Unifying standard and exotic duality through graded geometry

Gauge theories can often be formulated in different but physically equivalent ways, a concept referred to as duality. Apart from the well known Hodge duality of p-forms and (D-p-2)-forms in D dimensions, several further dualities have been suggested, including (i) dual gravitons, (ii) double dual gravitons, (iii) exotic (D-2,p) duals of p-forms and generalizations thereof. I will discuss how all these dualities can be described in a unified way through a formalism based on graded geometry and construct a universal first-order action for them. I will also comment on the role and status of double and exotic duals in comparison to standard duality and discuss some implications for exotic branes.