Abstract: 

We introduce the setup of discrete dynamics of a (polynomial) map both in real line and in the complex plane, and introduce the notion of ‘conjugacy’ classes among them. In the context of dynamics of quadratic maps in complex plane, we discuss the “Mandelbrot set” and its connection to dynamics. 

Finally in the last part of the talk we introduce the class of polynomial automorphisms of $\\mathbb{C}^2$, called the Hénon maps and discuss a few results related to the rigidity of Julia sets associated to such maps.

About the speaker : 

Currently Sayani is working as an assistant professor in Indian Association for the Cultivation of Science. Prior to that she had held post doctoral fellowships in HRI, Prayagraj (Harish Chandra Research Institute, Prayagraj) and RKM-VERI, Belur (Ramakrishna Vivekananda Educational Research Institute, Belur). She completed her Ph.D. from Indian Institute of Science, Bangalore in 2015, under the supervision of Dr. Kaushal Verma. Her area of specialisation is holomorphic dynamics in several complex variables.