Conferences: Future

• Maths 2010 (Joint BMC/BAMC Meeting) Edinburgh, UK April 6-9 2010.
• Young Researchers in Mathematics Cambridge, UK March 25-27 2010.

Conferences: Past

• The Diverse Faces of Arithmetic Norwich, UK December 14-16 2009.
• Workshop on Discovery and Experimentation in Number Theory Toronto, CA September 22-26 2009. (Invited Talk)
• Beyond Part III Cambridge, UK April 16-18 2009. (Contributed Talk)
• MAGIC Postgraduate Student Conference 2009 Manchester, UK January 12-14 2009. (Contributed Talk)
• 12th Workshop on Elliptic Curve Cryptography (ECC 2008) Utrecht, NL September 22-24 2008.
• Eighth Algorithmic Number Theory Symposium ANTS-VIII Banff, CA May 17-22 2008
• SAGE Days 6: Cryptology, Number theory, and Arithmetic Geometry Bristol, UK November 10/11 2007.
• ECC2007 11th Workshop on Elliptic Curve Cryptography Dublin, IE September 5-7 2007.
• Topics in Algebra, Geometry and Number Theory Utrecht, NL August 13-24 2007.
• 25th Journées Arithmétiques Edinburgh, UK July 2-6 2007.
• Prospects in Mathematics Durham, UK December 15-18 2005.

Talks Given

• Integer Matrices with constrained Eigenvalues Workshop on Discovery and Experimentation in Number Theory, September 2009
  30 minute presentation of the classification of maximal cyclotomic graphs in the rational integer case, and of 4-cyclotomic graphs in the imaginary quadratic extension case; plus evidence for the latter being all maximal cyclotomic graphs over such rings.
• Why Cryptography Doesn't Guarantee Security Geometry Club, April 29, 2009
  Brief overview of Public key cryptography, DLP, Diffie-Hellman key exchange and the man-in-the-middle attack; cryptographic protocol design- authentication, replay attacks, mutual authentication, reflection attacks, the undecidability of secrecy via reduction to Post's Correspondence Problem; the challenge of post-quantum computing cryptography, lattices and the shortest/closest vector problems. (Talk and chalk, so no slides; some related writings are available.)
• Cyclotomic Matrices and Graphs Beyond Part III conference, April 2009
  45 minute overview of the classification of cyclotomic matrices corresponding first to graphs, then charged signed graphs; plus some observations on my generalisations to cyclotomic matrices over rings of integers. (Sorry, no slides: this was a traditional 'talk and chalk'!)
• Integer Matrices with constrained eigenvalues MAGIC Postgraduate conference, January 2009
  15 minute introduction to a special case of my research problem, the classification of integer symmetric cyclotomic matrices: covers Mahler measure, cyclotomic matrices, interlacing and charged signed graphs.
• Public Key Cryptography and Secret-sharing Postgraduate Colloquium, October 30, 2008
  A brief discussion of the need for public key cryptography, an illustration of Diffie-Hellman by mixing paint, scalar multiplication/DLP as a potential one-way function, and some open problems.
• Computational Aspects of Elliptic Curve Cryptography Geometry Club, April 18, 2008
  A computer-science view of ECC: Diffie-Hellman and one-way functions for key exchange; the generic Discrete Logarithm Problem and BSGS algorithm; scalar multiplication- addition chains, fast exponentiation, m-ary methods and windowing; group law implementations, Side-channel attacks and the Edwards form.
  For a recent example of a side-channel attack, see this article from the Register.
• The Mathematics of Being Nice Postgraduate Colloquium, October 11, 2007
  A brief discussion of the Prisoner's Dilemma and the emergence of cooperation from a non-cooperative setting.
• First Year Report: Full report / OHP slides. (N.B. report does not include the source code appendix).
• Hyperelliptic Curves over finite fields Geometry Club, April 27, 2007
  An overview of the geometry of hyperelliptic curves as used in cryptography: the discrete logarithm problem and ElGamal; explicit construction of the Jacobian of the curve; Frobenius endomorphism, zeta functions and the point counting problem.

Outreach / Science Communication

During the 07/08 academic year, I participated in the University of Edinburgh Science Communication in Action scheme.

• Primary School Workshops University of Edinburgh, February 2008 (students from Gilmerton Primary).
  Contributed to two one-hour sessions for P7 (11-12 years old) students offering a range of mathematical activities: probability games, building platonic solids; counting in binary.
• Talk:Sharing secrets with Cryptography Royal High Secondary School Edinburgh, February 2008.
  A brief (15 min) overview of the need for public key cryptography; a secret-sharing algorithm by mixing paints; and a potential one way function. Audience was a group of S5 students, as part of a session on pursuing mathematics at advanced higher level and beyond.
• Article: The Mathematics of Being Nice
  In iSquared magazine: Issue 1, Autumn 2007.
• Article: The Limits of Computation (Cover story)
  In iSquared magazine: Issue 6, Winter 2008/9.

Seminars and courses

I often attend (and sometimes speak at) the Geometry club and Postgrad colloquia; attend occasional Informatics seminars from the LFCS, IPAB, or Interdisciplinary Tea series; and have participated in various transkills one-day events.

Extended courses

• 2009/10 Semester 1 Information Security: Design Fundamentals and Selected Research Topics.
• 2009/10 Term 1 Languages for all: Norwegian 1.1.
• 2006/07 Semester 2 Informatics: Formal analysis of cryptographic protocols.
• 2006/07 Semester 1 Informatics: Gröbner bases (informatics).
• 2006/07 Semester 1 Mathematics Course: Complex Algebraic Surfaces

Tutoring

• 2009/10 Semester 1: Honours 1 Practical calculus (MAT-1-PCa) / Solving equations (MAT-1-SEq) (Feedback)
• 2008/09 Semester 2: Honours 1 Geometry and Convergence (MAT-1-GCo) / Group theory (MAT-1-GTh) (Feedback)
• 2008/09 Semester 1: Honours 1 Practical calculus (MAT-1-PCa) / Solving equations (MAT-1-SEq); Mathsbase
• 2007/08 Semester 2: Honours 1 Geometry and Convergence (MAT-1-GCo) / Group theory (MAT-1-GTh); Honours 2 Discrete Mathematics (MAT-2-DiM)
• 2007/08 Semester 1: Honours 1 Practical calculus (MAT-1-PCa) / Solving equations (MAT-1-SEq); Mathsbase
• 2006/07 Semester 2: Honours 1 Geometry and Convergence (MAT-1-GCo) / Group theory (MAT-1-GTh)
• 2006/07 Semester 1: Honours 1 Practical calculus (MAT-1-PCa) / Solving equations (MAT-1-SEq); Mathsbase
• 2005/06 Semester 2: Sets and Sequences (MA10004- University of Bath)
• 2005/06 Semester 1: Numbers (MA10001- University of Bath)

Last updated - January 2010