Pre-Synopsis seminar by Subith G. on 25 March 2026 at 4 pm

We are very glad to announce the Pre-Synopsis Seminar Talk by Mr. Subith Gopinathan.

Speaker: Mr. Subith Gopinathan (PHD211038), IISERTVM

Title: Entropy and Pressure for holomorphic correspondences.

Time & Date: 4.00 PM on March 25, 2026
Venue: MSB215 Harish Chandra

Abstract: The subject of thermodynamic formalism for dynamics of continuous maps defined on compact metric spaces is very well studied. In this talk, we generalize certain notions studied in thermodynamic formalism of maps, to the context where the dynamics evolves via holomorphic correspondences defined on the Riemann sphere. Towards that end, we define the topological entropy of holomorphic correspondences using spanning sets. We then develop the concept of topological pressure of continuous functions with respect to holomorphic correspondences using separated sets and spanning sets. Alongside, we identify a class of measures supported on the Riemann sphere and introduce ways to define the measure-theoretic entropy of a holomorphic correspondence. This naturally leads us to the variational principle that relates the measure-theoretic entropy, the integral of the function and the topological pressure in appropriate settings. Finally, we define and investigate a Ruelle operator, however restricting the action of the correspondence on the support of the Dinh-Sibony measure and study its spectral properties.