Ravi Shankar Jaiswal receives best thesis commendation

The TIFR Alumni Association (TAA) has awarded the TAA-Harish Chandra Memorial Best Thesis Commendation in Mathematics for the year 2024-2025 to Dr. Ravi Shankar Jaiswal for his thesis titled

Boundary Behaviour of Biholomorphic Invariants on Infinite Type Domains

The citation from the award committee states

for significant discoveries regarding the behaviour of various objects on infinite type domains, adapting the scaling method and a localisation result.

Dr. Ravi Shankar Jaiswal is currently an Institute Postdoctoral Fellow at the Department of Mathematics, IIT Bombay.

About the thesis work

On domains in Cn, there is a deep interplay between the boundary geometry of the domain and function theory on the domain. This interplay is often captured in the boundary behaviour of various canonical objects associated to the domain, many of which are also biholomorphic invariants. Examining the boundary behaviour of these objects provides insights into the extension of holomorphic functions, the behaviour of holomorphic mappings, and the classification of domains up to biholomorphic equivalence.

In his PhD thesis, Ravi describes the boundary behaviour of the following ob-jects near exponentially flat infinite type boundary points of domains in C^n: the Bergman and Szeg˝o kernels, the Bergman metric, the Kobayashi andthe Kobayashi–Fuks metrics, holomorphic sectional curvature of the Bergmanmetric, Ricci and Scalar curvatures of the Bergman metric, and Bergman canon-ical invariant. Results on the boundary behaviour of these objects are alreadyavailable near finite type boundary points. An exponentially flat infinite typeboundary point is a generalisation of the origin in Rez1 + e−1/z′2= 0, for(z1, z′) ∈ C×Cn. To obtain his results, Ravi employs an astutely modified ver-sion of the powerful method of scaling and proves new localisation results usinga careful application of H¨ormander’s L2 estimates for the ∂ problem.