Talks

Based on the immense popularity of causal Bayesian networks and structural causal models, one might expect that these representations are appropriate to describe the causal semantics of any real-world system, at least in principle. In this talk, I will argue that this is not the case, and motivate the study of more general causal modeling frameworks. In particular, I will discuss bipartite graphical causal models. Real-world complex systems are often modelled by systems of equations with endogenous and independent exogenous random variables. Such models have a long tradition in physics and engineering. The structure of such systems of equations can be encoded by a bipartite graph, with variable and equation nodes that are adjacent if a variable appears in an equation. I will show how one can use Simon’s causal ordering algorithm and the Dulmage-Mendelsohn decomposition to derive a Markov property that states the conditional independence for (distributions of) solutions of the equations in terms of the bipartite graph. I will then show how this Markov property gives rise to a do-calculus for bipartite graphical causal models, providing these with a refined causal interpretation.

In the Statistics literature there are three main frameworks for causal modeling: counterfactuals (aka potential outcomes), non-parametric structural equation models (NPSEMs) and graphs (aka path diagrams or causal Bayes nets). These approaches are similar and, in certain specific respects, equivalent. However, there are important conceptual differences and each formulation has its own strengths and weaknesses. These divergences are of relevance both in theory and when the approaches are applied in practice. This talk will introduce the different frameworks, and describe, through examples, both the commonalities and dissimilarities. In particular, we will see that the “default” assumptions within these frameworks lead to different identification results when quantifying mediation and, more generally, path-specific effects.

Can the effectiveness of a medical treatment be determined without the expense of a randomized controlled trial? Can the impact of a new policy be disentangled from other factors that happen to vary at the same time? Questions such as these are the purview of the field of causal inference, a general-purpose science of cause and effect, applicable in domains ranging from epidemiology to economics. Researchers in this field seek in particular to find techniques for extracting causal conclusions from statistical data. Meanwhile, one of the most significant results in the foundations of quantum theory—Bell’s theorem—can also be understood as an attempt to disentangle correlation and causation. Recently, it has been recognized that Bell’s result is an early foray into the field of causal inference and that the insights derived from almost 60 years of research on his theorem can supplement and improve upon state-of-the-art causal inference techniques. In the other direction, the conceptual framework developed by causal inference researchers provides a fruitful new perspective on what could possibly count as a satisfactory causal explanation of the quantum correlations observed in Bell experiments. Efforts to elaborate upon these connections have led to an exciting flow of techniques and insights across the disciplinary divide. This tutorial will highlight some of what is happening at the intersection of these two fields.

This work investigates the ferroelectric properties of γ − In₂Se₃, a material that uniquely retains its spontaneous polarization at the nano-scale, making it resistant to depolarizing fields. With a direct band gap of 1.8 eV and the ability to switch between insulating and semiconducting phases at room temperature, γ − In₂Se₃ holds promise for next-gen memory devices, where its stable ferroelectricity could revolutionize data storage and processing.

The black hole information paradox is a fundamental conflict between the quantum-mechanical and thermodynamic descriptions of black holes, specifically of their particle-emission process known as the Hawking radiation. The paradox concerns whether the radiation of a black hole is a unitary time evolution or a thermal process that erases most information about the initial state of the black hole. Multiple black hole models (e.g. [1,2]) were shown to exhibit the Page curve behavior, suggesting the unitarity of the Hawking radiation. However, without a verified theory of quantum gravity, the exact structure of black holes remains undetermined, and we need a model-independent way to test black hole unitarity. My project thus aims to develop a general framework for testing black hole unitarity by searching for its physical signatures. In particular, we employ the "hybrid" RST model [3], which possesses a Page-curve behavior, and study whether the unitarity is manifested in the transition rate of the Unruh-DeWitt particle detector. [1] Hong Zhe Chen, Robert C. Myers, Dominik Neuenfeld, Ignacio A. Reyes, Joshua Sandor. Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane". https://doi.org/10.48550/arXiv.2010.00018. [2] Yohan Potaux, Sergey N. Solodukhin, and Debajyoti Sarkar. "Spacetime Structure, Asymptotic Radiation, and Information Recovery for a Quantum Hybrid State.” Physical Review Letters 130, no. 26 (June 30, 2023): 261501. https://doi.org/10.1103/PhysRevLett.130.261501. [3] Yohan Potaux, Debajyoti Sarkar, and Sergey N. Solodukhin. "Quantum States and Their Back-Reacted Geometries in 2D Dilaton Gravity.” Physical Review D 105, no. 2 (January 12, 2022): 025015. https://doi.org/10.1103/PhysRevD.105.025015.

It may be the case that a spacetime exhibits no asymptotia where gauge invariant observables can be defined in a natural way. On such occasions the introduction of a timeline boundary may be helpful. We therefore discuss the initial boundary value problem in the context of General Relativity.

The theory $S = \int\text{d}^{4-\epsilon}x\left(\frac{1}{2}|\partial\phi|^2 - \frac{m^2}{2}|\phi|^2-\frac{g}{16}|\phi|^4\right)$ exhibits a global $U(1)$ symmetry, and the operators $\phi^n$ ($\bar\phi^n$) have charge $n$ ($-n$) with respect to this symmetry. By rescaling the fields and the coupling constant, it is possible to work in a double limit $n\to\infty$, $g\to 0$ with $\lambda = gn$ kept constant. In this way, it is possible to compute 2-point functions of the form $\langle \phi^n(x) \bar\phi^n(0) \rangle$ in the large $n$ limit, either diagrammatically by a resummation of the leading contribution at all orders in $g$, or using semiclassical methods through the saddle point approximation. This second approach is particularly powerful because it can also be applied to the theory on a curved background. This allows obtaining the form of the 2-point function for an arbitrary metric, and by functionally differentiating with respect to it, it is also possible to obtain, in the flat theory, the 3-point function $\langle T^{ij}(z) \phi^n(x) \bar \phi^n(0) \rangle$ in which an energy-momentum tensor has been inserted. This allows for a non-trivial check of the conformal symmetry of this sector of the theory by verifying the Ward identities that this 3-point function should satisfy.

We discuss the concept of spontaneous symmetry breaking and illustrate it with a general example. We consider Wigner-Weyl and Nambu-Goldstone realisations of symmetry in the quantum theory. Next, we state Goldstone’s theorem and sketch its proof. We discuss why quantum chromodynamics is not realised in the Wigner-Weyl mode.