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      Dr Nicholas Sharples

      ROLE: Senior Lecturer in Mathematics
      SCHOOL: Science & Technology
      DEPARTMENT: Design Engineering & Maths
      TELEPHONE: +44 (0)20 8411 6928
      EMAIL: N.Sharples@mdx.ac.uk
      1. Biography &
        Qualifications
      2. Learning &
        Teaching Interests
      3. Research Outputs &
        Interests
      4. Funded Research &
        Knowledge Exchange Projects
      5. Engagement &
        Impact

      • Biography &
        Qualifications

        Qualifications:

        • PhD in Mathematics, University of Warwick, 2012.
        • MSc (distinction) in Mathematics, King's College London, 2007.
        • BA (first class honours) in Mathematics & Philosophy, King's College London, 2006.

        Previous positions:

        • Research Associate, Imperial College London, 2013-2014.
        • EPSRC Doctoral Prize Fellow, Imperial College London, 2012-2013.
        • Research Fellow, University of Warwick 2012

        Languages Spoken

      • Learning &
        Teaching Interests

        Modules:

        • MSO1140 - Data and information
        • MSO2120 - Mathematical analysis
        • MSO2140 - Problem solving methods
        • MSO3120 - Real and complex analysis
        • MSO3140 - Project
        • MSO4311 - Probability and stochastic processes
        • MSO4991 - Dissertation
        • PDE1430 - Formal systems

        Other:

        • R programming

      • Research Outputs &
        Interests

        My primary research interest is in the analysis of differential equations with irregular coefficients. Increasingly, these equations are used in a wide variety of mathematical models in fields as diverse as climate modelling, medical imaging, control theory, and stem-cell research yet the mathematical theory remains insufficiently developed for the requirements of modern scientific research. To address this gap and develop a broad mathematical theory of irregular differential equations my research draws upon the following:

        • Analysis of linear and non-linear PDEs and ODEs,
        • Singularities in PDEs
        • Dynamical systems
        • Fractal geometry

        I am particularly interested in problems motivated by fluid dynamics.

        I organise the Mathematics Research Seminar at Middlesex.

        Publication Feed

        Generalised Cantor sets and the dimension of products

        Olson, Eric J. and Robinson, James C. and Sharples, Nicholas (2016) Generalised Cantor sets and the dimension of products. Mathematical Proceedings of the Cambridge Philosophical Society , 160 (1). pp. 51-75. ISSN 0305-0041

        On the regularity of Lagrangian trajectories corresponding to suitable weak solutions of the Navier-Stokes equations

        Robinson, James and Sadowski, Witold and Sharples, Nicholas (2013) On the regularity of Lagrangian trajectories corresponding to suitable weak solutions of the Navier-Stokes equations. Procedia IUTAM , 7 . pp. 161-166.

        Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations

        Robinson, James and Sharples, Nicholas (2013) Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations. Journal of Differential Equations , 254 . pp. 4144-4167.

        Strict inequality in the box-counting dimension product formulas

        Robinson, James and Sharples, Nicholas (2012) Strict inequality in the box-counting dimension product formulas. Real Analysis Exchange , 38 (1). pp. 95-120.

      • Funded Research &
        Knowledge Exchange Projects

      • Engagement &
        Impact

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