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Generalized 't Hooft anomalies

't Hooft anomalies provide a unique handle to study the nonperturbative dynamics of strongly-coupled theories. Although this type of anomalies were known since the 80's, recently it has been realized that one can generalize them by turning on 't Hooft twists in the color, flavor, and baryon number directions. Such generalized anomalies put severe constraints on the possible realizations of the global symmetries of a given theory in the IR. In this talk, I will explain how one can construct such 't Hooft twists and give examples on the constrains the generalized anomalies can impose on strongly coupled gauge theories.