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There is an extremely rich history of interaction between physics and moduli spaces, for instance cohomological Hall algebras/algebras of BPS states, or vertex/chiral algebras. In this talk, I will explain a link between Joyce vertex algebras and one dimensional CoHAs, based on my paper 2110.14356, where quantum vertex algebras play a central role. The main technical tool is a ``bivariant" Euler class which makes torus localisation work in this context. I will also talk about ongoing work, in this area as well as in closely related projects.

Zoom Link: https://pitp.zoom.us/j/93045858347?pwd=N25FNVVjNEFFN09sdmFUV2M2YlZ5QT09

We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

Black hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation of multiple ringdown modes in gravitational waveforms could soon lead to high-precision gravitational spectroscopy, thus it is critical to understand if the quasinormal mode spectrum itself is stable against perturbations. In this talk, I will review the pseudospectrum, a mathematical tool which can shed light on the spectral stability of quasinormal modes, and discuss its novel applications in black holes and exotic compact objects. Furthermore, I will demonstrate that quasinormal spectra generically suffer from spectral instabilities and will argue how such
behavior may affect black hole spectroscopy.

Zoom Link: https://pitp.zoom.us/j/99111452809?pwd=bVp6TVdYQkJzU0Mvd2MxY2piclMzUT09

The Quantum Bayesian, or QBist, interpretation regards the quantum formalism to be a tool that a single agent may adopt to help manage their expectations for the consequences of their actions. In other words, quantum theory is an addition to decision theory, and its shape, we hope, can teach us something about the nature of reality. Beyond simple consistency, an interpretation is judged by its capacity to point the way forward. In the first half of the talk, I will highlight several ways in which my collaborators and I have applied QBist intuitions to pose and solve technical questions regarding the informational structure and conceptual function of quantum theory. At the root of many of these developments is the notion of a reference measurement, the key to a probabilistic representation of quantum theory. In this setting, we can explore the boundary of the quantum reasoning structure from a uniquely QBist angle. Working with such representations grants a new perspective and inspires questions which wouldn't have occurred otherwise; as examples, we will meet downstream results concerning quantum channels, discrete quasiprobability representations, and a variant of the information-disturbance tradeoff. Most recently, I have pursued ways in which QBism could be applied to the construction of new tools and strategies for existing problems in quantum information and computation. In the second half of the talk, we will encounter the first of these, an agent-based modeling proposal where multiple, suitably interacting, QBist decision-makers might collectively work out the solution to a task of interest in the right circumstances. I will describe some initial explorations of modeling agent belief dynamics in two contexts: first, an expectation sampling interaction with an eye to agential agreement, and, second, a setting where agents are players of quantum games. In the future, we imagine it is possible that a sufficiently mature development of the agent-based program we have begun could suggest new approaches to quantum algorithm design.

Zoom Link: https://pitp.zoom.us/j/95668668835?pwd=MUJtRGMxbEFzSEdVVmZ3TkR3dVVVZz09