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This lecture is the first part of a series on Fenchel-Nielsen Coordinates for SL(3,C) Representations of Surface Groups, delivered by John R. Parker at the International Centre for Theoretical Sciences. Learn about the latest developments in Teichmüller theory as part of the "New trends in Teichmüller theory" program organized by Krishnendu Gongopadhyay, Subhojoy Gupta, Ken'ichi Ohshika, and Athanase Papadopoulos. The lecture explores the intersection of complex analysis, hyperbolic geometry, dynamics, and other mathematical fields, focusing on how Fenchel-Nielsen coordinates can be applied to SL(3,C) representations of surface groups. This 74-minute presentation is ideal for researchers, postdocs, and students interested in Teichmüller theory, higher Teichmüller theory, and their connections to Higgs bundles, algebraic geometry, and Anosov representations.
