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This lecture, part of the "New trends in Teichmüller theory" program at the International Centre for Theoretical Sciences, explores methods for estimating distances between hyperbolic structures in the moduli space. Presented by Kashyap Rajeevsarathy, the 59-minute talk contributes to a two-week thematic program focusing on recent developments in Teichmüller theory. Delve into advanced mathematical concepts at the intersection of complex analysis, hyperbolic geometry, dynamics, and geometric group theory. The program, organized by Krishnendu Gongopadhyay, Subhojoy Gupta, Ken'ichi Ohshika, and Athanase Papadopoulos, features mini-courses and research talks by experts in the field, highlighting relationships between different theoretical perspectives and encouraging collaboration among participants, including students and postdocs interested in initiating research in these emerging areas.
