Matrix models offer non-perturbative descriptions of quantum gravity in simple settings, allowing us to study large-N dualities between gauge and string theories. However, the large-N expansions of matrix models lead to divergent series, only defined as asymptotic series. By fine-tuning the couplings of the matrix model we obtain models of pure gravity coupled to minimal conformal field theories. The free energy for the simplest of these "minimal models" is 2d gravity also admits an asymptotic expansion which formally satisfies the Painlevé I equation.

These asymptotic properties are connected to the existence of exponentially small contributions not captured by a perturbative analysis and whose physical interpretation can be elusive. The emerging structure can be accurately described by means of a resurgent transseries, capturing this perturbative/non-perturbative connection and its consequences. This talk will focus on the essential role of this resurgent transseries for the cases of Painlevé I and the quartic matrix model: together with exponentially accurate numerical and summation methods, one can show how to go beyond the asymptotic results and obtain (analytically and numerically) non-perturbative data.

If you are planning to attend, please send and email to pietro.benetti_genolini@kcl.ac.uk or alan.rios_fukelman@kcl.ac.uk so your name is added to the participants list in order to grant you access to the building.

Dissipative relativistic hydrodynamics is expected to describe the late times, thermalised behaviour of strongly coupled fluids such as a strongly coupled super Yang-Mills plasma. These systems are then accurately described by a hydrodynamic series expansion in small gradients. Surprisingly, this hydrodynamic expansion is accurate even when the systems are still quite anisotropic: the non-hydrodynamic modes governing the non-equilibrium behaviour at very early-times become exponentially close to the hydrodynamic solution in an early process called hydrodynamization.

This early success is intimately related with the fact that the hydrodynamic expansion is asymptotic. The theory of transseries and resurgence explicitly shows how the non hydrodynamic modes are in fact encoded in this late-time expansion. In this talk we will focus on a MIS-type model and use exponentially accurate summations of the the late-time resurgent transseries to recover the behaviour of the fluid before hydrodynamisation, and effectively match it to any given initial non-equilibrium condition. We will further show that such summations can provide analytic predictions beyond the late time regime.