McCoy, James A. Associate Professor

Director, Institute for Mathematics and its Applications

  • Faculty of Engineering and Information Sciences
  • School of Mathematics and Applied Statistics
  • Institute for Mathematics and its Applications

Top Publications


Research Overview


  • I am a 'geometric analyst' whose main research interests are questions related to curvature driven heat-type flows of hypersurfaces.  I am interested in second order and higher order nonlinear evolution equations (and corresponding elliptic problems).  Questions of interest include short- and long-time existence, formation of singularities (where the curvature becomes unbounded) and their classifications and extension of classical flow solutions beyond singularities using a 'surgery' procedure.  Such analysis relies heavily on techniques from differential geometry, partial differential equations, functional analysis and topology.

Available as Research Supervisor

Selected Publications


Available as Research Supervisor

Potential Supervision Topics


  • I am available to supervise theses in second or higher order elliptic or parabolic equations specifically related to geometric analysis and/or geometric flow problems.

Advisees


  • Graduate Advising Relationship

    Degree Research Title Advisee
    Doctor of Philosophy Gradient Flow of the Dirichlet Energy for the Mean Curvature of Closed Surfaces Fang, Yanqin
    Doctor of Philosophy Gradient Flow of the Dirichlet Energy for the Curvature of Plane Curves Wu, Yuhan

Education And Training


  • Ph.D. in Mathematics, Monash University, Department of Mathematics, The surface area preserving mean curvature flow 1999 - 2002
  • B Science (Hon) in Mathematics, Monash University, Department of Mathematics, The Ricci flow on surfaces 1995 - 1998
  • Australian National University, Centre for Mathematics and its Applications 2002 - 2005

Teaching Overview


  • I have taught many undergraduate subjects at three Australian universities over the last 15 or so years, to mathematics students and as service subjects to engineering, physics, computer science and IT students.  This includes first year single variable calculus, second year multivariable calculus, linear algebra, differential equations and complex analysis.  At third year level I have taught calculus of variations, geometry of curves and surfaces and numerical analysis.  I maintain an interest in teaching and learning theory of partial differential equations and regularly offer related undergraduate student projects.

Keywords


  • mathematics, pure mathematics, partial differential equations, differential geometry, geometric analysis, calculus of variations, geometric evolution equations, nonlinear partial differential equations, second order partial differential equations, higher order partial differential equations, elliptic partial differential equations, parabolic partial differential equations

Mailing Address


  • School of Mathematics and Applied Statistics

    University of Wollongong

    Wollongong

    NSW

    2522

    Australia

Web Of Science Researcher Id


  • C-8727-2013

Top Publications


Research Overview


  • I am a 'geometric analyst' whose main research interests are questions related to curvature driven heat-type flows of hypersurfaces.  I am interested in second order and higher order nonlinear evolution equations (and corresponding elliptic problems).  Questions of interest include short- and long-time existence, formation of singularities (where the curvature becomes unbounded) and their classifications and extension of classical flow solutions beyond singularities using a 'surgery' procedure.  Such analysis relies heavily on techniques from differential geometry, partial differential equations, functional analysis and topology.

Selected Publications


Potential Supervision Topics


  • I am available to supervise theses in second or higher order elliptic or parabolic equations specifically related to geometric analysis and/or geometric flow problems.

Advisees


  • Graduate Advising Relationship

    Degree Research Title Advisee
    Doctor of Philosophy Gradient Flow of the Dirichlet Energy for the Mean Curvature of Closed Surfaces Fang, Yanqin
    Doctor of Philosophy Gradient Flow of the Dirichlet Energy for the Curvature of Plane Curves Wu, Yuhan

Education And Training


  • Ph.D. in Mathematics, Monash University, Department of Mathematics, The surface area preserving mean curvature flow 1999 - 2002
  • B Science (Hon) in Mathematics, Monash University, Department of Mathematics, The Ricci flow on surfaces 1995 - 1998
  • Australian National University, Centre for Mathematics and its Applications 2002 - 2005

Teaching Overview


  • I have taught many undergraduate subjects at three Australian universities over the last 15 or so years, to mathematics students and as service subjects to engineering, physics, computer science and IT students.  This includes first year single variable calculus, second year multivariable calculus, linear algebra, differential equations and complex analysis.  At third year level I have taught calculus of variations, geometry of curves and surfaces and numerical analysis.  I maintain an interest in teaching and learning theory of partial differential equations and regularly offer related undergraduate student projects.

Keywords


  • mathematics, pure mathematics, partial differential equations, differential geometry, geometric analysis, calculus of variations, geometric evolution equations, nonlinear partial differential equations, second order partial differential equations, higher order partial differential equations, elliptic partial differential equations, parabolic partial differential equations

Mailing Address


  • School of Mathematics and Applied Statistics

    University of Wollongong

    Wollongong

    NSW

    2522

    Australia

Web Of Science Researcher Id


  • C-8727-2013
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Research Areas