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Lecture 2 in a series on Fenchel-Nielsen Coordinates for SL(3,C) Representations of Surfaces, delivered by John R. Parker at the International Centre for Theoretical Sciences as part of the "New trends in Teichmüller theory" program. Explore cutting-edge developments in Teichmüller theory, focusing on the mathematical framework for representing surfaces using SL(3,C) coordinates. This 80-minute lecture contributes to a two-week thematic program covering recent breakthroughs in areas including metric theory of Teichmüller spaces, higher Teichmüller theory, infinite-type surfaces, and connections to anti-de Sitter geometry. Drawing from complex analysis, hyperbolic geometry, dynamics, partial differential equations, and other mathematical disciplines, the program aims to foster collaboration and research initiatives among participants, including students and postdocs interested in these emerging fields.
