Overview
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 SchottkyKlein 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.
Information

Complex analysis
 Conformal mapping
 Special function theory
 Potential theory
 Ideal fluid mechanics
 Boundary integral equations

Complex analysis
 Calculus
 Ordinary differential equations
 Partial differential equations
 C. C. Green, A. Mahenthiram & L. A. Ward
Harmonicmeasure 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 harmonicmeasure distribution function for the middlethirds Cantor set.
Journal of Computational and Applied Mathematics.  T. K. DeLillo & C. C. Green (2023)
Computation of plane potential flow around multielement airfoils using the SchottkyKlein prime function.
Physica D: Nonlinear Phenomena.  C. C. Green, M. A. Snipes, L. A. Ward & D. G. Crowdy (2022)
Harmonicmeasure 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 HeleShaw 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.
Nonlinearity.  C. C. Green, C. J. Lustri & S. W. McCue (2017)
The effect of surface tension on steadily translating bubbles in an unbounded HeleShaw cell.
Proceedings of the Royal Society A.  D. G. Crowdy, E. H. Kropf, C. C. Green, & M. M. S. Nasser (2016)
The SchottkyKlein 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 HeleShaw channel.
Proceedings of the Royal Society A.  C. C. Green & J. S. Marshall (2013)
Green's function for the LaplaceBeltrami 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, 20182020
Value: 374,200 AUD.  National Science Foundation Collaborative Grant, 20162018
Value: 229,500 USD.

Codirector (with Prof. Thomas DeLillo) of WSU's Industrial Math Clinic. https://www.wichita.edu/academics/fairmount_las/mathematics/IMC/industrial_math_clinic.php
 Director of WSU's Mathematics & Statistics Lecture Series. https://www.wichita.edu/academics/fairmount_las/mathematics/mathstat/events/current_lecture.php