Intersection Theory and the Mandelbrot Set

Explore the fascinating world of the Mandelbrot set in this 49-minute lecture by Laura DeMarco at the Hausdorff Center for Mathematics. Delve into one of mathematics' most famous and enigmatic objects, defined as the set of complex numbers c for which the polynomial f_c(z)=z^2+c has a connected Julia set. Discover how the Mandelbrot set intersects with various mathematical domains and learn about recent developments in arithmetic geometry. Examine how tools from arithmetic intersection theory can be applied to complex dynamical systems, revealing new insights about the Mandelbrot set. Gain understanding of the collaborative research conducted by DeMarco and Myrto Mavraki, bridging the gap between complex dynamics and arithmetic geometry.