In holomorphic dynamics, the class of Hénon maps is the most important class of polynomial automorphisms in C2. For a Hénon map in C2, it is known that the sub-level sets of the associated Green's functions are Short C2's. A Short C2 is a proper domain of C2 that can be expressed as an increasing union of unit balls such that the Kobayashi metric vanishes identically therein but allows a bounded above pluri-subharmonic function.
In this talk, Dr Ratna will explore the holomorphic automorphism groups of the sub-level sets of Green's functions. She will show that although these sets admit exhaustions by biholomorphic images of the unit ball, the automorphism groups cannot be too large. On the other hand, examples will be provided to show that these automorphism groups are non-trivial in general. This is a joint work with Sayani Bera and Kaushal Verma.
ABOUT THE SPEAKER
Dr Ratna Pal is an Assistant Professor at ISI Bangalore working in the area of Holomorphic Dynamics, Complex Geometric Analysis, Potential Theory. She is a recipient of INSA (Indian National Science Academy) Young Associates 2024. She has authored numerous scholarly articles in highly prestigious international journals.
