Thurston's conjecture on the convergence of circle packings to the Riemann mapping is a constructive and geometric approach to the Riemann mapping theorem. The conjecture was solved elegantly by Rodin and Sullivan in 1987. In 2004, Bowers and Stephenson introduced the inversive distance circle packings as a natural generalization of Thurston's circle packings. They further conjectured that the discrete conformal maps induced by inversive distance circle packings converge to the Riemann mapping. In this talk, we will discuss some progress on Bowers-Stephenson's conjecture for Jordan domains. This is a joint work with Yuxiang Chen, Yanwen Luo and Siqi Zhang.
