Quantum Gravity and TQFTs: A New Chapter in a Troubled Love Story

• Matteo Bruno

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.

Dicussion

Collective excitations of superconductors

• Niccolò Sellati

The microscopic motion and oscillations of a large number of particles determine the macroscopic behaviour of solid compounds. In superconductors, metals that undergo a phase transition below a certain critical temperature, novel collective modes are present, associated with the fluctuations of the amplitude and phase of the complex order parameter. In this talk we will discuss how these excitations behave and how they can be observed experimentally. We will then focus on layered superconductors, in which the phase fluctuations, linked to electronic oscillations, have small excitation energy of the order of THz. These so-called "plasmons" are usually understood as longitudinal waves, although in more complex crystals they behave unexpectedly.

Discussion