# Sašo Grozdanov: How much information is required to reconstruct a QFT spectrum?

**Sašo Grozdanov: How much information is required to reconstruct a QFT spectrum?**

Assuming only a known dispersion relation of a single mode in the spectrum of a two-point function in some QFT, I will discuss when and how the reconstruction of the complete spectrum of physical excitations is possible. In particular, I will present a constructive algorithm based on the theorems of Darboux and Puiseux that allows for such a reconstruction of all modes connected by level-crossings. I will then discuss an example of a thermal holographic theory to show how this procedure works in practice by using the gapless (diffusive) dispersion relation described by the convergent hydrodynamic gradient expansion. Finally, I will ask the question of what is the `minimal amount of knowledge’ that suffices for such a reconstruction and provide a potential answer that utilises the phenomenon of pole-skipping.