manipulate, than conventional symbolic models of reasoning. Examples of areas in which these techniques are being used include logic, for the study of propositions and deductions [43]; physics, for the study of space and spacetime [8, 32]; linguistics, to model the interaction of words within a sentence [21]; knowledge, to represent information and belief revision [22]; and computation, for the study of data and computer programs [1, 10]. These diagrams have been provided with a rigorous underpinning using category theory, a powerful branch of mathematics which relates these the diagrammatic theories to algebraic structures. More deeply, this approach can also be applied to the study of diagrammatic theories themselves [12, 33]. As such, it is its own ‘metatheory’. One major goal of the project will be to understand to what extent this can serve as a foundation for mathematics itself, as a replacement for set theory. To work towards this, one goal will be to understand how various mathematical structures can be defined from this perspective, a rich line of enquiry for which some answers are already known, but much more is left to still be discovered.
    [Show full text]
  • ABSTRACT PHYSICAL TRACES 1. Introduction
    Theory and Applications of Categories, Vol. 14, No. 6, 2005, pp. 111–124. ABSTRACT PHYSICAL TRACES SAMSON ABRAMSKY AND BOB COECKE Abstract. We revise our ‘Physical Traces’ paper [Abramsky and Coecke CTCS‘02] in the light of the results in [Abramsky and Coecke LiCS‘04]. The key fact is that the notion of a strongly compact closed category allows abstract notions of adjoint, bipartite projector and inner product to be defined, and their key properties to be proved. In this paper we improve on the definition of strong compact closure as compared to the one presented in [Abramsky and Coecke LiCS‘04]. This modification enables an elegant characterization of strong compact closure in terms of adjoints and a Yanking axiom, and a better treatment of bipartite projectors. 1. Introduction In [Abramsky and Coecke CTCS‘02] we showed that vector space projectors P:V ⊗ W → V ⊗ W which have a one-dimensional subspace of V ⊗ W as fixed-points, suffice to implement any linear map, and also the categorical trace [Joyal, Street and Verity 1996] of the category (FdVecK, ⊗) of finite-dimensional vector spaces and linear maps over a base field K. The interest of this is that projectors of this kind arise naturally in quantum mechanics (for K = C), and play a key role in information protocols such as quantum teleportation [Bennett et al. 1993] and entanglement swapping [Zukowski˙ et al. 1993], and also in measurement-based schemes for quantum computation. We showed how both the category (FdHilb, ⊗) of finite-dimensional complex Hilbert spaces and linear maps, and the category (Rel, ×) of relations with the cartesian product as tensor, can be physically realized in this sense.
    [Show full text]
  • Scientific Curriculum Vitae of Bob Coecke
    Scientific Curriculum Vitae of Bob Coecke ID: Belgian - Born 23|07|1968 in Willebroek 1 Speech: Dutch/Flemish (mother tongue) - French (fluent) - English (fluent) Dynamic info: http://se10.comlab.ox.ac.uk:8080/BobCoecke/Home en.html Contact details: [email protected] - +44|(0)1865|27.38.67 (office) - +44|(0)785|529.81.83 (mobile) Present appointment: Oxford University Computing Laboratory, Parks Road, OX1 3QD Oxford, UK. RESEARCH FIELD • Fundamentals of Physics, Logic and Computation • Quantum Information and Computation (structures and applications) • Ordered (algebraic/toplogical) Structures, Probability Theory and Category Theory RESEARCH EXPERIENCE SYLLABUS • Quantum Entanglement, Quantum Computing, Quantum Probability, Quantum Information Theory; • Proof and Type Theory, Sequent Calculus, Type Theory, Categorical logic, Linear Logic, Dynamic Logic, Modal Logic, Intuitionistic Logic, Epistemic Logic, Quantum Logic; • Information Content and Entropy, Information-flow, Information Update in Multi-Agent Systems; • Lattices, Domains, Measure Theory, (multi-)Linear Algebra, Quantales, Enriched Categories, Traced and Closed Monoidal Categories, Bicategories. STUDIES at the Free University of Brussels • 1st & 2nd Kan. Polytechnics (Architecture - Engineering) July 1987/88 - High Distinction. • 1st & 2nd Kan. Mathematics (Pure Mathematics) July 1990 - the Highest Distinction. • 1st & 2nd Kan. Physics (Theoretical Physics) July 1990 - the Highest Distinction. • 1st & 2nd Lic. Physics (Theoretical Physics) July 1991/92 - the Highest Distinction.
    [Show full text]
  • Why the Quantum
    Deep Beauty: Mathematical Innovation and the Search for an Underlying Intelligibility of the Quantum World A Symposium and Book Publication Program Sponsored by Princeton University’s Department of Philosophy Supported by a Grant from the John Templeton Foundation Celebrating the Life and Legacy of John von Neumann and the 75th Anniversary of the Publication of His Classic Text: The Mathematical Foundations of Quantum Mechanics* Symposium: October 3 – October 4, 2007 Princeton, New Jersey _______________________ Revised 09-11-07, PContractor ________________ * von Neumann, Johann. Mathematische grundlagen der quantenmechanik. Berlin: J. Springer, 1932. Deep Beauty:Mathematical Innovation and the Search for an Underlying Intelligibility of the Quantum World John von Neumann,1903-1957 Courtesy of the Archives of the Institute for Advanced Study (Princeton)* The following photos are copyrighted by the Institute for Advanced Study, and they were photographed by Alan Richards unless otherwise specified. For copyright information, visit http://admin.ias.edu/hslib/archives.htm. *[ED. NOTE: ELLIPSIS WILL WRITE FOR PERMISSION IF PHOTO IS USED; SEE http://www.physics.umd.edu/robot/neumann.html] Page 2 of 14 Deep Beauty:Mathematical Innovation and the Search for an Underlying Intelligibility of the Quantum World Project Overview and Background DEEP BEAUTY: Mathematical Innovation and the Search for an Underlying Intelligibility of the Quantum World celebrates the life and legacy of the scientific and mathematical polymath John Von Neumann 50 years after his death and 75 years following the publication of his renowned, path- breaking classic text, The Mathematical Foundations of Quantum Mechanics.* The program, supported by a grant from the John Templeton Foundation, consists of (1) a two-day symposium sponsored by the Department of Philosophy at Princeton University to be held in Princeton October 3–4, 2007 and (2) a subsequent research volume to be published by a major academic press.
    [Show full text]
  • Categorical Quantum Models and Logics
    Categorical quantum models and logics The work in this thesis has been carried out while the author was employed at the Radboud University Nijmegen, financially supported by the Netherlands Or- ganisation for Scientific Research (NWO) within the Pionier projects “Program security and correctness” during August 2005–August 2007, and “Quantization, noncommutative geometry and symmetry” during August 2007–August 2009. Typeset using LATEX and XY-pic ISBN 978 90 8555 024 2 NUR 910 c C. Heunen / Pallas Publications — Amsterdam University Press, 2009 This work is licensed under a Creative Commons Attribution-No Derivative Works 3.0 Netherlands License. To view a copy of this license, visit: http://creativecommons.org/licenses/by-nd/3.0/nl/. Categorical quantum models and logics een wetenschappelijke proeve op het gebied van de Natuurwetenschappen, Wiskunde en Informatica PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Radboud Universiteit Nijmegen op gezag van de rector magnificus prof. mr. S.C.J.J. Kortmann, volgens besluit van het College van Decanen in het openbaar te verdedigen op 7 januari 2010 om 13.30 uur precies door Christiaan Johan Marie Heunen geboren op 21 maart 1982 te Nijmegen Promotores: prof. dr. B.P.F. Jacobs prof. dr. N.P.L. Landsman Doctoral thesis committee: prof. dr. S. Abramsky University of Oxford prof. dr. M. Gehrke Radboud University Nijmegen prof. dr. P.T. Johnstone University of Cambridge prof. dr. I. Moerdijk Utrecht University dr. M. Muger¨ Radboud University Nijmegen Preface I cannot allow this thesis to be published without thanking those without whom it could not have been.
    [Show full text]
  • Curriculum Vitae
    Curriculum Vitae Prakash Panangaden 26th January 2021 Personal Born 11 March 1954 in Pun´e,India. Citizen of Canada and the USA Education • M.S. in Computer Science, University of Utah, August 1985. Research Area: Semantics of Nondeterminism. Thesis adviser: Robert M. Keller. • Ph.D. in Physics, University of Wisconsin - Milwaukee, Summer 1980. Research Area: Quantum Field Theory in Curved Spacetime. Thesis adviser: Leonard Parker. • M.S. in Physics, University of Chicago, Spring 1978. Research Area: Radiation from Black Holes. Adviser: Robert M. Wald. • M.Sc. in Physics, Indian Institute of Technology, Kanpur, Spring 1975. Experience Positions Held • Dec 1996 - present : Professor, School of Computer Science, McGill University. • July 1990 - Nov 1996: Associate Professor, School of Computer Science, McGill Uni- versity. • Jan 1990 - June 1990: Associate Professor, Department of Computing and Information Science, Queen's University. • Aug 1985 - Dec 1989: Assistant Professor, Department of Computer Science, Cornell University. 1 • Jan 1985 to July 1985: Research Associate, Department of Computer Science, Cornell University. • 1983-1984: Instructor, Department of Computer Science, University of Utah. • Jan-June 1983: Associate Instructor, Department of Computer Science, University of Utah. • 1980-1982: Research Associate, Department of Physics, University of Utah. Other Positions 1. May 2018 to June 2018: Visiting Fellow, The Alan Turing Institute, London, U.K. 2. Jan 2018 to Feb 2018: Distinguished Visiting Professor, Fondation Sciences Math´ematiques de Paris. 3. Jan 2012 to Dec 2014: Honorary Professor, University of Edinburgh. 4. July 2011: SICSA Distinguished Fellow, University of Edinburgh. 5. Sept 2010 to Aug 2011: EPSRC Visiting Fellow, Department of Computer Science, Oxford University.
    [Show full text]
  • Towards Quantum Field Theory in Categorical Quantum Mechanics
    Towards Quantum Field Theory in Categorical Quantum Mechanics Stefano Gogioso Fabrizio Genovese University of Oxford University of Oxford [email protected] [email protected] In this work, we use tools from non-standard analysis to introduce infinite-dimensional quantum systems and quantum fields within the framework of Categorical Quantum Mechanics. We define a dagger compact category ∗ Hilb suitable for the algebraic manipulation of unbounded operators, Dirac deltas and plane-waves. We cover in detail the construction of quantum systems for particles in boxes with periodic boundary conditions, particles on cubic lattices, and particles in real space. Not quite satisfied with this, we show how certain non-separable Hilbert spaces can also be modelled in our non-standard framework, and we explicitly treat the cases of quantum fields on cubic lattices and quantum fields in real space. 1 Introduction The rigorous diagrammatic methods of Categorical Quantum Mechanics [1,3,5,6,7,8] have found widely successful application to quantum information, quantum computation and the foundations of quantum theory. Until very recently, however, a major limitation of the framework was its lack of applicability to infinite-dimensional quantum systems, which include many iconic examples from textbook quantum mechanics and quantum field theory. Previous work by the authors [11] partially overcame this limitation, using non-standard analysis a` la Robinson [23] to define a dagger compact category ?Hilb of infinite- dimensional separable Hilbert spaces. A non-standard approach was chosen because it enables a consistent mathematical treatment of infinitesimal and infinite quantities, such as those involved in the manipulation of unbounded operators, Dirac deltas, plane waves, and many other gadgets and structures featuring in traditional approaches to quantum mechanics.
    [Show full text]
  • Picturing Quantum Processes Bob Coecke , Aleks Kissinger Frontmatter More Information
    Cambridge University Press 978-1-107-10422-8 — Picturing Quantum Processes Bob Coecke , Aleks Kissinger Frontmatter More Information PICTURING QUANTUM PROCESSES The unique features of the quantum world are explained in this book through the language of diagrams, setting out an innovative visual method for presenting complex theories. Requiring only basic mathematical literacy this book employs a unique formalism that builds an intuitive understanding of quantum features while eliminating the need for com- plex calculations. This entirely diagrammatic presentation of quantum theory represents the culmination of 10 years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations. Written in an entertaining and user-friendly style and including more than 100 exercises, this book is an ideal first course in quantum theory, foundations, and computation for students from undergraduate to PhD level, as well as an opportunity for researchers from a broad range of fields, from physics to biology, linguistics, and cognitive science, to discover a new set of tools for studying processes and interaction. bob coecke is Professor of Quantum Foundations, Logic and Structures at Oxford University, where he also heads the multidisciplinary Quantum Group. His pioneering research stretches from categorical quantum mechanics to the compositional structure of natural language meaning, and recent interests include causality and cognitive architecture. aleks kissinger is
    [Show full text]
  • Categorical Quantum Mechanics
    CATEGORICAL QUANTUM MECHANICS Samson Abramsky and Bob Coecke 1 INTRODUCTION Our aim is to revisit the mathematical foundations of quantum mechanics from a novel point of view. The standard axiomatic presentation of quantum mechanics in terms of Hilbert spaces, essentially due to von Neumann [1932], has provided the mathematical bedrock of the subject for over 70 years. Why, then, might it be worthwhile to revisit it now? First and foremost, the advent of quantum information and computation (QIC) as a major field of study has breathed new life into basic quantum mechanics, asking new kinds of questions and making new demands on the theory, and at the same time reawakening interest in the foundations of quantum mechanics. As one key example, consider the changing perceptions of quantum entanglement and its consequences. The initial realization that this phenomenon, so disturbing from the perspective of classical physics, was implicit in the quantum-mechanical formalism came with the EPR Gedanken-experiment of the 1930’s [Einstein et al., 1935], in the guise of a “paradox”. By the 1960’s, the paradox had become a theorem — Bell’s theorem [Bell, 1964], demonstrating that non-locality was an essential feature of quantum mechanics, and opening entanglement to experimental confirmation. By the 1990’s, entanglement had become a feature, used in quantum teleportation [Bennett et al., 1993], in protocols for quantum key distribution [Ekert, 1991], and, more generally, understood as a computational and informatic resource [Bouwmeester et al., 2001]. 1.1 The Need for High-Level Methods arXiv:0808.1023v1 [quant-ph] 7 Aug 2008 The current tools available for developing quantum algorithms and protocols, and more broadly the whole field of quantum information and computation, are defi- cient in two main respects.
    [Show full text]
  • Curriculum Vitae
    Sean Tull - Curriculum Vitae Personal details • Nationality: British • Date of Birth: 9th November 1990 • Email: [email protected] • Address: Topos Institute, 17 Beaumont Street Oxford, OX1 2LZ. Research interests I am a researcher in applied category theory. I have used categories to study quantum theory and more general theories of physical processes, including: • reconstructions of quantum theory from simple categorical principles (see papers [3, 4, 5] below); • formalisations of operational physical theories [8,9,13,14] and quantum protocols [12]; • categorical models of spatiality and causality [7,10]. I am also interested in pure category theory [6,11]. More recently I am studying categorical approaches to natural language processing, cognition and consciousness [1, 2]. Education Oct. 2014 - DPhil student in Computer Science, St. Catherine's College, University of Oxford. June 2018. Thesis title: Categorical Operational Physics. Supervisors: Bob Coecke (Oxford) and Chris Heunen (Edinburgh). Thesis explores connections between general probabilistic theories and categorical quantum me- chanics. Includes a categorical reconstruction of finite-dimensional quantum theory. Presentations on research given at numerous conferences and workshops. Supported by EPSRC Studentship. Oct. 2009 - MMath and BA in Mathematics, Selwyn College, University of Cambridge. June 2013. First Class in all BA years. Distinction in MMath with 91% marks, placing 11th in year of 226. Final year courses include category theory, computability and logic, quantum foundations. Master's essay on Locally Presentable and Accessible Categories awarded distinction level. BA courses include quantum mechanics, general relativity and logic and set theory. Sep. 2002 - John Kyrle High School, and Hereford Sixth Form College. June 2009. 5 A-Levels including Mathematics, Further Mathematics and Physics.
    [Show full text]
  • Non-Locality in Categorical Quantum Mechanics
    Non-locality in Categorical Quantum Mechanics William Edwards Wolfson College, Oxford Oxford University Computing Laboratory Submitted for the degree of Doctor of Philosophy Michaelmas Term 2009 Abstract Interest has grown in recent years in the construction of ‘quantum-like’ theories, toy theories which exhibit some but not all features of quantum mechanics. Such theories are expressed in diverse mathematical terms which may impede comparison of their properties. In this thesis we present a unifying mathematical framework in which we can compare a variety of ‘quantum-like’ theories, based on Abramsky and Coecke’s work on applying category theory to quantum mechanics. By doing so we hope to gain a clearer insight into the precise ways in which these theories differ mathematically, and whether this relates to the differences in phenomena which they predict. As an example of this kind of approach, we express Spekkens’s toy bit theory within the categorical framework, in the process proving its consistency. The toy bit theory reproduces many features of quantum mechanics, and this is reflected in the fact that within the categorical framework it shares many structural features with quantum mechanics. It differs however, in that it is, by construction, a local hidden variable theory. We develop a categorical treatment of hidden variables, and then demonstrate that the categorical structures which differ between quantum mechanics and the toy theory are exactly those which relate to the question of hidden variables. We extend this to a general result applying to a wider range of theories. i ii Acknowledgements I was fortunate to have not one but two excellent supervisors throughout my time at Oxford, Samson Abramsky and Bob Coecke.
    [Show full text]
  • Bob Coecke. Complementary Quantum Observables and Resulting Information Flows in Algorithms and Protocols. Office of Naval
    — Proposal narrative — Complementary quantum observables and resulting information flows in algorithms and protocols: high-level methods & tool development Bob Coecke Oxford University Computing Laboratory Wolfson Building, Parks Road, OX1 3QD Oxford, UK. [email protected] — +447855298183 (cell) — +441865273839 (fax) Institution proposal number: ... BRC topic title: Quantum information sciences and the future of secure computation 1 Contents 1 Statement of work (SOW) 3 2 Background 5 2.1 Context . 5 2.2 Categorical quantum computational semantics . 7 2.3 Basic setup . 8 2.3.1 General theories: -SMCs . 8 2.3.2 Accommodating Bell† states: -compact categories . 10 2.3.3 Quantum versus classical: commutative† special -Frobenius algebras . 11 2.4 Interacting quantum observables . .† . 12 2.4.1 Observables separated by a phase . 12 2.4.2 Complementary observables . 13 2.4.3 Example application: quantum Fourier transform . 13 3 Research program and methodology 14 3.1 Case study: quantum communication and cryptography . 14 3.1.1 Objectives . 16 3.1.2 Milestones . 16 3.2 Normalisation, models, completeness and automation . 16 3.2.1 Objectives . 18 3.2.2 Milestones . 18 3.3 Informatic ordering, C*-algebras and emerging quantities . 19 3.3.1 Objectives . 20 3.3.2 Milestones . 20 3.4 Digest: a high-level and quantitative account of quantum communication and cryptography . 21 3.4.1 Objectives . 21 4 Diagrammatic workplan 21 5 Management approach 21 5.1 Research track of the PI . 22 5.2 Host institution . 23 5.3 Research track of the RAs . 23 5.4 Other ongoing research projects of the PI .
    [Show full text]