Since their formulation, Topological Quantum Field Theories (TQFTs) have been a source of inspiration for developing Quantum Gravity models due to conceptual similarities between the two. Despite significant mathematical and physical results, TQFTs remain an open field with many aspects still not fully understood, and their application to Gravity remains incomplete.
TQFTs are also of great interest to mathematicians, thanks to the axiomatization provided by M. Atiyah, which describes these theories in a topological-algebraic framework.
One particularly intriguing approach to Quantum Gravity is Spin Foam. This approach exhibits an algebraic-combinatorial structure, making it suitable for analysis within a rigorous mathematical framework.
In this talk, we will demonstrate that Spin Foam can be formulated within the same mathematical language as TQFTs. This rigorous setting allows us to explore the properties of the gravitational partition function and the behavior of Quantum General Relativity.
