PhD. seminar (online) by Mr. A. Chavan, Jagiellonian University, Krakow, Poland. on 11 November 2025

We are very glad to announce the (online) talk by Mr. Anand Chavan, PhD student, Jagiellonian University, Krakow, Poland, in our seminar series. The speaker, Mr Anand Chavan is an alumni of IISER Thiruvananthapuram. He was part of the BSMS program here and worked with Dr. Shrihari Sridharan for his major project.

Speaker: Anand Chavan, Jagiellonian University, Krakow, Poland.
Title of the talk: Holomorphic Rigidity for Kobayashi Isometries.
Broad area of research: Invariant metrics and pseudodistances in several complex variables

Date: 11/11/2025
Time: 4 pm IST
Venue: MSB 410

Abstract

The Poincaré metric on the unit disc in one complex variable is a “good” metric, whose remarkable properties are evident from the Schwarz–Pick lemma. In several complex variables, the analogues of the Poincaré metric are the class of invariant metrics, such as the Kobayashi and Carathéodory metrics. One of the interesting problems for invariant metrics is to determine whether an isometry between two domains, with respect to the invariant metric, is holomorphic, i.e. whether it is holomorphically rigid.

The plan of the talk is to introduce “good” invariant metrics in several complex variables, state a few important results, and then focus on the holomorphic rigidity of Kobayashi isometries, which will be the main theme of this talk. We will conclude by showing that, for a special domain $D_{a,b}$, the Kobayashi isometry is holomorphically rigid.

Another aim this talk could serve is as an introduction to the topic of invariant distances and metrics, and to see how these ideas work practice.The talk will focus more on ideas and results than on detailed proofs, though some parts might get technical. This talk will not be a complete introduction to the topic by any measure.