We relate the existence problem of universal objects to the properties of corresponding enriched categories (lifts or expansions). In particular, extending earlier results, we prove that for every regular set F of finite connected structures there exists a (countable) ω-categorical universal structure U for the class Forbh(F) (of all countable structures not containing any homomorphic image of ...

Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families Hamiltonians endowed with a given duality and provide universal description Hamiltonian near self-dual points. We focus on tight-binding models (also known as coupled-mode theories), which an effective composed coupled harmonic oscillators ...

The idea of duality is at the core of the most relevant developments in recent fundamental physics. During the last forty years theoretical physics has used the notion of duality in different ways and frameworks: in the so-called dual resonance model of the late sixties, which gave birth to early string theory; in the context of quantum field theory, where a groundbreaking generalization of ele...

Brascamp-Lieb inequalities are entropy which have a dual formulation as generalized Young inequalities. In this work, we introduce fully quantum version of duality, relating relative to matrix exponential type. We demonstrate novel duality by means examples from information theory -- including entropic uncertainty relations, strong data-processing inequalities, super-additivity and many more. A...

Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations dualities, which is not immediately obvious. A prime example Scherk-Schwarz reductions double theory, have been shown to be one-to-one correspondence with Poisson-Lie T-duality. Here we demonstrate that this relation only the tip of iceberg. Currently, most general known...

A note on dualities in Einstein's gravity in the presence of a non-minimally coupled