Here is an article from SIAM News Jan./Feb. 2008 on our work to extend the Schwarz-Christoffel mapping for polygonal domains to the multiply connected case:SIAM News article

Here is a tutorial (preliminary version) on Fourier series methods for numerical conformal mapping.

Here is an extended version of a talk I gave at Aalto University, Helsinki, Finland on my work on conformal mapping with Alan Elcrat and John Pfaltzgraff.

M. Badreddine, T, K. DeLillo, and S. Sahraei, A comparison of some numerical conformal mapping methods for simply and multiply connected domains, to appear in: Discrete and Continuous Dynamical Systems - B.

R. Balu and T. K. DeLillo, Numerical methods for Riemann-Hilbert problems in multiply connected circle domains, J. Comput. Appl. Math., 307, (2016), pp. 248--261.

D. G. Crowdy, S. Tanveer, and T. DeLillo, Hybrid basis scheme for computing electrostatic fileds exterior to close-to-touching discs, IMA J. Numer. Anal., 36 (2016), pp. 743--769.

T. K. DeLillo, A. R. Elcrat, E. H. Kropf, and J. A. Pfaltzgraff Efficient calculation of Schwarz-Christoffel transformations for multiply connected domains using Laurent series, Comput. Methods Funct. Theory, 13, (2013), pp. 307--336.

T. K. DeLillo, A. R. Elcrat, and E. H. Kropf, Calculation of resistances for multiply connected domains using Schwarz-Christoffel transformations, Comput. Methods Funct. Theory, 11 (2011), pp. 725--745.

T. K. DeLillo and E. H. Kropf, Numerical computation of the Schwarz-Christoffel transformation for multiply connected domains, SIAM J. Sci. Comput., 33, (2011), pp. 1369--1394.

T. K. DeLillo and E. H. Kropf, Slit maps and Schwarz-Christoffel maps for multiply connected domains, Electron. Trans. Numer. Anal., 36, (2010), pp. 195--223.

T. K. DeLillo, T. A Driscoll, A. R. Elcrat, and J. A. Pfaltzgraff, Radial and circular slit maps of unbounded multiply connected circle domains, Proc. R. Soc. A, 464, (2008), pp. 1719--1737.

N. Benchama, T. K. DeLillo, T. Hyrcak, and L. Wang, A simplified Fornberg-like method for the conformal mapping of multiply connected regins--Comparisons nd crowding, J. Comput. Appl. Math., 209 (2007), pp. 1--21.

T. K. DeLillo, T. A Driscoll, A. R. Elcrat, and J. A. Pfaltzgraff, Computation of multiply connected Schwarz-Christoffel maps for exterior domains, Comput. Methods Funct. Theory, 6, (2006), pp. 301--315.

T. K. DeLillo, Schwarz-Christoffel mapping of bounded, multiply connected domains, Comput. Methods Funct. Theory, 6, (2006), pp. 275--300.

T. K. DeLillo, A. R. Elcrat, and C. Hu, Computation of the Helmholtz-Kirchhoff and rentrant jet flows using Fourier series, Appl. Math. and Computation, 163, (2005), pp. 397--422.

T. K. DeLillo, A. R Elcrat, and J. A. Pfaltzgraff, Schwarz-Christoffel mapping of multiply connected domains, J. D'Analyse Mathematique, 94, (2004), pp. 17--47.

N. Benchama and T. K. DeLillo, A brief overview of Fornberg-lik methods for conformal mapping of simply and multiply connected regions, Bull. Malaysian Math. Sc. Soc. (Second Series), 26, (2003), pp. 53--62.

T. K. DeLillo, A. R Elcrat, and J. A. Pfaltzgraff, Schwarz-Christoffel mapping of the annulus, SIAM Review, 43, (2001), pp. 469--477.

T. K. DeLillo, M. A. Horn, and J. A. Pfaltzgraff, Numerical conformal mapping of multiply connected regions by Fornberg-like methods, Numer. Math., 83, (1999), pp. 205--230.

T. K. DeLillo and J. A. Pfaltzgraff, Numerical conformal mapping methods for simply and doubly connected regions, SIAM J. Sci. Comput., 19, (1998), pp. 155--171.

R. H. Chan, T. K. DeLillo, and M. A. Horn, Superlinear convergence estimates for a conjugate gradient method for the biharmonic equation, SIAM J. Sci. Comput., 19, (1998), pp. 139--147.

R. H. Chan, T. K. DeLillo, and M. A. Horn, The numerical solution of the biharmonic equation by conformal mapping, SIAM J. Sci. Comput., 18, (1997), pp. 1571--1582.

T. K. DeLillo, A. R. Elcrat, and J. A. Pfaltzgraff, Numerical conformal mapping methods based on Faber series, J. Comput. Appl. Math., 83, (1997), pp. 205--236.

T. K. DeLillo, The accuracy of numerical conformal mapping methods: A survey of examples and results, SIAM J. Numer. Anal., 31, (1994), pp. 788--812.

T. K. DeLillo and A. R. Elcrat, Numerical conformal mapping methods for exterior regions with corners, J. Comput. Phys., 108, (1993), pp. 199--208.

T. K. DeLillo and J. A. Pfaltzgraff, Extremal distance, harmonic measure and numerical conformal mapping, J. Comput. Appl. Math., 46, (1993), pp. 103--113.

T. K. DeLillo and A. R. Elcrat, A Fornberg-like conformal mapping method for slender regions, J. Comput. Appl. Math., 46, (1993), pp. 49--64.

T. K. DeLillo and A. R. Elcrat, A comparison of some numerical conformal mapping methods for exterior regions, SIAM J. Sci. Stat. Comput., 12, (1991), pp. 399--422.

T. K. DeLillo, A. R. Elcrat, and K. G. Miller, Constant vorticity Riabouchinsky flows froma variational principle, J. Appl. Math. Phys.(ZAMP), 41, (1990), pp. 775-765.

T, K. DeLillo, A note on Rengel's inequality and the crowding phenomenon in conofrmal mapping, Appl. Math. Letters, 3 (1990), pp. 25-27. (Some of the textt and a figure were botched. I'll post a correction soon.)

T. K. DeLillo, On some relations among numerical conformal mapping methods, J. Comput. Appl. Math., 19, (1987), pp. 363--377.

T. K. DeLillo, On the use of numerical conformal mapping methods in solving boundary value problems for the Laplace equation, in R. Vichnevetsky, D. Knight, and G. Richter, Eds., Advances in Computer Methods for Partial Differential Equations-VII, Seventh IMACS Symposium Proceedings, Rutgers University (1992), pp. 190--194.

T. K. DeLillo, Comparisons of some numerical conformal mapping methods, in W. F. Ames, Ed., Proceedings of the 14th IMACS World Congress on Computation and Applied Mathematics, Vol. 1, (1994) Georgia Institute of Technology, Atlanta, Georgia, pp. 115--118.

T. K. DeLillo and J. A. Pfaltzgraff, Numerical conformal mapping methods for exterior and doubly connected regions, Proceedings of the Copper Mountain Conference on Iterative Methods, Vol 1, 4/9 to 4/13/96, Copper Mountain, CO.

T. K. DeLillo and E. H. Kropf, A Fornberg-like method for the numerical conformal mapping of bounded multiply connected domains, 2013.

T. DeLillo and L. Wang, A MATLAB Toolbox (FFTCONF) for Computing Conformal Maps with Fourier Series Methods, 2006.

- Yuri Antipov, Louisiana State University
- Christopher Bishop, Stony Brook
- Philip Brown, Texas A&M
- Darren Crowdy, Imperial College
- Toby Driscoll, University of Delaware
- Alan Elcrat, Wichita State University
- Xianfeng David Gu, Stony Brook
- Donald Marshall, Univerity of Washington
- Timothy McNicholl, Lamar University
- Vladimir Mityushev, Pedagogical Academy in Krakow
- Mohamed M. S. Nasser, Ibb University
- Nicolas Papamichael, University of Cyprus
- John Pfaltzgraff, UNC Chapel Hill
- Michael Porter, Cinvestav (Centro de Investigacion y de Estudios Avanzados)
- Antti Rasila, Aalto University, Finland
- Ken Stephenson, University of Tennessee
- Nikos Stylianopoulos, University of Cyprus
- Nick Trefethen, University of Oxford
- Rudolf Wegmann, Max Planck Institut fur Astrophysik,