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Explore the mathematical concept of "triality" through this lecture that establishes isomorphisms between generalized tame frieze patterns, linear difference equations, and moduli spaces of projective point configurations. Learn how this geometric approach provides new insights into cluster algebras, symplectic geometry, and dynamical systems while offering simple proofs for frieze properties like periodicity. Discover the connections between classical Coxeter frieze patterns and configurations of points in one-dimensional projective space P¹, including the resulting presymplectic structure on the space of Coxeter friezes. Master fundamental projective geometry concepts including cross-ratios and Schwarzian derivatives as they apply to frieze theory. Examine applications ranging from defining coordinates on moduli spaces to creating new types of friezes and counting methods for specific frieze categories, based on collaborative research with Sophie Morier-Genoud, Sergei Tabachnikov, Charles Conley, and Richard Schwartz.
