Dr. Green is currently an Assistant Professor of Applied Mathematics in the Department of Mathematics, Statistics & Physics at Wichita State University. He graduated with a PhD from Imperial College London (London, UK) under the supervision of Prof. Darren Crowdy, and subsequently held postdoctoral appointments at the University of California San Diego (La Jolla CA, USA) and the Queensland University of Technology (Brisbane, Australia). Before moving to Wichita State University, he was a Lecturer in Applied Mathematics at Macquarie University (Sydney, Australia), where he was also an ARC DECRA Fellow.

Dr. Green is an applied and computational complex analyst. His main research focus is the development of new constructive techniques in complex analysis for solving problems in multiply connected domains (i.e. domains with more than one boundary component). He is also interested in ideal fluid mechanics in multiply connected domains. Dr. Green employs a classical special function -- known as the Schottky-Klein prime function -- little used by mathematicians until relatively recently, but now increasingly recognized as the natural object to consider when solving problems in geometrically complicated domains. It also has a particularly rich function theory, which allows many elegant solutions to these problems to be constructed. 


Areas of Research Interest
  • Complex analysis

  • Conformal mapping
  • Special function theory
  • Potential theory
  • Ideal fluid mechanics
  • Boundary integral equations
Areas of Teaching Interest
  • Complex analysis

  • Calculus
  • Ordinary differential equations
  • Partial differential equations
  • C. C. Green, A. Mahenthiram & L. A. Ward
    Harmonic-measure distribution functions of multiply connected domains with various geometries.
    under review at Proceedings of the Royal Society A.)
  • M. M. S. Nasser, C. C. Green & M. Vuorinen (2024)
    Fast computation of analytic capacity.
    Computational Methods and Function Theory.
  • C. C. Green & M. M. S. Nasser (2024)
    Towards computing the harmonic-measure distribution function for the middle-thirds Cantor set.
    Journal of Computational and Applied Mathematics.
  • T. K. DeLillo & C. C. Green (2023)
    Computation of plane potential flow around multi-element airfoils using the Schottky-Klein prime function.
    Physica D: Nonlinear Phenomena.
  • C. C. Green, M. A. Snipes, L. A. Ward & D. G. Crowdy (2022)
    Harmonic-measure distribution functions for a class of multiply connected symmetrical slit domains.
    Proceedings of the Royal Society A.
  • C. J. Lustri, C. C. Green & S. W. McCue (2020)
    Selection of a Hele-Shaw bubble via exponential asymptotics.
    SIAM Journal on Applied Mathematics.
  • M. M. S. Nasser & C. C. Green (2018)
    A fast numerical method for ideal fluid flow in domains with multiple stirrers.
  • C. C. Green, C. J. Lustri & S. W. McCue (2017)
    The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell.
    Proceedings of the Royal Society A.
  • D. G. Crowdy, E. H. Kropf, C. C. Green, & M. M. S. Nasser (2016)
    The Schottky-Klein prime function: a theoretical and computational tool for applications.
    IMA Journal of Applied Mathematics.
  • C. C. Green (2015)
    Analytical solutions for two hollow vortex configurations in an infinite channel.
    European Journal of Mechanics B/Fluids.
  • C. C. Green & G. L. Vasconcelos (2014)
    Multiple steadily translating bubbles in a Hele-Shaw channel.
    Proceedings of the Royal Society A.
  • C. C. Green & J. S. Marshall (2013)
    Green's function for the Laplace-Beltrami operator on a toroidal surface.
    Proceedings of the Royal Society A.
  • D. G. Crowdy & C. C. Green (2012)
    Analytical solutions for von Karman streets of hollow vortices.
    Physics of Fluids.
  • D. G. Crowdy, A. S. Fokas & C. C. Green (2011)
    Conformal mappings to multiply connected polycircular arc domains.
    Computational Methods and Function Theory.
  • Australian Research Council Discovery Early Career Researcher Award, 2018-2020
    Value:  374,200 AUD.
  • National Science Foundation Collaborative Grant, 2016-2018
    Value:  229,500 USD.
Areas of Service