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Explore the mathematical concepts of finite index subgroups of free groups and residual finiteness in this 53-minute lecture by Arpan Kabiraj from the International Centre for Theoretical Sciences. This talk is part of the "New trends in Teichmüller theory" program organized by Krishnendu Gongopadhyay, Subhojoy Gupta, Ken'ichi Ohshika, and Athanase Papadopoulos. The lecture contributes to a two-week thematic program focusing on recent developments in Teichmüller theory, which encompasses metric theory, higher Teichmüller theory, infinite-type surfaces, and relations with anti-de Sitter geometry. Drawing from complex analysis, hyperbolic geometry, dynamics, group theory, and other mathematical fields, the program aims to foster interaction between different perspectives and encourage research collaborations, particularly among young mathematicians.
