Alterfold Theory for TQFT and Topological Orders in All Dimensions

Explore the alterfold theory for Topological Quantum Field Theory (TQFT) and topological orders across all dimensions in this comprehensive lecture. Begin with an examination of 2+1 alterfold theory, tracing its development from planar algebras to 2+1 alterfold TQFT. Discover how both Turaev-Viro TQFT and Reshetikhin-Turaev TQFT are naturally embedded within the alterfold TQFT through the blow-up procedure. Delve into the concept of Dn algebra, equipped with a piecewise-linear isotopic invariant partition function that satisfies reflection positivity and finiteness. Learn about the construction of n+1 alterfold TQFT for all dimensions n, and how this process can be iterated to infinity, resulting in a non-trivial TQFT across all dimensions. Understand the alterfold theory's role as a mathematical foundation for studying topological orders in all dimensions, and its function as a fruitful picture language where "what you see is what you get." Explore how various concepts from different topics can be represented naturally within this unified framework, and witness how many remarkable results can be extensively generalized and proved in a conceptual and intuitive manner.