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Derived categories, introduced by Verdier in the 60s, are nowaday a widespread tools for studying the geometry of smooth projective varieties, and that of their moduli spaces of stable sheaves. However the majority of techniques employed in this investigation rely heavily on Hodge theory and Torelli theorems and so can be applied only to varieties defined over the complex numbers, or, more generally (thanks to the Lefschetz principle), to varieties over algebraically closed fields of characteristic 0. Till very recently the more general setting of varieties defined over (possibly finite) fields of positive characteristic had been barely explored. This workshop aims at bringing together international experts -- in both the fields of derived categories, and of positive characteristic algebraic geometry -- in order to build a bridge between the two fields, disseminate the latest research techniques, promote mutual learning, forging new research connections and encourage the discussion on recent development and open problems.