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The notion of duality in physics has a rich history, going back at least as far as the observation that Maxwell’s theory of elctromagnetism is symmetric after swapping electric and magnetic fields. More generally, dualities in physics can provide a way of relating two seemingly very different physical theories via a nontrivial duality transformation. For instance, S-duality in physics provides a way to swap strongly coupled physical theories for weakly coupled ones [MO77], for which we may use perturbative methods to exactly solve the equations governing the system.

The theoretical study of quantum many-body systems is a challenging task due to the amazing complexity induced by the huge number of degrees of freedom of these systems. Equilibrium properties of such systems have been deeply studied in the last decades. In particular, at one-dimension, it is possible for some systems to have access to exact solutions, for instance, within Bethe Ansatz methods. Where exact solutions are not accessible, it is possible to use field theoretical approaches or numerical techniques.

This term focuses on rigidity of group actions with some focus on issues that arise out of Zimmer's groundbreaking work in the 1980's. Areas of interest range from local and global rigidity of group actions to special rigidity phenomena in small dimensions to symmetry groups of geometric structures to measure rigidity results for quite general group actions with hyperbolicity. This broad area has seen a very large number of dramatic breakthroughs in recent years.