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BPS line defects in 4d N=2 supersymmetric QFT are described by a monoidal category with a list of desired properties. For example, the Grothendieck group of this category is supposed to coincide with quantization of functions on Coulomb branch of the theory compactified on a circle. Based on an observation, that at a given vacuum the spectrum of PBS particles can be quipped with an algebra structure – cohomological Hall algebra of the corresponding BPS quiver – we propose a category generated by certain bimodules over this algebra that possesses expected properties of the category of lines. Based on a joint work with Davide Gaiotto and Wei Li. 

The standard perspective on subsystems in quantum theory is a bottom-up, compositional one: one starts with individual "small" systems, viewed as primary, and composes them together to form larger systems. The top-down, decompositional perspective goes the other way, starting with a "large" system and asking what it means to partition it into smaller parts. In this talk, I will 1/ argue that the adoption of the top-down perspective is the key to progress in several current areas of foundational research; and 2/ present an integrated mathematical framework for partitions into three or more subsystems, using sub-C* algebras. Concerning the first item, I will explain how the top-down perspective becomes crucial whenever the way in which a quantum system is partitioned into smaller subsystems is not unique, but might depend on the physical situation at hand. I will display how that precise feature lies at the heart of a flurry of current hot foundational topics, such as quantum causal models, Wigner's friend scenarios, superselection rules, quantum reference frames, and debates over the implementability of the quantum switch. Concerning the second item, I will argue that partitions in (finite-dimensional) quantum theory can be naturally pinned down using sub-C* algebras. Building on simple illustrative examples, I will discuss the often-overlooked existence of non-factor C*-algebras, and how it leads to numerous subtleties -- in particular a generic failure of local tomography. I will introduce a sound framework for quantum partitions that overcomes these challenges; it is the first top-down framework that allows to consider three or more subsystems. Finally, as a display of this framework's technical power, I will briefly present how its application to quantum causal modelling unlocked the proof that all 1D quantum cellular automata admit causal decompositions.

(This is joint work with Octave Mestoudjian and Pablo Arrighi. This talk is complementary to my Causalworlds 2024 presentation, which will focus on the issue of causal decompositions.)

In this talk, I will present a published and an ongoing work in the direction of emergent gravity. The first is what I dubbed as the generalized Unruh effect, a mapping from arbitrary states in the Fock space of positive Minkowski (Kruskal) modes to Rindler (Schwarzschild) modes obtained by Bogoliubov transformation. The special case of vacuum state -- thermal bath mapping has been well known in the textbooks, the original Unruh effect. I will discuss the interesting physical implications of the generalized Unruh effect on the black hole information paradox. In the second part, I will give a novel conjecture of the dark energy when considering the spacetime as a 4d volume-conserved fluid. Einstein's equation with an always-positive metric term (Lambda, but not necessarily constant) can be interpreted as the differential version of this assumed conservation of 4d volume at linear order. The rich phenomenology of this theory will be discussed, including its solution to the anthropic problem of our currently dark-energy-dominated universe, and high-redshift over-evolved astrophysical objects that have been recently popping up in the JWST survey.