In condensed matter physics, it is known that some topological properties of quantum systems are related to the topology of the Hamiltonian operator as a self-adjoint operator with a spectral gap. In particular, recent researches reveal that symmetries of quantum systems, such as time-reversal or particle-hole symmetries, provide a rich physical and mathematical theory. In this talk, we introdu...

The role of measurement in quantum theory remains both perplexing and controversial, especially for no-collapse interpretations (e.g., many-worlds, or the ``existential'' view). One of the outstanding challenges in these frameworks is to explain preferred bases -i.e., why measurements and observations always break unitary invariance. In this talk, I'll present a framework, motivated by informat...

Kreweras’ conjecture [1] asserts that any perfect matching of the hypercubeQd, d ≥ 2, can be extended to a Hamiltonian cycle. We proved this conjec-ture in [2] but here we present an idea of a simplified proof. The matchinggraph M(G) of a graph G is a graph whose vertex set consists of all per-fect matchings of G, with two vertices being adjacent whenever the unionof the cor...