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Mathematics Seminar Date: Thursday, 09 November 2023 Time: 3:30 - 4:30 PM Venue: Seminar Hall Henon maps, short $\mathbb{C}^2$ and beyond Ratna Pal IISER Mohali. 09-11-23 Abstract In the first part of the talk, we will discuss some results that come under the umbrella of Holomorphic Dynamics. We shall see a couple of rigidity properties of Henon maps, which happen to be the most important class of polynomial automorphisms of $\mathbb{C}^2$ from the perspective of holomorphic dynamics. Loosely speaking, by rigidity properties, we mean those properties of Henon maps which determine the underlying Henon maps almost uniquely. Describing the structure of the final union in terms of its exhausting domains is referred to in literature as union problem. The genesis of this problem goes back to the early days of classical SCV and a complete answer to this problem seems to be a tangled one. Domains which are an increasing union of unit balls hold a special stature in literature. In the next part of the talk, we shall survey a few recent results obtained for one such class of domains in $\mathbb{C}^k$, namely the Short $\mathbb{C}^k$'s. If time permits then we shall also address the union problem for more general exhausting domains. A large part these results are obtained in several joint works with Sayani Bera, John Erik Fornaess, Kaushal Verma and Erlend Wold.
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