Tue, 24 Nov 2026
13:00
13:00
L2
Emergent Hamiltonians from boundary symmetries
Jose Garre Rubio
(Universidad Complutense de Madrid)
Abstract
We introduce a systematic framework for constructing emergent local commuting Hamiltonians in (d+1) dimensions from symmetries defined on a d-dimensional boundary. Starting from a generic d-dimensional symmetry, we gauge it by introducing layers of gauge fields carrying dual symmetries, which can in turn be gauged. The fixed points of this iterative gauging procedure yield (d+1)-dimensional stabilizer Hamiltonians built from local Gauss-law constraints. These Hamiltonians encode the emergent bulk order while realizing the original symmetry on the boundary.
I will show how, starting in one dimension, this construction reproduces familiar two-dimensional topological codes, such as the toric code, and naturally realizes all gapped boundary conditions as different one-dimensional symmetric phases at the boundary. The framework extends to higher-form and subsystem symmetries in arbitrary dimensions, yielding, for example, three-dimensional fracton models.
If time permits, I will also discuss how these symmetries can be classified within the framework of tensor networks.
Based on arXiv: 2403.07575, 2410.09044, and 2203.12563.
A data-driven approach for safety quantification of non-linear stochastic systems with unknown additive noise distribution
Mathiesen, F
Romao, L
Calvert, S
Laurenti, L
Abate, A
Automatica
volume 193
113187
(Nov 2026)
doi:10.1016/j.automatica.2026.113187
Tue, 13 Oct 2026
13:00
13:00
L2
Entanglement bootstrap for (edge) conformal field theories
Xiang Li
(Oxford )
Abstract
Entanglement bootstrap (EB) aims to uncover the universal data and structural properties of quantum many-body systems from local entanglement properties. In this talk, I will discuss our past progress on EB for 1+1D conformal field theories, including anomalous CFTs that can arise only as boundaries of 2+1D topological quantum field theories. Explicitly, I will discuss a locally checkable condition for 1+1D CFT ground states, as well as the reconstruction of Virasoro generators directly from the wavefunction. This allows us to diagnose if a given state is a CFT ground state or not, and if it is then how to extract CFT data from it.
Although these results are motivated by continuum field theory, they are also applicable to critical lattice systems. This opens the possibility of using entanglement bootstrap as a systematic framework for enumerating and potentially discovering new CFTs.
Tue, 20 Oct 2026
13:00
13:00
L2
Approaching Black Hole Extremality
Frans Pretorius
(Princeton)
Abstract
Today we have a solid theoretical understanding of the dynamics of black holes, as predicted by classical general relativity, for the typical binary merger expected as an astrophysical gravitational wave source. However, in more "extreme" situations, namely, black holes that collide with velocities close to the speed of light and non-linear perturbations of (near-)extremal black holes, less is known, in some respects even qualitatively. In these lectures I will discuss some of these open questions, describe some recent results, and speculate about possible answers.
Extremal black holes are those with the maximum amount of charge and/or angular momentum allowed by general relativity, and are characterized by having zero surface gravity (zero temperature in the thermodynamic analogue
description). Results from linear perturbation theory show that extremal holes can behave very differently from their subextremal counterparts, including the fact that exactly extremal black holes are unstable (the celebrated Aretakis instability), and that in the limit of extremality a subset of the black hole's quasi-normal modes approach zero damping. This has inspired some to argue that turbulent-like dynamics may occur on the horizons of perturbed near-extremal black holes, and that the Aretakis instability survives at the non-linear level with sufficiently fine-tuned perturbations that could furthermore exhibit some form of critical phenomena.
In this lecture I will describe recent work studying the non-linear dynamics of (near-) extremal charged black holes, albeit restricted to spherical symmetry. Though in this setting we cannot address the turbulence question, we
can address aspects of putative fine-tuned critical behavior.