The Non-Equilibrium
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The equilibrium theory of matter is one of the triumphs of modern physics. It organizes the collective behaviour of countless particles through a handful of central ideas: symmetry, topology, and universality. Those principles tell us which phases of matter can exist, how they morph into one another, and why seemingly different materials display the same long-distance behaviour.

The quantum systems now being built and investigated do not sit still. They are driven by external fields, continuously measured, and open to their environment, producing forms of order that have no counterpart at rest. Programmable quantum simulators produce such dynamics routinely, and a catalogue of striking phenomena is accumulating faster than existing theory can explain them.

Our team sets out to find the organizing principles behind this rapidly expanding catalogue, extending the language of symmetry, topology, and entanglement to systems whose defining feature is that they never settle into equilibrium. The program runs across four directions: the mathematical foundations of quantum dynamics, the classification of intrinsically dynamical phases of matter, fault-tolerant quantum computation understood as a non-equilibrium phase of matter in its own right, and the nature of complexity in evolving quantum systems. The aim is not only to describe the dynamical world but to organize and ultimately predict it, laying the conceptual groundwork for the second century of quantum science.

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