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Thick subcategories on smooth curves and orbifold curves

I will talk about the classification problem for thick triangulated subcategories in triangulated categories, such as derived categories of coherent sheaves on algebraic varieties, or derived categories of modules over algebras. In some cases such classification is possible, but in general thick subcategories are abundant and hardly controllable. Nevertheless, one can classify thick subcategories in the derived category of a smooth projective curve up to an equivalence: every thick subcategory has a simple explicit description in terms of some quiver. Moreover, one can describe all quivers that arise in this way. If time permits, I will explain how these results generalise to weighted projective curves.