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The spectral theory of complex systems has long been a topic of central interest in mathematical physics. In this context, the study of random and quasi-periodic Schrödinger operators reveals the consequences of complex long-range order or the lack thereof. While considerable progress has been made on some issues (e.g., conditions ensuring spectral and dynamical localization), our understanding of many other issues is partial at best. Examples include the issues of dynamical and spectral properties of operators with weak extensive disorder, multiparticle systems and asymptotic spectral properties of finite-volume truncations. One particularly fascinating aspect is the recently realized multifaceted connection to random matrix theory, a connection that is made both through analogy and certain conjectures of “universal” behaviour.

This workshop plans to bring together leading researchers in closely related fields of quasi-periodic spectral theory, random spectral theory, and many-body localization, in the hope that this interaction may shed light on the outstanding open problems in their respective fields and forge new directions of research.