Measurements inevitably affect the state of a quantum system, via wavefunction collapse. This means that the dynamics of a system which is continually being monitored by an observer is fundamentally different from the dynamics of a closed system. In particular, for a spatially extended system, local measurements of the degrees of freedom can “compete" with chaotic dynamics: while chaotic dynamics tends to produce complex, entangled quantum wavefunctions, local measurements tend to collapse the wavefunction into something simpler. I will briefly describe how this leads to a dynamical phase transition between a weak monitoring phase, where the state is complex and entangled, and a strong monitoring phase, where the state is simple and “classical”. I will then describe more recent work on simplified models, based on tree tensor networks, where these entanglement phase transitions become analytically tractable. LOCATION:The link will be sent to you after registration END:VEVENT END:VCALENDAR