Scientific Series

Vertex operator algebras (VOAs) arise in many corners of supersymmetric quantum field theory. One particularly influential instance is in 4d N=2 superconformal field theories, whereby the VOA is realized as the cohomology of a suitable supercharge. Unitarity of the underlying SCFT imposes strong constraints on the structure of the resulting VOA. In this talk, I will describe one aspect of how the unitary of the underlying SCFT constrains this VOA: in the context of superconformal gauge theories, the resulting BRST complex shares a striking resemblance to the de Rham complex of a compact Kähler manifolds. I will finish with several consequences of this observation, e.g. the formality of these BRST complexes as in the work of Deligne-Griffiths-Morgan-Sullivan on compact Kähler manifold. This is based on work in progress with C. Beem.

We introduce 'Lattice Cosmology’ as an emergent field encompassing a set of techniques capable of solving the non-linear dynamics of interactive fields in an expanding Universe. As a demonstration of the power of these techniques, we solve two very different problems of early Universe cosmology: i) the non-linear dynamics of axion inflation, and ii) the dynamics and gravitational wave emission of cosmic string loops.

In this talk, I will present a proof that extremal Reissner-Nordström arises on the black hole formation threshold for the Einstein equations coupled to a self-gravitating plasma. This constitutes the first rigorous result on critical collapse. I will then discuss a formulation of the stability problem for extremal black holes, and present a positive resolution in the case of extremal Reissner-Nordström perturbed by a self-gravitating neutral scalar field in spherical symmetry, despite the presence of the celebrated Aretakis instability. This is based on joint work with Yannis Angelopoulos (Caltech) and Christoph Kehle (MIT) (2402.10190, 2410.16234).

A large amount of effort has recently been put into understanding the barren plateau phenomenon. In this perspective talk, we face the increasingly loud elephant in the room and ask a question that has been hinted at by many but not explicitly addressed: Can the structure that allows one to avoid barren plateaus also be leveraged to efficiently simulate the loss classically? We present a case-by-case argument that commonly used models with provable absence of barren plateaus are also in a sense classically simulable, provided that one can collect some classical data from quantum devices during an initial data acquisition phase. This follows from the observation that barren plateaus result from a curse of dimensionality, and that current approaches for solving them end up encoding the problem into some small, classically simulable, subspaces. We end by discussing caveats in our arguments including the limitations of average case arguments, the role of smart initializations, models that fall outside our assumptions, the potential for provably superpolynomial advantages and the possibility that, once larger devices become available, parametrized quantum circuits could heuristically outperform our analytic expectations.