I will discuss a two-dimensional dilaton gravity theory with a sine potential. At the disk level, this theory admits a microscopic holographic realization as the double-scaled SYK model. Remarkably, in the open channel canonical quantization of the theory, the momentum conjugate to the length of two-sided Cauchy slices becomes periodic. As a result, the ERB length in sine dilaton gravity is discretized upon gauging this symmetry. For closed Cauchy slices, a similar discretization occurs in the physical Hilbert space, corresponding to a discrete spectrum for the length of the necks of trumpet geometries. By appropriately gluing two such trumpets together, one can then construct a wormhole geometry in sine dilaton gravity, whose amplitude matches the spectral correlation functions of a one-cut matrix integral. This correspondence suggests that the theory provides a path integral formulation of q-deformed JT gravity, where the matrix size is large but finite. Finally, I will describe how this theory of gravity can be regarded as a realization of q-deformed holography and propose a possible implementation of this framework to study the near-horizon dynamics of near-extremal de Sitter black holes.

The organisers asked me to give a brief talk on what I’ve been thinking about lately. So, I’ll tell you about Schwinger-Keldysh EFTs: an EFT framework for non-equilibrium dissipative systems such as hydrodynamics. These are built on a closed-time contour that runs forward and backward in time, allowing access to a variety of non-equilibrium observables. However, these EFTs fundamentally miss a wider class of observables, called out-of-time-ordered correlators (OTOCs), which are closely tied to quantum chaos. In this talk, I’ll share some thoughts on extending Schwinger-Keldysh EFTs to multifold contours that capture such observables. I’ll also touch on the discrete KMS symmetry of thermal systems, which generalises from Z_2 in the single-fold case to the dihedral group D_n in the n-fold case. With any luck, I’ll reach the point where I’m stuck and you can help me figure it out.

Two different, almost orthogonal approaches to QFT are: (1) the study of von Neumann algebras of local observables in flat space, and (2) the study of extended and topological defects in general spacetime manifolds. While naively the two focus on different aspects, it has been recently pointed out that some of the axioms of approach (1) clash with certain expectations from approach (2). In this JC talk, I’ll give a brief introduction to both approaches and review the recent discussion in [2008.11748], [2503.20863], and [2509.03589], explaining (i) what the tensions are, (ii) a recent proposal to solve them, and (iii) why it can be useful.

to follow

What do the roots of random polynomials look like? Classical works of Erdős-Turán and others show that most roots are near the unit circle and they are approximately rotationally equidistributed. We will begin with an understanding of why this happens and see how ideas from extremal combinatorics can mix with analytic and probabilistic arguments to show this. Another main feature of random polynomials is that their roots tend to "repel" each other. We will see various quantitative statements that make this rigorous. In particular, we will study the smallest separation $m_n$ between pairs of roots and show that typically $m_n$ is on the order of $n^{-5/4}$. We will see why this reflects repulsion between roots and discuss where this repulsion comes from. This is based on joint work with Oren Yakir.

Permutons are a framework set up for understanding large permutations, and are instrumental in pattern densities. However, they miss most of the algebraic properties of permutations. I will discuss what can still be said in this direction, and some possible ways to move beyond permutons. Joint with Fiona Skerman and Peter Winkler.

We propose a new framework of Markov α-potential games to study Markov games. 

We show that any Markov game with finite-state and finite-action is a Markov α-potential game, and establish the existence of an associated α-potential function. Any optimizer of an α-potential function is shown to be an α-stationary Nash equilibrium. We study two important classes of practically significant Markov games, Markov congestion games and the perturbed Markov team games, via the framework of Markov α-potential games, with explicit characterization of an upper bound for αand its relation to game parameters. 

Additionally, we provide a semi-infinite linear programming based formulation to obtain an upper bound for α for any Markov game. 

Furthermore, we study two equilibrium approximation algorithms, namely the projected gradient- ascent algorithm and the sequential maximum improvement algorithm, along with their Nash regret analysis.

This talk is part of the Erlangen AI Hub.