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Since its very beginnings, topology has forged strong links with physics and the last Nobel prize in physics, awarded in 2016 to Thouless, Haldane and Kosterlitz for theoretical discoveries of topological phase transitions and topological phases of matter, confirmed that these connections have been maintained up to contemporary physics. To give some (very) selected illustrations of what is, and still will be, a cross fertilization between topology and physics, hydrodynamics provides a natural domain through the common theme offered by the notion of vortex, relevant both in classical (S 2) and in quantum fluids (S 3). Before getting into the details, I will sketch in S 1 a general perspective from which this intertwining between topology and physics can be appreciated: the old dichotomy between discreteness and continuity, first dealing with antithetic thesis, eventually appears to be made of two complementary sides of a single coin.
Analogous to Godels incompleteness theorems is a theorem in physics to the effect that the set of explanations of given evidence is uncountably infinite. An implication of this theorem is that contact between theory and experiment depends on activity
Topological states of fermionic matter can be induced by means of a suitably engineered dissipative dynamics. Dissipation then does not occur as a perturbation, but rather as the main resource for many-body dynamics, providing a targeted cooling into
Characterization of equilibrium topological quantum phases by non-equilibrium quench dynamics provides a novel and efficient scheme in detecting topological invariants defined in equilibrium. Nevertheless, most of the previous studies have focused on
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities play complementary roles: the Fub
I describe the occurence of Eulerian numbers and Stirling numbers of the second kind in the combinatorics of the Statistical Curse of the Second Half Rank problem.