Phase Structure of Strongly Interacting Theories and Finite-Size Effects

Strongly interacting theories of fermions are of great interest both experimentally and theoretically. While heavy-ion collision experiments provide us with information on hot and dense QCD, experiments with ultracold trapped atoms provide an accessible and controllable system where quantum many-body phenomena can be studied experimentally in great detail. Our theoretical understanding of these theories has improved in recent years. However, finite-size effects in these systems are not yet fully understood. We review some aspects related to finite-size effects and the role that these effects are playing in strongly-interacting fermionic theories.