This minisymposium was planned to be part of the "2020 SIAM Conference on Nonlinear Waves and Coherent Structures", which was supposed to take place in Bremen in July 2020, but was canceled. It will now be happening as an online minisymposium on October 1 and 2, 2020.

Note: a registration is necessary in order to participate.

**Nonlinear evolution equations** arise in quantum mechanics in certain scaling limits from the linear many-body Schrödinger equation. A prominent example is the **cubic nonlinear Schrödinger equation** coming from the **Gross-Pitaevskii scaling limit**. Such effective equations are a physicist's standard tool to describe the dynamics of **Bose-Einstein condensates**. Recently a lot of research activity has been devoted to understanding and deriving scaling limits of the Schrödinger dynamics rigorously in many different settings, e.g., for the dynamics of Bose gases with singular or **mean-field interaction**, Fermi gases with Coulomb interaction, or particles coupled to a quantum field. Moreover, an active recent research direction is to go beyond the first order approximation in terms of a nonlinear Schrödinger equation, and describe higher order approximations. One prominent example is **Bogoliubov theory** for Bose gases, which describes the quadratic fluctuations around the nonlinear Schrödinger equation. One goal of this minisymposium is to introduce non-experts to the exciting field of **effective quantum dynamics**, and thus provide one example of an answer to the question of how nonlinear dynamics arises in physics from an underlying microscopic theory. At the same time, the minisymposium aims to discuss some of the most recent progress in the field, thus being attractive to experts.

**Organizer:** Sören Petrat