Graduate Students' Group Seminar, IISER Mohali (April 22, 2026)
Title: Chaos in Two Dimensions: Complex Hénon Maps.
Abstract: Complex Hénon maps are the simplest examples of polynomial automorphisms in two variables with interesting dynamical properties which bring deep questions in modern dynamics. In the first part of this talk, we will build a picture of how these maps move points around $\mathbb{C}^2$. We introduce the filtration properties, a method of sorting points based on whether they stay nearby or escape to infinity. This allows us to define two fundamental objects: the filled Julia set, and the escaping set. We will see how these sets are described by the Green's function, a tool from potential theory that measures how fast points escape.
In the final portion of the talk, we will discuss few rigidity results, the idea that the shape of a set can sometimes force the underlying map to take a very specific form.
Young Mathematicians' Symposium 2026, IISER Mohali (May 12, 2026)
Title: Rigidity of Automorphisms of the Escaping sets of Complex Hénon maps.
Abstract: Complex Hénon maps are the central class of polynomial automorphisms of $\mathbb{C}^2$ with rich dynamical behavior. In this talk, we study automorphisms of the escaping set. After briefly recalling the basic dynamical framework and key tools—such as filtration properties, the intermediate cover of Hubbard and Oberste-Vorth, and the Green function—we review known rigidity phenomena for these automorphisms. We then present a new rigidity result showing that automorphisms of the escaping set are highly constrained. The proof combines both dynamical and complex-analytic methods.