de Sitter spacetime admits distinct Friedmann-Robertson-Walker foliations with cosh, sinh and exponential time evolution laws. In three or more spacetime dimensions, these foliations have respectively positive, negative and vanishing spatial curvature. In two spacetime dimensions, by contrast, there is no spatial curvature, and all three evolution laws allow spatial sections with S^1 topology and a freely specifiable spatial circumference parameter. We identify geometrically preferred quantum states for a massive scalar field on these locally de Sitter 1+1 cosmologies, some singled out by adiabatic criteria, others induced from the Euclidean vacuum by a quotient construction. We show how a comoving quantum observer, modelled as an Unruh-DeWitt detector, can distinguish these states by local measurements. (Joint work with Vladimir Toussaint, 2304.10395)

The concept of non-ergodicity in quantum many body systems can be discussed in the context of the wave functions of the many body system or as a property of the dynamical observables, such as time-dependent spin correlators. In the former approach the non-ergodic delocalized state is defined as the one in which the wave functions occupy a volume that scales as a non-trivial power of the full phase space. In this work we study the simplest quantum spin glass model and find that in the delocalized non-ergodic regime the spin–spin correlators decay with the characteristic time that scales as non-trivial power of the full Hilbert space volume. The long time limit of this correlator also scales as a power of the full Hilbert space volume. We identify this phase with the glass phase whilst the many body localized phase corresponds to a ’hyperglass’ n which dynamics is practically absent. We discuss the implications of these findings to quantum information problems.

I will discuss the distribution of geometrically and topologically nearly geodesic random surfaces in a closed hyperbolic 3-manifold M, and describe the resulting PSL(2,R) invariant measures on the Grassmann bundle of M. (Joint work with J. Kahn and I. Smilga.)

We will overview a construction of p-adic L-functions for GSp(4) by Loeffler-Pilloni-Skinner-Zerbes and discuss some recent work on interpolating them in a family of Hecke character twists.

I will talk about the history of the Erdos-Renyi random graph model G(n,p), and its critical point, p=1/n. The critical window is a range of p, in which the largest components have the same scaling but not exactly the same distributional limit as at criticality itself. I will discuss several aspects of the behaviour of these graphs within the critical window, including a surprising connection to the mixing of random permutations.

The Swampland program aims at formulating a complete set of criteria in order to identify theories that can be uplifted in the UV to a theory of quantum gravity. The distance conjecture in particular diagnoses viable low energy effective theories by examining their breakdown at infinite distance in their parameter space. At the same time, infinite distance points in parameter space are naturally intertwined with string dualities and in particular T-duality. In this talk, we will show that this relation becomes much richer and intricate when the internal space is curved or supported by fluxes. Consistency of T-duality then leads us to suggest an extension to the Swampland distance conjecture. This work is in collaboration with Thomas Raml and Dieter Lüst.

We will explore the interplay between thermodynamic cost, in terms of energy dissipated, and precision of a physical system whose only accessible information is a time series of discrete events. The analytical derivations - based on variational methods of large deviations - reveal universal bounds, extending beyond the thermodynamic uncertainty relation to diverse nonequilibrium driven systems and general time-asymmetric observables. Additionally, we will see how optimal precision saturating the bounds can be physically achieved and showcase practical applications. This includes distinguishing voluntary actions controlled by the sensorimotor cortex of rats and detecting coherence effects in atomic clocks.

In these lectures we will discuss various aspects of conformal field theories in Lorentzian signature. First, we will study the general properties of Lorentzian correlation functions, including their global conformal structure and the relation to Euclidean correlators. We will then consider the Regge limit of correlation functions and how this limit requires the introduction of complex spin. We will define complex spin using the Lorentzian inversion formula, and interpret it in terms of non-local light-ray operators. Finally, we will discuss applications of light-ray operators to even shape observables.

Seiberg Seifnashri & Shao
arXiv:2401.12281

Smooth constant mean curvature (CMC) hypersurfaces serve as effective tools to study the geometry and topology of Riemannian manifolds. In high dimensions however, one in general must account for their singular behaviour. I will discuss how such hypersurfaces are constructed via min-max techniques and some recent progress on their generic regularity, allowing for certain isolated singularities to be perturbed away.

In holographic duality, a higher dimensional quantum gravity system is equivalent to a lower dimensional conformal field theory (CFT) with a large number of degrees of freedom. In this talk, I will introduce a framework to describe using the CFT how geometric notions in the gravity system, such as spacetime subregions, different notions of times, causal structure, and spacetime connectivity, emerge in the semi-classical limit.

Double-scaled SYK (DSSYK) is a model with interesting dynamics, and many known exact results. Yet, the gravitational behavior of the system is not fully understood. I will discuss the reasoning behind a suggested connection between DSSYK and de Sitter holography. We will mention the general form of the correspondence as well as the mapping of parameters between the two sides. On the SYK side we consider two copies of DSSYK at infinite temperature with an equal energy constraint. We will discuss explicitly the two-point function in double-scaled SYK and compare it to de Sitter.