Anti-holomorphic Dynamical Systems on a Torus - Applications to Weierstrass Functions

Watch a lecture from the Simons Semester on Dynamics series exploring an anti-holomorphic dynamical system on a torus and its applications to complex analysis and geometry. Discover how to count solutions of the Weierstrass zeta-function equation ζ(z) + az + bz = 0, where specific constants make the left-hand side periodic relative to a lattice. Learn about the dual interpretations of these solutions as critical points of the Green function on the torus and as metrics of constant curvature 1 with a 6π conic singularity. Examine the parameter plane of this anti-holomorphic dynamical system, which uniquely features two hyperbolic components divided by a smooth curve.