NCMW - Quasiconformal mappings and Holomorphic Dynamics

Venue: Presidency University, Kolkata

Dates: 29 Jul 2024 to 3 Aug 2024

There are three important cornerstones in Complex Analysis which are used in Holomorphic Dynamics. The first one is the theory of Normal families which is generally covered in an advanced course on Complex Analysis, the second one is the Uniformization theorem, which requires advanced techniques for a proof. And finally the third one is the study of the Quasiconformal mappings, which is another topic beyond the regular postgraduate curriculum. The workshop gives an opportunity to learn the main steps of the proofs of the Uniformization theorem and the Measurable Riemann Mapping theorem, the latter being the first important result in the theory of quasiconformal mappings. It will also be discussed how these two important aspects of Complex Analysis along with the theory of Normal families are used in proving several important topics of Holomorphic Dynamics like Sullivan's no wandering domain theorem, straightening theorem for polynomial-like maps, parametrization of the hyperbolic components of the Mandelbrot set, J-stability and holomorphic motion etc.

The workshop is aimed at PhD students, postdocs, advanced MSc students (especially those who are doing projects on Complex Analysis) and researchers interested in Geometric Function Theory, Holomorphic Dynamics, Fractal Geometry, Kleinian Groups and Teichmüler Theory.