Jonathan Fraser

I am a 24 year old Ph.D student at the University of St Andrews. I am a member of the Analysis Research Group and am currently jointly supervised by Professor Kenneth Falconer and Professor Lars Olsen. I am in my third year.

I am funded by the E.P.S.R.C.

If you wish to contact me you can find the appropriate details at the bottom of the page.

Curriculum Vitae

My Erdös number is 3

      with shortest path: J. Fraser → K. J. Falconer → H. T. Croft → P. Erdös

Research Interests
  • Fractal geometry and dimension theory
  • Multifractal geometry
  • Geometric measure theory
Publications
    1) The horizon problem for prevalent surfaces (with K. J. Falconer), arXiv
            - Math. Proc. Cambridge Philos. Soc., 151, (2011), 355-372.
    2) Multifractal spectra of random self-affine multifractal Sierpiński sponges in Rd (with L. Olsen), preprint
            -to appear in Indiana Univ. Math. J.
    3) The visible part of plane self-similar sets (with K. J. Falconer), arXiv
            -to appear in Proc. American. Math. Soc.
    4) The Hausdorff dimension of graphs of prevalent continuous functions (with J. T. Hyde), arXiv
            -to appear in Real Analysis Exchange.
    5) On the packing dimension of box-like self-affine sets in the plane, submitted, arXiv
    6) Dimension and measure for typical random fractals, submitted, arXiv
    7) Inhomogeneous self-similar sets and box dimensions, submitted
Current research
  • Generalised dimensions of self-affine measures
  • Self-affine attractors of infinite iterated function systems
  • Choquet-Deny functional equations relating to self-affine fractals
Teaching

2009-10 S1 MT2002 Algebra and Analysis3 tutorials per week
S2 MT1003 Pure and Applied Maths3 tutorials per week
2010-11 S1 MT2002 Algebra and Analysis3 tutorials per week
S2 MT1003 Pure and Applied Maths2 tutorials per week
2011-12 S1 MT3501 Linear Mathematics2 tutorials per week
MT1002 Introductory Mathematics1 tutorials per week
S2 MT1003 Pure and Applied Maths3 tutorials per week
MT4513 Fractal Geometrycover

  • Martinmas semester 2010: Maths tutor for SALTIRE.
  • Summer 2011: Ran final two weeks of Analysis Summer School.
    		• Conferences and Meetings Attended
    • Winter School on 'Operators and Fractals': Siegmundsburg 08/03/10 - 12/03/10
    • CODY Autumn Workshop on 'Fractals in deterministic and random dynamics': Warsaw 11/10/10 - 16/10/10
    • EPSRC workshop on 'Dynamical Systems and Dimension Theory': Warwick 18/04/11 - 21/04/11
    • Symposium on 'Ergodic Theory and Dynamical Systems': Warwick 16/04/12 - 20/04/12
    Talks
    • The visible part of fractal sets: 03/03/10, The University of Bremen
    • The visibility conjecture: 09/03/10, Siegmundsburg, slides
    • Random self-affine multifractal Sierpiński sponges in Rd: 14/10/10, Warsaw, slides
    • The horizon problem for prevalent surfaces: 19/04/11, Warwick, slides
    • The Hausdorff dimension of graphs of prevalent continuous functions : 16/06/11, Porquerolles Island, slides
    • Dimension and measure for typical random fractals: 16/04/11, Warwick.
    Education
    • 2009- : Ph.D., Pure Mathematics, University of St Andrews
    • 2005-2009 : M.Math., Mathematics (1st Class), University of St Andrews
    Other Interests
    • golf, badminton, table tennis
    • playing the guitar (or trying to)
    • music: Bob Dylan, Leonard Cohen, Cat Stevens

    Contact Details
      Mathematical Institute,
      University of St Andrews,
      North Haugh,
      St Andrews,
      Fife,
      Scotland,
      KY16 9SS.

    jmf32@st-andrews.ac.uk
    Room 103
    Phone: +44 (0)1334 463767

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