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Explore the mathematical foundations of correlators in two-dimensional conformal field theories through this colloquium lecture delivered at BIMSA. Learn how quantum field theoretic correlation functions can be precisely characterized as elements within conformal block spaces derived from conformal symmetries. Discover multiple construction methods for building all correlators of a CFT while satisfying infinitely many consistency conditions. Examine how algebraic structures from tensor categories and higher categories integrate into these mathematical frameworks. The presentation assumes no prior knowledge of category theory, making advanced concepts accessible to a broader audience. Gain insights into the intersection of theoretical physics and advanced mathematics through the lens of conformal field theory applications.
